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Sample records for previously completed mathematics

  1. "My math and me": Nursing students' previous experiences in learning mathematics.

    Science.gov (United States)

    Røykenes, Kari

    2016-01-01

    In this paper, 11 narratives about former experiences in learning of mathematics written by nursing students are thematically analyzed. Most students had a positive relationship with the subject in primary school, when they found mathematics fun and were able to master the subject. For some, a change occurred in the transition to lower secondary school. The reasons for this change was found in the subject (increased difficulty), the teachers (movement of teachers, numerous substitute teachers), the class environment and size (many pupils, noise), and the student him- or herself (silent and anonymous pupil). This change was also found in the transition from lower to higher secondary school. By contrast, some students had experienced changes that were positive, and their mathematics teacher was a significant factor in this positive change. The paper emphasizes the importance of previous experiences in learning mathematics to nursing students when learning about drug calculation. Copyright © 2015. Published by Elsevier Ltd.

  2. Student and high-school characteristics related to completing a science, technology, engineering or mathematics (STEM) major in college

    Science.gov (United States)

    LeBeau, Brandon; Harwell, Michael; Monson, Debra; Dupuis, Danielle; Medhanie, Amanuel; Post, Thomas R.

    2012-04-01

    Background: The importance of increasing the number of US college students completing degrees in science, technology, engineering or mathematics (STEM) has prompted calls for research to provide a better understanding of factors related to student participation in these majors, including the impact of a student's high-school mathematics curriculum. Purpose: This study examines the relationship between various student and high-school characteristics and completion of a STEM major in college. Of specific interest is the influence of a student's high-school mathematics curriculum on the completion of a STEM major in college. Sample: The sample consisted of approximately 3500 students from 229 high schools. Students were predominantly Caucasian (80%), with slightly more males than females (52% vs 48%). Design and method: A quasi-experimental design with archival data was used for students who enrolled in, and graduated from, a post-secondary institution in the upper Midwest. To be included in the sample, students needed to have completed at least three years of high-school mathematics. A generalized linear mixed model was used with students nested within high schools. The data were cross-sectional. Results: High-school predictors were not found to have a significant impact on the completion of a STEM major. Significant student-level predictors included ACT mathematics score, gender and high-school mathematics GPA. Conclusions: The results provide evidence that on average students are equally prepared for the rigorous mathematics coursework regardless of the high-school mathematics curriculum they completed.

  3. Self-Perceptions of Pre-Service Mathematics Teachers Completing a Graduate Diploma of Secondary Education

    Science.gov (United States)

    Hine, Gregory S. C.

    2015-01-01

    This qualitative research project explored the self-perceptions of pre-service secondary mathematics teachers completing a Graduate Diploma of Secondary Education. Specifically, the researcher investigated the extent to which teachers perceived their readiness to commence a secondary mathematics teaching position. The project relied principally on…

  4. Lectures on constructive mathematical analysis

    CERN Document Server

    Kushner, B A

    1984-01-01

    The basis of this book was a special course given by the author at the Mechanics-Mathematics Faculty of Moscow University. The material presumes almost no previous knowledge and is completely understandable to a reader who is in command of a standard course of mathematical analysis. There are an extensive bibliography and indexes which will be helpful to students.

  5. THE INFLUENCE OF THE ASSESSMENT MODEL AND METHOD TOWARD THE SCIENCE LEARNING ACHIEVEMENT BY CONTROLLING THE STUDENTS? PREVIOUS KNOWLEDGE OF MATHEMATICS.

    OpenAIRE

    Adam rumbalifar; I. g. n. Agung; Burhanuddin tola.

    2018-01-01

    This research aims to study the influence of the assessment model and method toward the science learning achievement by controlling the students? previous knowledge of mathematics. This study was conducted at SMP East Seram district with the population of 295 students. This study applied a quasi-experimental method with 2 X 2 factorial design using the ANCOVA model. The findings after controlling the students\\' previous knowledge of mathematics show that the science learning achievement of th...

  6. Mathematical modeling of the complete thermodynamic cycle of a new Atkinson cycle gas engine

    International Nuclear Information System (INIS)

    Shojaeefard, Mohammad Hassan; Keshavarz, Mojtaba

    2015-01-01

    The Atkinson cycle provides the potential to increase the efficiency of SI engines using overexpansion concept. This also will suggest decrease in CO_2 generation by internal combustion engine. In this study a mathematical modeling of complete thermodynamic cycle of a new two-stroke Atkinson cycle SI engine will be presented. The mathematical modeling is carried out using two-zone combustion analysis in order to make the model predict exhaust emission so that its values could be compared with the values of conventional SI engine. The model also is validated against experimental tests in that increase in efficiency is achieved compared to conventional SI engines. - Highlights: • The complete cycle model for the rotary Atkinson engine was developed. • Comparing the results with experimental data shows good model validity. • The model needs further improvement for the scavenging phase. • There is 5% increment in thermal efficiency with new engine compared to conventional SI engines.

  7. Mathematical modeling of biological processes

    CERN Document Server

    Friedman, Avner

    2014-01-01

    This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.

  8. The Relationships among Mathematics Teaching Efficacy, Mathematics Self-Efficacy, and Mathematical Beliefs for Elementary Pre-Service Teachers

    Science.gov (United States)

    Briley, Jason S.

    2012-01-01

    Ninety-five elementary pre-service teachers enrolled in a mathematics content course for elementary school teachers completed 3 surveys to measure mathematics teaching efficacy, mathematics self-efficacy, and mathematical beliefs. The pre-service teachers who reported stronger beliefs in their capabilities to teach mathematics effectively were…

  9. The Relationships among Pre-Service Mathematics Teachers' Beliefs about Mathematics, Mathematics Teaching, and Use of Technology in China

    Science.gov (United States)

    Yang, Xinrong; Leung, Frederick K. S.

    2015-01-01

    This paper investigated pre-service mathematics teachers' mathematics beliefs, beliefs about information and communication technology (ICT), and their relationships. 787 pre-service mathematics teachers in China completed a survey questionnaire measuring their beliefs about the nature of mathematics, beliefs about mathematics learning and…

  10. The Relationship among Elementary Teachers’ Mathematics Anxiety, Mathematics Instructional Practices, and Student Mathematics Achievement

    OpenAIRE

    Hadley, Kristin M.; Dorward, Jim

    2011-01-01

    Many elementary teachers have been found to have high levels of mathematics anxiety but the impact on student achievement was unknown. Elementary teachers (N = 692) completed the modified Mathematics Anxiety Rating Scale-Revised (Hopko, 2003) along with a questionnaire probing anxiety about teaching mathematics and current mathematics instructional practices. Student mathematics achievement data were collected for the classrooms taught by the teachers. A positive relationship was found betwee...

  11. Perfection Of Methods Of Mathematical Analysis For Increasing The Completeness Of Subsoil Development

    Science.gov (United States)

    Fokina, Mariya

    2017-11-01

    The economy of Russia is based around the mineral-raw material complex to the highest degree. The mining industry is a prioritized and important area. Given the high competitiveness of businesses in this sector, increasing the efficiency of completed work and manufactured products will become a central issue. Improvement of planning and management in this sector should be based on multivariant study and the optimization of planning decisions, the appraisal of their immediate and long-term results, taking the dynamic of economic development into account. All of this requires the use of economic mathematic models and methodsApplying an economic-mathematic model to determine optimal ore mine production capacity, we receive a figure of 4,712,000 tons. The production capacity of the Uchalinsky ore mine is 1560 thousand tons, and the Uzelginsky ore mine - 3650 thousand. Conducting a corresponding analysis of the production of OAO "Uchalinsky Gok", an optimal production plan was received: the optimal production of copper - 77961,4 rubles; the optimal production of zinc - 17975.66 rubles. The residual production volume of the two main ore mines of OAO "UGOK" is 160 million tons of ore.

  12. "Mathematics Is Like a Lion": Elementary Students' Beliefs about Mathematics

    Science.gov (United States)

    Markovits, Zvia; Forgasz, Helen

    2017-01-01

    The aim of this study was to explore the beliefs of elementary school students about mathematics and about themselves as mathematics learners. The participants, Israeli grade 4 and grade 6 students, completed questionnaires. Using an "animal metaphor" to tap beliefs, some students perceived mathematics as difficult and complicated, while…

  13. The Context of the History of Mathematics as Previous Organizer O Contexto da História da Matemática como Organizador Prévio

    Directory of Open Access Journals (Sweden)

    José Messildo Viana Nunes

    2010-06-01

    Full Text Available This article consists of a reflection on the possibility of using the History of the Mathematics as a pedagogical resource for introduction of mathematical concepts, allied to the David Ausubel’s theory of significant learning. This overlap can help us in the elaboration/organization of didactic sequences that can favor the construction of the mathematical knowledge by the pupil himself. In this case, we use some examples from Euclidean Geometry as a reference to present our conception on how and why we conceive the context of the history of the mathematics as a legitimate previous organizer. Keywords: History of Mathematics. Significant Learning. Previous Organizer.Este artigo consiste em uma reflexão sobre a possibilidade de uso da História da Matemática como recurso pedagógico, para introdução de conceitos matemáticos, aliada à teoria da aprendizagem significativa de David Ausubel. Tal imbricação pode nos auxiliar na elaboração/organização de sequências didáticas que possam favorecer a construção do conhecimento matemático pelo próprio aluno. Nesse caso utilizamos alguns exemplos da Geometria Euclidiana como referência para apresentar nossa concepção sobre como e por que concebemos o contexto da história da matemática como um legítimo organizador prévio. Palavras-chave: História da Matemática. Aprendizagem significativa. Organizador Prévio.

  14. Prevalence of Mathematic Disability in Primary Schools

    Directory of Open Access Journals (Sweden)

    Siavash Talepasand

    2012-04-01

    Full Text Available Objectives: One of the issues that have consistently been the concern for the health affair specialists and cure and massive social governors in health fields is the rate of disorders prevalence, diseases and the related subjects to epidemiology. Purpose of this study was to estimate the prevalence of mathematic disability amongst primary schools of Karaj. Methods: Totally 432 students were selected with multi-stage sampling method. Participants completed Raven test, Frostig Visual-Perception test and Wepman Auditory discrimination test, Rutter behavioral questionnaire and Iran Key-math test. In order to diagnosis mathematic disability, inter criterion was normal quotient intelligence and out criteria were to have one of visual perception, auditory and behavioral problems. The participants whose total standard scores in Iran Key-math test were one standard deviation below the mean were selected as a mathematical disability (MD. Results: The mathematic disability prevalence in primary students was estimated 0.46%. In addition, proportion of mathematic disability prevalence was not function of gender or grade. Discussion: The findings demonstrated that the prevalence of mathematic disability is much less than the previous researches. A possible explanation was that inappropriate screening co morbid disorders with the mathematic disability. The theoretical implications of findings are discussed in detail.

  15. Effects of an Additional Mathematics Content Course on Elementary Teachers' Mathematical Beliefs and Knowledge for Teaching

    Science.gov (United States)

    Smith, Marvin E.; Swars, Susan L.; Smith, Stephanie Z.; Hart, Lynn C.; Haardorfer, Regine

    2012-01-01

    This longitudinal study examines the effects of changes in an elementary teacher preparation program on mathematics beliefs and content knowledge for teaching of two groups of prospective teachers (N = 276): (1) those who completed a program with three mathematics content courses and two mathematics methods courses and (2) those who completed a…

  16. Developmental Mathematics Students: Who are They and What is Their Mathematics Self-Efficacy?

    OpenAIRE

    Ryan Baxter; Alan Bates; Adel Tawfig Al-Bataineh

    2016-01-01

    The purpose of this quantitative study was to determine differences in developmental mathematics students’ self-efficacy within the demographic data from the survey. Data from a sample of 240 Intermediate Algebra students at a single four-year university using the Mathematics Self-Efficacy Results indicate that males possess higher levels of mathematics self-efficacy and confidence with their mathematical abilities than females. Students who completed a lower developmental mathematics course ...

  17. Structural Modeling for Influence of Mathematics Self-Concept, Motivation to Learn Mathematics and Self-Regulation Learning on Mathematics Academic Achievement

    OpenAIRE

    Hamideh Jafari Koshkouei; Ahmad Shahvarani; Mohammad Hassan Behzadi; Mohsen Rostamy-Malkhalifeh

    2016-01-01

    The present study was carried out to investigate the influence of mathematics self-concept (MSC), motivation to learn mathematics (SMOT) and self-regulation learning (SRL) on students' mathematics academic achievement. This study is of a descriptive survey type. 300 female students at the first grade of high school (the second period) in City Qods, were selected by multiple step cluster sampling method and completed MSC, SMOT and SRL questionnaires. Mathematics academic achievement was measur...

  18. Stories about Math: An Analysis of Students' Mathematical Autobiographies

    Science.gov (United States)

    Latterell, Carmen M.; Wilson, Janelle L.

    2016-01-01

    This paper analyzes 16 preservice secondary mathematics education majors' mathematical autobiographies. Participants wrote about their previous experiences with mathematics. All participants discussed why they wanted to become mathematics teachers with the key factors being past experience with mathematics teachers, previous success in mathematics…

  19. How to solve mathematical problems

    CERN Document Server

    Wickelgren, Wayne A

    1995-01-01

    Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.

  20. Some unsolved problems in discrete mathematics and mathematical cybernetics

    Science.gov (United States)

    Korshunov, Aleksei D.

    2009-10-01

    There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

  1. Some unsolved problems in discrete mathematics and mathematical cybernetics

    International Nuclear Information System (INIS)

    Korshunov, Aleksei D

    2009-01-01

    There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

  2. A Multisite Study of High School Mathematics Curricula and the Impact of Taking a Developmental Mathematics Course in College

    Science.gov (United States)

    Harwell, Michael; Dupuis, Danielle; Post, Thomas R.; Medhanie, Amanuel; LeBeau, Brandon

    2014-01-01

    The relationship between high school mathematics curricula and the likelihood of students who enroll in a developmental (non-credit bearing) course in college taking additional mathematics courses was studied. The results showed that high school mathematics curriculum, years of high school mathematics completed, and ACT mathematics scores were…

  3. Interactive Mathematics Textbooks

    DEFF Research Database (Denmark)

    Sinclair, Robert

    1999-01-01

    We claim that important considerations have been overlooked in designinginteractive mathematics educational software in the past.In particular,most previous work has concentrated on how to make use ofpre-existing software in mathematics education, rather than firstasking the more...... fundamentalquestion of which requirements mathematics education puts on software, and thendesigning software to fulfil these requirements.We present a working prototype system which takes a script defining an interactivemathematicaldocument and then provides a reader with an interactive realization of thatdocument....

  4. Some unsolved problems in discrete mathematics and mathematical cybernetics

    Energy Technology Data Exchange (ETDEWEB)

    Korshunov, Aleksei D [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)

    2009-10-31

    There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

  5. Constructivism in mathematics

    CERN Document Server

    Troelstra, AS

    1988-01-01

    Studies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras.The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The te

  6. Implicational (semilinear) logics III: completeness properties

    Czech Academy of Sciences Publication Activity Database

    Cintula, Petr; Noguera, Carles

    2018-01-01

    Roč. 57, 3-4 (2018), s. 391-420 ISSN 0933-5846 R&D Projects: GA ČR GA13-14654S EU Projects: European Commission(XE) 689176 - SYSMICS Institutional support: RVO:67985807 ; RVO:67985556 Keywords : abstract algebraic logic * protoalgebraic logics * implicational logics * disjunctional logics * semilinear logics * non-classical logics * completeness theorems * rational completeness Subject RIV: BA - General Mathematics; BA - General Mathematics (UTIA-B) OBOR OECD: Computer science s, information science , bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 0.394, year: 2016

  7. Implicational (semilinear) logics III: completeness properties

    Czech Academy of Sciences Publication Activity Database

    Cintula, Petr; Noguera, Carles

    2018-01-01

    Roč. 57, 3-4 (2018), s. 391-420 ISSN 0933-5846 R&D Projects: GA ČR GA13-14654S EU Projects: European Commission(XE) 689176 - SYSMICS Institutional support: RVO:67985807 ; RVO:67985556 Keywords : abstract algebraic logic * protoalgebraic logics * implicational logics * disjunctional logics * semilinear logics * non-classical logics * completeness theorems * rational completeness Subject RIV: BA - General Mathematics; BA - General Mathematics (UTIA-B) OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 0.394, year: 2016

  8. Teachers mathematical communication profile in explaining subject matter

    Science.gov (United States)

    Umami, Rohmatul; Budayasa, I. Ketut; Suwarsono, St.

    2017-12-01

    This study aimed to see a teachers mathematical communication profile in explaining a subject matter. It is a qualitative research. A high-school junior teacher (i.e., a teacher with 1- to 5-year experience) teaching mathematics at X-Social Class was selected as the subject of this study. The data was collected by observing the teachers mathematical communication in explaining a given material (i.e., the rule of sine) in class and an in-depth interview would be organized respectively. The result showed that the junior teacher explained the subject matter in systematic, complete, fluent, and centered manner. In this case, she began with reminding students on the previous material related to the current material to be learned, informing the current learning objectives, and finally delivering the subject matter. To support her explanation, the teacher also provided some related information, led the students attention into the given material by asking them particular related questions, and did not use any confusing terms. However, the study found that some of high-school teachers still used less appropriate language in explaining materials.

  9. Early Years Students' Relationships with Mathematics

    Science.gov (United States)

    Takeuchi, Miwa Aoki; Towers, Jo; Plosz, Jennifer

    2016-01-01

    Early years mathematics experiences have been shown to be a significant predictor for students' school readiness and future mathematics achievement. Previous research also indicates an important connection between emotion and mathematics learning. How do students in early years education in Alberta describe their emotional relationship with…

  10. Interpolation for completely positive maps: Numerical solutions

    Czech Academy of Sciences Publication Activity Database

    Ambrozie, Calin-Grigore; Gheondea, A.

    2018-01-01

    Roč. 61, č. 1 (2018), s. 13-22 ISSN 1220-3874 Institutional support: RVO:67985840 Keywords : Choi matrix * completely positive * convex minimization Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.362, year: 2016 http://ssmr.ro/bulletin/volumes/61-1/node3.html

  11. An Aristotelian realist philosophy of mathematics mathematics as the science of quantity and structure

    CERN Document Server

    Franklin, J

    2014-01-01

    Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.

  12. Mathematics Anxiety: One Size Does Not Fit All

    Science.gov (United States)

    Stoehr, Kathleen Jablon

    2017-01-01

    Mathematics educators agree elementary teachers should possess confidence and competence in teaching mathematics. Many prospective elementary teachers (particularly women) pursue careers in elementary teaching despite personal repeated experiences of mathematics anxiety. Previous studies of mathematics anxiety have tended to focus on physical…

  13. A Tangent Bundle Theory for Visual Curve Completion.

    Science.gov (United States)

    Ben-Yosef, Guy; Ben-Shahar, Ohad

    2012-07-01

    Visual curve completion is a fundamental perceptual mechanism that completes the missing parts (e.g., due to occlusion) between observed contour fragments. Previous research into the shape of completed curves has generally followed an "axiomatic" approach, where desired perceptual/geometrical properties are first defined as axioms, followed by mathematical investigation into curves that satisfy them. However, determining psychophysically such desired properties is difficult and researchers still debate what they should be in the first place. Instead, here we exploit the observation that curve completion is an early visual process to formalize the problem in the unit tangent bundle R(2) × S(1), which abstracts the primary visual cortex (V1) and facilitates exploration of basic principles from which perceptual properties are later derived rather than imposed. Exploring here the elementary principle of least action in V1, we show how the problem becomes one of finding minimum-length admissible curves in R(2) × S(1). We formalize the problem in variational terms, we analyze it theoretically, and we formulate practical algorithms for the reconstruction of these completed curves. We then explore their induced visual properties vis-à-vis popular perceptual axioms and show how our theory predicts many perceptual properties reported in the corresponding perceptual literature. Finally, we demonstrate a variety of curve completions and report comparisons to psychophysical data and other completion models.

  14. Mathematics year 5 answers

    CERN Document Server

    Alexander, Serena; Poggo, Tammy

    2014-01-01

    Features the complete set of answers to the exercises in Mathematics Year 5, to save you time marking work and enable you to identify areas requiring further attention. The book includes diagrams and workings where necessary, to ensure pupils understand how to present their answers. Also available from Galore Park www.galorepark.co.uk :. - Mathematics Year 5. - Mathematics Year 6. - 11+ Maths Practice Exercises. - 11+ Maths Revision Guide. - 10-Minute Maths Tests Workbook Age 8-10. - 10-Minute Maths Tests Workbook Age 9-11. - Mental Arithmetic Workbook Age 8-10. - Mental Arithmetic Workbook Ag

  15. A history of folding in mathematics mathematizing the margins

    CERN Document Server

    Friedman, Michael

    2018-01-01

    While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is ∛2 with these instruments – the Italian mathematician Margherita Beloch Piazzolla's discovery in 1934 that one can in fact construct a segment of length ∛2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few question immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study...

  16. Role of Mathematics Learning Development Centres in HEIs

    Science.gov (United States)

    Nzekwe-Excel, C.

    2010-01-01

    Background and Rationale: Student withdrawal and non-completion in institutions have been an issue of considerable concern. The lack of mathematical ability has been identified as a factor resulting to non-completion in higher institutions. Several students in higher education approach mathematics with a lot of anxiety. This has created the need…

  17. The many faces of the mathematical modeling cycle

    NARCIS (Netherlands)

    Perrenet, J.C.; Zwaneveld, B.

    2012-01-01

    In literature about mathematical modeling a diversity can be seen in ways of presenting the modeling cycle. Every year, students in the Bachelor’s program Applied Mathematics of the Eindhoven University of Technology, after having completed a series of mathematical modeling projects, have been

  18. The written mathematical communication profile of prospective math teacher in mathematical proving

    Science.gov (United States)

    Pantaleon, K. V.; Juniati, D.; Lukito, A.; Mandur, K.

    2018-01-01

    Written mathematical communication is the process of expressing mathematical ideas and understanding in writing. It is one of the important aspects that must be mastered by the prospective math teacher as tool of knowledge transfer. This research was a qualitative research that aimed to describe the mathematical communication profile of the prospective mathematics teacher in mathematical proving. This research involved 48 students of Mathematics Education Study Program; one of them with moderate math skills was chosen as the main subject. Data were collected through tests, assignments, and task-based interviews. The results of this study point out that in the proof of geometry, the subject explains what is understood, presents the idea in the form of drawing and symbols, and explains the content/meaning of a representation accurately and clearly, but the subject can not convey the argument systematically and logically. Whereas in the proof of algebra, the subject describes what is understood, explains the method used, and describes the content/meaning of a symbolic representation accurately, systematically, logically, but the argument presented is not clear because it is insufficient detailed and complete.

  19. International mathematical olympiad

    OpenAIRE

    Hanjš, Ž.

    1999-01-01

    Today mathematical competitions are very popular with primary and secondary school students and there are many countries all around the world where they are regularly organised. There are several rounds and a lot of students are included, especially at the beginning rounds. The best students from the previous round have the right to continue on the higher level of competition. The final level for the secondary school student competitors is the International Mathematical Olympiad (IMO). The te...

  20. Mathematical foundations of image processing and analysis

    CERN Document Server

    Pinoli, Jean-Charles

    2014-01-01

    Mathematical Imaging is currently a rapidly growing field in applied mathematics, with an increasing need for theoretical mathematics. This book, the second of two volumes, emphasizes the role of mathematics as a rigorous basis for imaging sciences. It provides a comprehensive and convenient overview of the key mathematical concepts, notions, tools and frameworks involved in the various fields of gray-tone and binary image processing and analysis, by proposing a large, but coherent, set of symbols and notations, a complete list of subjects and a detailed bibliography. It establishes a bridg

  1. New mathematical cuneiform texts

    CERN Document Server

    Friberg, Jöran

    2016-01-01

    This monograph presents in great detail a large number of both unpublished and previously published Babylonian mathematical texts in the cuneiform script. It is a continuation of the work A Remarkable Collection of Babylonian Mathematical Texts (Springer 2007) written by Jöran Friberg, the leading expert on Babylonian mathematics. Focussing on the big picture, Friberg explores in this book several Late Babylonian arithmetical and metro-mathematical table texts from the sites of Babylon, Uruk and Sippar, collections of mathematical exercises from four Old Babylonian sites, as well as a new text from Early Dynastic/Early Sargonic Umma, which is the oldest known collection of mathematical exercises. A table of reciprocals from the end of the third millennium BC, differing radically from well-documented but younger tables of reciprocals from the Neo-Sumerian and Old-Babylonian periods, as well as a fragment of a Neo-Sumerian clay tablet showing a new type of a labyrinth are also discussed. The material is presen...

  2. Challenging Transitions and Crossing Borders: Preparing Novice Mathematics Teacher Educators to Support Novice K-12 Mathematics Teachers

    Science.gov (United States)

    Yow, Jan A.; Eli, Jennifer A.; Beisiegel, Mary; McCloskey, Andrea; Welder, Rachael M.

    2016-01-01

    Sixty-nine recently graduated doctoral students in mathematics education completed a survey to determine their perceptions of transitioning from a doctoral program into an academic position at an institution of higher education. Research literature for novice mathematics school teachers was also reviewed to document their experiences transitioning…

  3. Friend Influence and Susceptibility to Influence: Changes in Mathematical Reasoning as a Function of Relative Peer Acceptance and Interest in Mathematics

    Science.gov (United States)

    DeLay, Dawn; Laursen, Brett; Kiuru, Noona; Poikkeus, Anna-Maija; Aunola, Kaisa

    2016-01-01

    This study investigated friend influence over mathematics achievement in 202 same-sex friendship dyads (106 girl dyads). Participants were in the third grade (around age 9) at the outset. Each friend completed a questionnaire describing interest in mathematics and a standardized mathematical reasoning assessment. Peer nominations provided a…

  4. Early Engagement in Course-Based Research Increases Graduation Rates and Completion of Science, Engineering, and Mathematics Degrees

    Science.gov (United States)

    Rodenbusch, Stacia E.; Hernandez, Paul R.; Simmons, Sarah L.; Dolan, Erin L.

    2016-01-01

    National efforts to transform undergraduate biology education call for research experiences to be an integral component of learning for all students. Course-based undergraduate research experiences, or CUREs, have been championed for engaging students in research at a scale that is not possible through apprenticeships in faculty research laboratories. Yet there are few if any studies that examine the long-term effects of participating in CUREs on desired student outcomes, such as graduating from college and completing a science, technology, engineering, and mathematics (STEM) major. One CURE program, the Freshman Research Initiative (FRI), has engaged thousands of first-year undergraduates over the past decade. Using propensity score–matching to control for student-level differences, we tested the effect of participating in FRI on students’ probability of graduating with a STEM degree, probability of graduating within 6 yr, and grade point average (GPA) at graduation. Students who completed all three semesters of FRI were significantly more likely than their non-FRI peers to earn a STEM degree and graduate within 6 yr. FRI had no significant effect on students’ GPAs at graduation. The effects were similar for diverse students. These results provide the most robust and best-controlled evidence to date to support calls for early involvement of undergraduates in research. PMID:27252296

  5. Water Resources Research Program. Surface thermal plumes: evaluation of mathematical models for the near and complete field

    International Nuclear Information System (INIS)

    Dunn, W.E.; Policastro, A.J.; Paddock, R.A.

    1975-08-01

    This report evaluates mathematical models that may be used to predict the flow and temperature distributions resulting from heated surface discharges from power-plant outfalls. Part One discusses the basic physics of surface-plume dispersion and provides a critical review of 11 of the most popular and promising plume models developed to predict the near- and complete-field plume. Part Two compares predictions from the models to prototype data, laboratory data, or both. Part Two also provides a generic discussion of the issues surrounding near- and complete-field modeling. The principal conclusion of the report is that the available models, in their present stage of development, may be used to give only general estimates of plume characteristics; precise predictions are not currently possible. The Shirazi-Davis and Pritchard (No. 1) models appear superior to the others tested and are capable of correctly predicting general plume characteristics. (The predictions show roughly factor-of-two accuracy in centerline distance to a given isotherm, factor-of-two accuracy in plume width, and factor-of-five accuracy in isotherm areas.) The state of the art can best be improved by pursuing basic laboratory studies of plume dispersion along with further development of numerical-modeling techniques

  6. Mathematics for multimedia

    CERN Document Server

    Wickerhauser, Mladen Victor

    2003-01-01

    Mathematics and Multimedia focuses on the mathematics behind multimedia applications. This timely and thoroughly modern text is a rigorous survey of selected results from algebra and analysis, requiring only undergraduate math skills.The topics are `gems' chosen for their usefulness in understanding and creating application software for multimedia signal processing and communication.The book is aimed at a wide audience, including computer science and mathematics majors and those interested in employing mathematics in multimedia design and implementation. For the instructor, the material is divided into six chapters that may be presented in six lecture hours each. Thus, the entire text may be covered in one semester, with time left for examinations and student projects. For the student,there are more than 100 exercises with complete solutions, and numerous example programs in Standard C. Each chapter ends with suggestions for further reading. A companion website provides more insight for both instructors and s...

  7. [Building mathematics in imagination].

    Science.gov (United States)

    Patras, Frédéric

    2015-01-01

    The extraordinary quantitative achievements of contemporary science often hide their qualitative dimension. In mathematics, the understanding of fundamental theoretical phenomena we have got today goes much beyond that achieved in previous periods. This also holds when it comes to the theorisation of mathematical practice.Philosophically, these changes remain largely to be properly analyzed. The present article will address this issue from the point of view of Bachelard's epistemology.

  8. Research in collegiate mathematics education VII

    CERN Document Server

    Hitt, Fernando; Thompson, Patrick W

    2010-01-01

    The present volume of Research in Collegiate Mathematics Education, like previous volumes in this series, reflects the importance of research in mathematics education at the collegiate level. The editors in this series encourage communication between mathematicians and mathematics educators, and as pointed out by the International Commission of Mathematics Instruction (ICMI), much more work is needed in concert with these two groups. Indeed, editors of RCME are aware of this need and the articles published in this series are in line with that goal. Nine papers constitute this volume. The first

  9. Mathematical preparedness for tertiary mathematics – a need for ...

    African Journals Online (AJOL)

    Ongoing action research at the University of Pretoria investigates first-year students' preparedness for a study in calculus. In 2005 first-year engineering students completed a mathematics diagnostic survey at the beginning and end of the year. In this article the results of the 2005 survey are compared with the students' final ...

  10. TIMSS 2011 International Results in Mathematics

    Science.gov (United States)

    Mullis, Ina V. S.; Martin, Michael O.; Foy, Pierre; Arora, Alka

    2012-01-01

    The "TIMSS 2011 International Results in Mathematics" summarizes fourth and eighth grade student achievement in each of the 63 countries and 14 benchmarking entities which participated in TIMSS 2011. The report includes trends in mathematics achievement over time for participants in the previous TIMSS 1995, 1999, 2003, and 2007…

  11. Eighth Grade Algebra Course Placement and Student Motivation for Mathematics

    Science.gov (United States)

    Simzar, Rahila M.; Domina, Thurston; Tran, Cathy

    2016-01-01

    This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics. PMID:26942210

  12. Eighth Grade Algebra Course Placement and Student Motivation for Mathematics.

    Science.gov (United States)

    Simzar, Rahila M; Domina, Thurston; Tran, Cathy

    2016-01-01

    This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics.

  13. MATHEMATICS LANGUAGE IN-CLASS INSTRUCTION

    Directory of Open Access Journals (Sweden)

    Jasmina KARIKJ

    2010-11-01

    Full Text Available The goal of the research was to compare the level of mathematic language acquisition between students of lower grades in special elementary schools for children who are hearing impaired and students of a mainstream elementary school. A total of 239 children attending mainstream and special schools in the territory of Serbia were included in the research. Instruction of mathematics in schools for students who are hearing impaired has a different character as it contains elements of native language instruction. Obtained results show a significant difference in some fields. A conclusion stating that the level of language acquisition is in direct correlation with the level of acquisition of mathematics language imposes itself. What that means is that hearing impaired children have not only to comprehend mathematics relations, but also to learn mathematics terms in a completely different way as compared to children who are hearing.

  14. Noncommutative mathematics for quantum systems

    CERN Document Server

    Franz, Uwe

    2016-01-01

    Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physi...

  15. Mathematics intervention for prevention of neurocognitive deficits in childhood leukemia.

    Science.gov (United States)

    Moore, Ida M; Hockenberry, Marilyn J; Anhalt, Cynthia; McCarthy, Kathy; Krull, Kevin R

    2012-08-01

    Despite evidence that CNS treatment is associated with cognitive and academic impairment, interventions to prevent or mitigate these problems are limited. The purpose was to determine if early intervention can prevent declines in mathematics abilities. Fifty-seven children with ALL were enrolled and randomized to a Mathematics Intervention or Standard Care. Subjects completed neurocognitive assessments prior to the intervention, post-intervention, and 1 year later. Parents received written results and recommendations for use with their school. The Mathematics Intervention was based on Multiple Representation Theory and delivered individually over 1 year. Thirty-two of 57 subjects completed the study and were included in data analyses. These 32 subjects completed all neurocognitive assessments and, for those in the Intervention Group, 40-50 hours of the Mathematics Intervention. There were no group differences on relevant demographic variables; risk stratification; number of intrathecal methotrexate injections; or high dose systemic methotrexate. Significant improvements in calculation and applied mathematics from Baseline to Post-Intervention (P = 0.003 and 0.002, respectively) and in visual working memory from Baseline to 1 year Follow-up (P = 0.02) were observed in the Intervention but not the Standard Care Group. Results from repeated measures ANOVA demonstrated significant between group differences for applied mathematics [F(2,29) = 12.47, P Mathematics Intervention improved mathematics abilities and visual working memory compared to standard care. Future studies are needed to translate the Mathematics Intervention into a "virtual" delivery method more readily available to parents and children. Copyright © 2011 Wiley Periodicals, Inc.

  16. Difference, inclusion, and mathematics education

    DEFF Research Database (Denmark)

    Figueiras, Lourdes; Healy, Lulu; Skovsmose, Ole

    2016-01-01

    The round-table discussion on Difference, Inclusion and Mathematics Education was in included in the scientific programme of VI SIPEM in recognition and celebration of the emerging body of research into the challenges of building a culture of mathematics education which values and respects...... the diversity of learners in different educational contexts – in Brazil and beyond. This paper presents the contributions to the discussion, which focus on the problematisation of the term “inclusion”, explorations of how the practices of previously marginalized students can bring new resources to the teaching...... and learning of mathematics and reflections upon the potentially discriminatory nature of the structures which currently mould school mathematics. The paper aims to serve as material for the developing research agenda of the thirteenth working group of the Brazilian Society of Mathematics Education, which met...

  17. G.W. Leibniz, interrelations between mathematics and philosophy

    CERN Document Server

    Goethe, Norma B; Rabouin, David

    2015-01-01

    Up to now there have been scarcely any publications on Leibniz dedicated to investigating the interrelations between philosophy and mathematics in his thought. In part this is due to the previously restricted textual basis of editions such as those produced by Gerhardt. Through recent volumes of the scientific letters and mathematical papers series of the Academy Edition scholars have obtained a much richer textual basis on which to conduct their studies - material which allows readers to see interconnections between his philosophical and mathematical ideas which have not previously been manifested. The present book draws extensively from this recently published material. The contributors are among the best in their fields. Their commissioned papers cover thematically salient aspects of the various ways in which philosophy and mathematics informed each other in Leibniz's thought.

  18. Structural Completeness in Fuzzy Logics

    Czech Academy of Sciences Publication Activity Database

    Cintula, Petr; Metcalfe, G.

    2009-01-01

    Roč. 50, č. 2 (2009), s. 153-183 ISSN 0029-4527 R&D Projects: GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10300504 Keywords : structral logics * fuzzy logics * structural completeness * admissible rules * primitive variety * residuated lattices Subject RIV: BA - General Mathematics

  19. Mathematical models of incompressible fluids as singular limits of complete fluid systems

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard

    2010-01-01

    Roč. 78, č. 2 (2010), s. 523-560 ISSN 1424-9286 R&D Projects: GA ČR GA201/08/0315 Institutional research plan: CEZ:AV0Z10190503 Keywords : scale analysis * Navier-Stokes-Fourier system * incompressible limit Subject RIV: BA - General Mathematics Impact factor: 0.933, year: 2010 http://link.springer.com/article/10.1007%2Fs00032-010-0128-1

  20. Hemomath the mathematics of blood

    CERN Document Server

    Fasano, Antonio

    2017-01-01

    This book illustrates applications of mathematics to various processes (physiological or artificial) involving flowing blood, including hemorheology, microcirculation, coagulation, kidney filtration and dialysis, offering a historical overview of each topic. Mathematical models are used to simulate processes normally occurring in flowing blood and to predict the effects of dysfunctions (e.g. bleeding disorders, renal failure), as well as the effects of therapies with an eye to improving treatments. Most of the models have a completely new approach that makes patient-specific simulations possible. The book is mainly intended for mathematicians interested in medical applications, but it is also useful for clinicians such as hematologists, nephrologists, cardio-surgeons, and bioengineers. Some parts require no specific knowledge of mathematics. The book is a valuable addition to mathematics, medical, biology, and bioengineering libraries.

  1. Brain correlates of mathematical competence in processing mathematical representations

    Directory of Open Access Journals (Sweden)

    Roland H. Grabner

    2011-11-01

    Full Text Available The ability to extract numerical information from different representation formats (e.g., equations, tables, or diagrams is a key component of mathematical competence but little is known about its neural correlate. Previous studies comparing mathematically less and more competent adults have focused on mental arithmetic and reported differences in left angular gyrus activity which were interpreted to reflect differential reliance on arithmetic fact retrieval during problem solving. The aim of the present functional magnetic resonance imaging (fMRI study was to investigate the brain correlates of mathematical competence in a task requiring the processing of typical mathematical representations. Twenty-eight adults of lower and higher mathematical competence worked on a representation matching task in which they had to evaluate whether the numerical information of a symbolic equation matches that of a bar chart. Two task conditions without and one condition with arithmetic demands were administered. Both competence groups performed equally well in the non-arithmetic conditions and only differed in accuracy in the condition requiring calculation. Activation contrasts between the groups revealed consistently stronger left angular gyrus activation in the more competent individuals across all three task conditions. The finding of competence-related activation differences independently of arithmetic demands suggests that more and less competent individuals differ in a cognitive process other than arithmetic fact retrieval. Specifically, it is argued that the stronger left angular gyrus activity in the more competent adults may reflect their higher proficiency in processing mathematical symbols. Moreover, the study demonstrates competence-related parietal activation differences that were not accompanied by differential experimental performance.

  2. The completion of the mathematical model by parameter identification for simulating a turbofan engine

    Directory of Open Access Journals (Sweden)

    Irina Carmen ANDREI

    2015-09-01

    Full Text Available The purpose of this paper is to set up a method to determine the missing engine design parameters (turbine inlet temperature T3T, airflow rate which significantly influence the jet engines thrust. The authors have introduced a new non-linear equation connecting the fan specific work with the temperature T3T, customized for turbofan. The method of chords, since it converges unconditionally, has been used for solving the non-linear equation of variable temperature T3T. An alternate method, based for the same relation between fan specific work and T3T, has been presented in purpose to determine airflow rate and fan pressure ratio. Two mixed flows turbofans have been considered as study cases. For case #1 it was determined a value comparable to the Turbomeca Larzac turbofan series 04-C6 and 04-C20 which power the AlphaJet machines (series A - Luftwaffe, series E - Dassault Dornier. For the F100-PW229 turbofan, as case #2, being given T3T, then have been determined the airflow rate, fan pressure ratio and fan specific work. After completing the mathematical model with the missing parameters, the performances of the engines at off-design regimes and the operational envelopes revealing i.e. the variations of thrust, specific thrust and fuel specific consumption with altitude and Mach number have been calculated.

  3. Opportunity to learn first year mathematics in teacher training ...

    African Journals Online (AJOL)

    African Journal of Educational Studies in Mathematics and Sciences ... topics in the first year teacher training mathematics syllabus were not taught by the end ... that the teacher training college tutors make efforts to complete the PS1 syllabus.

  4. Mathematical implications of Einstein-Weyl causality

    International Nuclear Information System (INIS)

    Borchers, H.J.; Sen, R.N.

    2006-01-01

    The present work is the first systematic attempt at answering the following fundamental question: what mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The authors propose an axiomatization of Einstein-Weyl causality (inspired by physics), and investigate the topological and uniform structures that it implies. Their final result is that a causal space is densely embedded in one that is locally a differentiable manifold. The mathematical level required of the reader is that of the graduate student in mathematical physics. (orig.)

  5. High School Algebra Students Busting the Myth about Mathematical Smartness: Counterstories to the Dominant Narrative “Get It Quick and Get It Right”

    Directory of Open Access Journals (Sweden)

    Teresa K. Dunleavy

    2018-04-01

    Full Text Available This article continues to challenge the robust myth that mathematical smartness is exemplified in individuals who consistently complete mathematics problems quickly and accurately. In so doing, I present a set of counterstories from three students in one ninth-grade Algebra 1 classroom. These students described transformative experiences in their perceptions of mathematical smartness. Analysis of interviews revealed four themes about their perceptions of mathematical smartness, including: (1 consistently and unapologetically affording time and space to value multiple solution strategies, (2 belief in mathematical justification and explanation as the goal for demonstrating mastery of mathematical content, (3 valuing mathematically valid ideas from all class members, and (4 valuing collaborative problem solving as a way to help group members, distribute mathematical knowledge and orient students toward learning with one another. I found that their interpretations of mathematical smartness are counter to the still-dominant myths around speed and accuracy. While the four themes that emerged have been previously studied in the frame of teacher practices, this research provides needed additional empirical evidence of students’ voices describing what mathematical smartness can and should look like.

  6. Kurt Gödel, completeness, incompleteness

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr

    2007-01-01

    Roč. 82, č. 1 (2007), 012005_1-012005_4 E-ISSN 1742-6596. [Brno Kurt Gödel Days. Brno, 25.04.2007-28.04.2007] R&D Projects: GA AV ČR IAA100300503 Institutional research plan: CEZ:AV0Z10300504 Keywords : Kurt Gödel * completeness * incompleteness Subject RIV: BA - General Mathematics

  7. A Note on Axiomatizations of Pavelka-style Complete Fuzzy Logics

    Czech Academy of Sciences Publication Activity Database

    Cintula, Petr

    2016-01-01

    Roč. 292, 1 June (2016), s. 160-174 ISSN 0165-0114 R&D Projects: GA ČR GAP202/10/1826 Institutional support: RVO:67985807 Keywords : mathematical fuzzy logic * Pavelka-style completeness * MTL logic * Lukasiewicz logics * Product Logic * truth constants * Monteiro–Baaz delta Subject RIV: BA - General Mathematics Impact factor: 2.718, year: 2016

  8. EULER - A Real Virtual Library for Mathematics

    CERN Document Server

    Jost, Michael

    2004-01-01

    The EULER project completed its work in November 2002. It forms the last part of a very successful project in the specialized but global discipline of mathematics. After a successful RTD project had created the technology, a take-up project has effectively exploited it to the point where its future is assured through a not-for-profit consortium. EULER is a European based, world class, real virtual library for mathematics with up-to-date technological solutions, well accepted by users. In particular, EULER provides a world reference and delivery service, transparent to the end user and offering full coverage of the mathematics literature world-wide, including bibliographic data, peer reviews and/or abstracts, indexing, classification and search, transparent access to library services, co-operation with commercial information providers (publishers, bookstores). The EULER services provide a gateway to the electronic catalogues and repositories of participating institutions, while the latter retain complete respo...

  9. What's Past Is Prologue: Relations between Early Mathematics Knowledge and High School Achievement

    Science.gov (United States)

    Watts, Tyler W.; Duncan, Greg J.; Siegler, Robert S.; Davis-Kean, Pamela E.

    2014-01-01

    Although previous research has established the association between early-grade mathematics knowledge and later mathematics achievement, few studies have measured mathematical skills prior to school entry, and few have investigated the predictive power of early gains in mathematics ability. The current paper relates mathematical skills measured at…

  10. Number sense how the mind creates mathematics

    CERN Document Server

    Dehaene, Stanislas

    2011-01-01

    Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and that human infants also have a rudimentary number sense. Dehaene suggests that this rudime

  11. Exhibition - Mathematics, A Beautiful Elsewhere

    CERN Multimedia

    2011-01-01

    From 21 October 2011 to 18 March 2012, the Fondation Cartier pour l’art contemporain will present the exhibition Mathematics: A Beautiful Elsewhere, an exhibition developed in association with the Institut des Hautes Études Scientifiques (IHÉS) and under the patronage of UNESCO. For this unprecedented event, the foundation invited mathematicians to work with artists with whom it has previously worked to create an exhibition that allows visitors to see, hear, do, interpret and think about mathematics. By bringing mathematics into its premises, the Fondation Cartier is itself undergoing the “sudden change of scenery” described by mathematician Alexandre Grothendieck. More information is available here. Fondation Cartier pour l’art contemporain 261, boulevard Raspail 75014 Paris http://fondation.cartier.com Private Visit For professors, researchers and all the staff of Mathematics departments...

  12. Water Resources Research Program. Surface thermal plumes: evaluation of mathematical models for the near and complete field

    International Nuclear Information System (INIS)

    Dunn, W.E.; Policastro, A.J.; Paddock, R.A.

    1975-05-01

    This report evaluates mathematical models that may be used to predict the flow and temperature distributions resulting from heated surface discharges from power-plant outfalls. Part One discusses the basic physics of surface-plume dispersion and provides a critical review of 11 of the most popular and promising plume models developed to predict the near- and complete-field plume. The principal conclusion of the report is that the available models, in their present stage of development, may be used to give only general estimates of plume characteristics; precise predictions are not currently possible. The Shirazi-Davis and Pritchard (No. 1) models appear superior to the others tested and are capable of correctly predicting general plume characteristics. (The predictions show roughly factor-of-two accuracy in centerline distance to a given isotherm, factor-of-two accuracy in plume width, and factor-of-five accuracy in isotherm areas.) The state of the art can best be improved by pursuing basic laboratory studies of plume dispersion along with further development of numerical-modeling techniques

  13. Profile of mathematics anxiety of 7th graders

    Science.gov (United States)

    Udil, Patrisius Afrisno; Kusmayadi, Tri Atmojo; Riyadi

    2017-08-01

    Mathematics anxiety is one of the important factors affect students mathematics achievement. This present research investigates profile of students' mathematics anxiety. This research focuses on analysis and description of students' mathematics anxiety level generally and its dominant domain and aspect. Qualitative research with case study strategy was used in this research. Subject in this research involved 15 students of 7th grade chosen with purposive sampling. Data in this research were students' mathematics anxiety scale result, interview record, and observation result during both mathematics learning activity and test. They were asked to complete mathematics anxiety scale before interviewed and observed. The results show that generally students' mathematics anxiety was identified in the moderate level. In addition, students' mathematics anxiety during mathematics test was identified in the high level, but it was in the moderate level during mathematics learning process. Based on the anxiety domain, students have a high mathematics anxiety on cognitive domain, while it was in the moderate level for psychological and physiological domains. On the other hand, it was identified in low level for psychological domain during mathematics learning process. Therefore, it can be concluded that students have serious and high anxiety regarding mathematics on the cognitive domain and mathematics test aspect.

  14. The logical foundations of mathematics

    CERN Document Server

    Hatcher, William S

    1981-01-01

    The Logical Foundations of Mathematics offers a study of the foundations of mathematics, stressing comparisons between and critical analyses of the major non-constructive foundational systems. The position of constructivism within the spectrum of foundational philosophies is discussed, along with the exact relationship between topos theory and set theory.Comprised of eight chapters, this book begins with an introduction to first-order logic. In particular, two complete systems of axioms and rules for the first-order predicate calculus are given, one for efficiency in proving metatheorems, and

  15. Improvement of Self-regulated Learning in Mathematics through a Hypermedia Application: Differences based on Academic Performance and Previous Knowledge.

    Science.gov (United States)

    Cueli, Marisol; Rodríguez, Celestino; Areces, Débora; García, Trinidad; González-Castro, Paloma

    2017-12-04

    Self-regulation on behalf of the student is crucial in learning Mathematics through hypermedia applications and is an even greater challenge in these IT environments. Two aims are formulated. First, to analyze the effectiveness of a hypermedia tool in improving perceived knowledge of self-regulatory strategies and the perceived usage of the planning, executing and assessment strategy on behalf of students with low, medium and high levels of academic performance. Second, to analyze the effectiveness of the hypermedia tool in improving perceived usage of the strategy for planning, monitoring and evaluating on behalf of students with a perceived knowledge (low, medium and high). Participants were 624 students (aged 10-13), classified into a treatment group (TG; 391) and a comparative group (CG; 233). They completed a questionnaire on perceived knowledge (Perceived Knowledge of Self-Regulatory Strategies) and another one on perceived usage of the strategy for planning, performing and evaluating (Inventory of Self-regulatory Learning Processes). Univariate covariance analyses (ANCOVAs) and Student-t tests were used. ANCOVA results were not statistically significant. However, the linear contrast indicated a significant improvement in perceived knowledge of strategies among the TG with low, medium and high academic performance (p ≤ .001). Results are discussed in the light of past and future research.

  16. The Effects of a Tier 3 Intervention on the Mathematics Performance of Second Grade Students With Severe Mathematics Difficulties.

    Science.gov (United States)

    Bryant, Brian R; Bryant, Diane Pedrotty; Porterfield, Jennifer; Dennis, Minyi Shih; Falcomata, Terry; Valentine, Courtney; Brewer, Chelsea; Bell, Kathy

    2016-01-01

    The purpose of this study was to determine the effectiveness of a systematic, explicit, intensive Tier 3 (tertiary) intervention on the mathematics performance of students in second grade with severe mathematics difficulties. A multiple-baseline design across groups of participants showed improved mathematics performance on number and operations concepts and procedures, which are the foundation for later mathematics success. In the previous year, 12 participants had experienced two doses (first and second semesters) of a Tier 2 intervention. In second grade, the participants continued to demonstrate low performance, falling below the 10th percentile on a researcher-designed universal screener and below the 16th percentile on a distal measure, thus qualifying for the intensive intervention. A project interventionist, who met with the students 5 days a week for 10 weeks (9 weeks for one group), conducted the intensive intervention. The intervention employed more intensive instructional design features than the previous Tier 2 secondary instruction, and also included weekly games to reinforce concepts and skills from the lessons. Spring results showed significantly improved mathematics performance (scoring at or above the 25th percentile) for most of the students, thus making them eligible to exit the Tier 3 intervention. © Hammill Institute on Disabilities 2014.

  17. Minimal free resolutions over complete intersections

    CERN Document Server

    Eisenbud, David

    2016-01-01

    This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957. The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics.

  18. Mathematics for natural scientists fundamentals and basics

    CERN Document Server

    Kantorovich, Lev

    2016-01-01

    This book, the first in a two part series, covers a course of mathematics tailored specifically for physics, engineering and chemistry students at the undergraduate level. It is unique in that it begins with logical concepts of mathematics first encountered at A-level and covers them in thorough detail, filling in the gaps in students' knowledge and reasoning. Then the book aids the leap between A-level and university-level mathematics, with complete proofs provided throughout and all complex mathematical concepts and techniques presented in a clear and transparent manner. Numerous examples and problems (with answers) are given for each section and, where appropriate, mathematical concepts are illustrated in a physics context. This text gives an invaluable foundation to students and a comprehensive aid to lecturers. Mathematics for Natural Scientists: Fundamentals and Basics is the first of two volumes. Advanced topics and their applications in physics are covered in the second volume.

  19. Mathematical models in radiogeochronology

    International Nuclear Information System (INIS)

    Abril, J.M.; Garcia Leon, M.

    1991-01-01

    The study of activity vs. depth profiles in sediment cores of some man-made and natural ocurring radionuclides have shown to be a poweful tool for dating purposes. Nevertheless, in most cases, an adecuate interpretation of such profiles requires mathematical models. In this paper, by considering the sediment as a continuum, a general equation for diffusion of radionuclides through it is obtained. Consequentely, some previously published dating models are found to be particular solutions of such general advenction-diffusion problem. Special emphasis is given to the mathematical treatment of compactation effect and time dependent problems. (author)

  20. Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

    Science.gov (United States)

    Mumcu, Hayal Yavuz

    2016-01-01

    The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

  1. Mathematics Teacher Educators' Perceptions and Use of Cognitive Research

    Science.gov (United States)

    Laski, Elida V.; Reeves, Todd D.; Ganley, Colleen M.; Mitchell, Rebecca

    2013-01-01

    Instructors ("N"?=?204) of elementary mathematics methods courses completed a survey assessing the extent to which they value cognitive research and incorporate it into their courses. Instructors' responses indicated that they view cognitive research to be fairly important for mathematics education, particularly studies of domain-specific topics,…

  2. An assessment experiment for Mathematics at the University of ...

    African Journals Online (AJOL)

    Formative assessment in distance teaching is a complex issue, particularly when diverse students are involved. At Unisa many students from previously disadvantage backgrounds need to be accommodated in tertiary mathematics and science. However, many such students have limited entry-level mathematical knowledge

  3. Supporting metacognitive monitoring in mathematics learning for young people with autism spectrum disorder: A classroom-based study.

    Science.gov (United States)

    Maras, Katie; Gamble, Tim; Brosnan, Mark

    2017-10-01

    Previous research suggests impaired metacognitive monitoring and mathematics under-achievement in autism spectrum disorder. Within educational settings, metacognitive monitoring is supported through the provision of feedback (e.g. with goal reminders and by explicitly correcting errors). Given the strength of the relationship between metacognition, learning and educational attainment, this research tested new computer-based metacognitive support (the 'Maths Challenge') for mathematics learners with autism spectrum disorder within the context of their classroom. The Maths Challenge required learners to engage in metacognitive monitoring before and after answering each question (e.g. intentions and judgements of accuracy) and negotiate with the system the level of difficulty. Forty secondary school children with autism spectrum disorder and 95 typically developing learners completed the Maths Challenge in either a Feedback condition, with metacognitive monitoring support regarding the accuracy of their answers, goal reminders and strategy support, or with No Feedback. Contrary to previous findings, learners with autism showed an undiminished ability to detect errors. They did, however, demonstrate reduced cohesion between their pre- and post-test intentions. Crucially, support from the Feedback condition significantly improved task performance for both groups. Findings highlight important implications for educational interventions regarding the provision of metacognitive support for learners with autism to ameliorate under-performance in mathematics within the classroom.

  4. Factors involved in making post-performance judgments in mathematics problem-solving.

    Science.gov (United States)

    García Fernández, Trinidad; Kroesbergen, Evelyn; Rodríguez Pérez, Celestino; González-Castro, Paloma; González-Pienda, Julio A

    2015-01-01

    This study examines the impact of executive functions, affective-motivational variables related to mathematics, mathematics achievement and task characteristics on fifth and sixth graders’ calibration accuracy after completing two mathematical problems. A sample of 188 students took part in the study. They were divided into two groups as function of their judgment accuracy after completing the two tasks (accurate= 79, inaccurate= 109). Differences between these groups were examined. The discriminative value of these variables to predict group membership was analyzed, as well as the effect of age, gender, and grade level. The results indicated that accurate students showed better levels of executive functioning, and more positive feelings, beliefs, and motivation related to mathematics. They also spent more time on the tasks. Mathematics achievement, perceived usefulness of mathematics, and time spent on Task 1 significantly predicted group membership, classifying 71.3% of the sample correctly. These results support the relationship between academic achievement and calibration accuracy, suggesting the need to consider a wide range of factors when explaining performance judgments.

  5. Mathematical Footprints Discovering Mathematics Everywhere

    CERN Document Server

    Pappas, Theoni

    1999-01-01

    MATHEMATICAL FOOTPRINTS takes a creative look at the role mathematics has played since prehistoric times, and will play in the future, and uncovers mathematics where you least expect to find it from its many uses in medicine, the sciences, and its appearance in art to its patterns in nature and its central role in the development of computers. Pappas presents mathematical ideas in a readable non-threatening manner. MATHEMATICAL FOOTPRINTS is another gem by the creator of THE MATHEMATICS CALENDAR and author of THE JOY OF MATHEMATICS. "Pappas's books have been gold mines of mathematical ent

  6. Prediction Method for the Complete Characteristic Curves of a Francis Pump-Turbine

    Directory of Open Access Journals (Sweden)

    Wei Huang

    2018-02-01

    Full Text Available Complete characteristic curves of a pump-turbine are essential for simulating the hydraulic transients and designing pumped storage power plants but are often unavailable in the preliminary design stage. To solve this issue, a prediction method for the complete characteristics of a Francis pump-turbine was proposed. First, based on Euler equations and the velocity triangles at the runners, a mathematical model describing the complete characteristics of a Francis pump-turbine was derived. According to multiple sets of measured complete characteristic curves, explicit expressions for the characteristic parameters of characteristic operating point sets (COPs, as functions of a specific speed and guide vane opening, were then developed to determine the undetermined coefficients in the mathematical model. Ultimately, by combining the mathematical model with the regression analysis of COPs, the complete characteristic curves for an arbitrary specific speed were predicted. Moreover, a case study shows that the predicted characteristic curves are in good agreement with the measured data. The results obtained by 1D numerical simulation of the hydraulic transient process using the predicted characteristics deviate little from the measured characteristics. This method is effective and sufficient for a priori simulations before obtaining the measured characteristics and provides important support for the preliminary design of pumped storage power plants.

  7. Critical analysis of the policy practice of mathematics education in ...

    African Journals Online (AJOL)

    Ensuring a smooth mathematics education programme requires the formulation and implementation of appropriate instructional policies. This study is a survey of some practices of the instructional policies and their influence on mathematics education. Completed Basic School Annual Census (CBSAC) forms and ...

  8. Mathematical background and attitudes toward statistics in a sample of Spanish college students.

    Science.gov (United States)

    Carmona, José; Martínez, Rafael J; Sánchez, Manuel

    2005-08-01

    To examine the relation of mathematical background and initial attitudes toward statistics of Spanish college students in social sciences the Survey of Attitudes Toward Statistics was given to 827 students. Multivariate analyses tested the effects of two indicators of mathematical background (amount of exposure and achievement in previous courses) on the four subscales. Analysis suggested grades in previous courses are more related to initial attitudes toward statistics than the number of mathematics courses taken. Mathematical background was related with students' affective responses to statistics but not with their valuing of statistics. Implications of possible research are discussed.

  9. What’s Past is Prologue: Relations Between Early Mathematics Knowledge and High School Achievement

    OpenAIRE

    Watts, Tyler W.; Duncan, Greg J.; Siegler, Robert S.; Davis-Kean, Pamela E.

    2014-01-01

    © 2014 AERA. Although previous research has established the association between early-grade mathematics knowledge and later mathematics achievement, few studies have measured mathematical skills prior to school entry, and few have investigated the predictive power of early gains in mathematics ability. The current paper relates mathematical skills measured at 54 months to adolescent mathematics achievement using multisite longitudinal data. We find that preschool mathematics ability predicts ...

  10. Assessment Mathematics Teacher's Competencies

    Science.gov (United States)

    Alnoor, A. G.; Yuanxiang, Guo; Abudhuim, F. S.

    2007-01-01

    This paper aimed to identifying the professional efficiencies for the intermediate schools mathematics teachers and tries to know at what level the math teachers experience those competencies. The researcher used a descriptive research approach, the study data collected from specialist educators and teacher's experts and previous studies to…

  11. Early Engagement in Course-Based Research Increases Graduation Rates and Completion of Science, Engineering, and Mathematics Degrees.

    Science.gov (United States)

    Rodenbusch, Stacia E; Hernandez, Paul R; Simmons, Sarah L; Dolan, Erin L

    2016-01-01

    National efforts to transform undergraduate biology education call for research experiences to be an integral component of learning for all students. Course-based undergraduate research experiences, or CUREs, have been championed for engaging students in research at a scale that is not possible through apprenticeships in faculty research laboratories. Yet there are few if any studies that examine the long-term effects of participating in CUREs on desired student outcomes, such as graduating from college and completing a science, technology, engineering, and mathematics (STEM) major. One CURE program, the Freshman Research Initiative (FRI), has engaged thousands of first-year undergraduates over the past decade. Using propensity score-matching to control for student-level differences, we tested the effect of participating in FRI on students' probability of graduating with a STEM degree, probability of graduating within 6 yr, and grade point average (GPA) at graduation. Students who completed all three semesters of FRI were significantly more likely than their non-FRI peers to earn a STEM degree and graduate within 6 yr. FRI had no significant effect on students' GPAs at graduation. The effects were similar for diverse students. These results provide the most robust and best-controlled evidence to date to support calls for early involvement of undergraduates in research. © 2016 S. Rodenbusch et al. CBE—Life Sciences Education © 2016 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

  12. Enhancing Students’ Interest through Mathematics Learning

    Science.gov (United States)

    Azmidar, A.; Darhim, D.; Dahlan, J. A.

    2017-09-01

    A number of previous researchers indicated that students’ mathematics interest still low because most of them have perceived that mathematics is very difficult, boring, not very practical, and have many abstract theorems that were very hard to understand. Another cause is the teaching and learning process used, which is mechanistic without considering students’ needs. Learning is more known as the process of transferring the knowledge to the students. Let students construct their own knowledge with the physical and mental reflection that is done by activity in the new knowledge. This article is literature study. The purpose of this article is to examine the Concrete-Pictorial-Abstract approach in theoretically to improve students’ mathematics interest. The conclusion of this literature study is the Concrete-Pictorial-Abstract approach can be used as an alternative to improve students’ mathematics interest.

  13. Socio-functional dynamics of the mathematical contents

    Directory of Open Access Journals (Sweden)

    Isabel Alonso-Berenguer

    2018-01-01

    Full Text Available The article presents a model of the socio-functional dynamics of the mathematical contents that offers a novel theoretical-methodological basement for the development of the process of teaching-learning of the mathematical one. The investigation, of theoretical character, used the methods of analysis-synthesis, inductive-deductive and historical-logical to elaborate the one mentioned model that leaves of considering that the future professors have appropriated previously of the mathematical contents, foreseen in the curriculum, and they are, therefore, under conditions of understanding the potentialities of the same ones to facilitate the formation of socio-functional values.   

  14. Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation

    Science.gov (United States)

    Anhalt, Cynthia Oropesa; Cortez, Ricardo

    2016-01-01

    This study examines the evolution of 11 prospective teachers' understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include…

  15. Pharmacy students' perceptions of natural science and mathematics subjects.

    Science.gov (United States)

    Prescott, Julie; Wilson, Sarah Ellen; Wan, Kai-Wai

    2014-08-15

    To determine the level of importance pharmacy students placed on science and mathematics subjects for pursuing a career in pharmacy. Two hundred fifty-four students completed a survey instrument developed to investigate students' perceptions of the relevance of science and mathematics subjects to a career in pharmacy. Pharmacy students in all 4 years of a master of pharmacy (MPharm) degree program were invited to complete the survey instrument. Students viewed chemistry-based and biology-based subjects as relevant to a pharmacy career, whereas mathematics subjects such as physics, logarithms, statistics, and algebra were not viewed important to a career in pharmacy. Students' experience in pharmacy and year of study influenced their perceptions of subjects relevant to a pharmacy career. Pharmacy educators need to consider how they can help students recognize the importance of scientific knowledge earlier in the pharmacy curriculum.

  16. A Multifaceted Mathematical Approach for Complex Systems

    Energy Technology Data Exchange (ETDEWEB)

    Alexander, F.; Anitescu, M.; Bell, J.; Brown, D.; Ferris, M.; Luskin, M.; Mehrotra, S.; Moser, B.; Pinar, A.; Tartakovsky, A.; Willcox, K.; Wright, S.; Zavala, V.

    2012-03-07

    Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significant impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee.

  17. Mathematical symbol hypothesis recognition with rejection option

    OpenAIRE

    Julca-Aguilar , Frank; Hirata , Nina ,; Viard-Gaudin , Christian; Mouchère , Harold; Medjkoune , Sofiane

    2014-01-01

    International audience; In the context of handwritten mathematical expressions recognition, a first step consist on grouping strokes (segmentation) to form symbol hypotheses: groups of strokes that might represent a symbol. Then, the symbol recognition step needs to cope with the identification of wrong segmented symbols (false hypotheses). However, previous works on symbol recognition consider only correctly segmented symbols. In this work, we focus on the problem of mathematical symbol reco...

  18. Activities report 1977--78. Applied mathematics department 5640

    International Nuclear Information System (INIS)

    1979-03-01

    This report is a compilation of independent articles highlighting some of the work done in the Applied Mathematics Department during the years 1977 and 1978. It is neither an exhaustive report on all activities in the department during this period nor a list of the most substantial mathematical contributions. Instead, it is a selection of topics which are thought to be of greatest interest because of their importance to Sandia. The report is divided into four principal sections which reflect the department's major areas of interest: Mathematical Physics, Computational Mathematics, Probability and Statistics, and Discrete Mathematics. To provide a smoother narrative, references are omitted from the text. However, a complete department bibliography of corporate and open publications as well as technical presentations for the period October 1977 through December 1978 is appended. 4 figures, 3 tables

  19. Elementary Mathematics Specialists: Ensuring the Intersection of Research and Practice

    Science.gov (United States)

    McGatha, Maggie B.

    2017-01-01

    This paper provides a historical overview of the role and impact of elementary mathematics specialists as well as current implications and opportunities for the field. Furthermore, suggestions are offered for the mathematics education field for ensuring the intersection of practice and research. [For complete proceedings, see ED581294.

  20. Completeness for coherent states in a magnetic–solenoid field

    International Nuclear Information System (INIS)

    Bagrov, V G; Gavrilov, S P; Gitman, D M; Górska, K

    2012-01-01

    This paper completes our study of coherent states in the so-called magnetic–solenoid field (a collinear combination of a constant uniform magnetic field and Aharonov–Bohm solenoid field) presented in Bagrov et al (2010 J. Phys. A: Math. Theor. 43 354016, 2011 J. Phys. A: Math. Theor. 44 055301). Here, we succeeded in proving nontrivial completeness relations for non-relativistic and relativistic coherent states in such a field. In addition, we solve here the relevant Stieltjes moment problem and present a comparative analysis of our coherent states and the well-known, in the case of pure uniform magnetic field, Malkin–Man’ko coherent states. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

  1. On Strong Standard Completeness in Some MTL-Delta Expansions

    Czech Academy of Sciences Publication Activity Database

    Vidal, Amanda; Bou, F.; Esteva, F.; Godo, L.

    2017-01-01

    Roč. 21, č. 1 (2017), s. 125-147 ISSN 1432-7643 R&D Projects: GA ČR(CZ) GF15-34650L Grant - others:Austrian Science Fund(AT) I1897-N25 Institutional support: RVO:67985807 Keywords : mathematical fuzzy logic * left-continuous t-norms * monoidal t-norm logic * infinitary rules * standard completeness Subject RIV: BA - General Mathematics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 2.472, year: 2016

  2. Mathematical expeditions chronicles by the explorers

    CERN Document Server

    Laubenbacher, Reinhard

    1999-01-01

    This book contains the stories of five mathematical journeys into new realms, told through the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, while others had more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realization that still greater vistas remained to be explored. The authors tell these stories by guiding the reader through the very words of the mathematicians at the heart of these events, and thereby provide insight into the art of approaching mathematical problems. The book can be used in a variety of ways. The five chapters are completely independent, each with varying levels of mathematical sophistication. The book will be enticing to students, to instructors, and to the intellectually curious reader. By working through some of the original sources and supplemental exercises, which discuss and solve - or attempt to solve - a great problem, this book helps the reader discover the roots ...

  3. Virtual Manipulatives: Tools for Teaching Mathematics to Students with Learning Disabilities

    Science.gov (United States)

    Shin, Mikyung; Bryant, Diane P.; Bryant, Brian R.; McKenna, John W.; Hou, Fangjuan; Ok, Min Wook

    2017-01-01

    Many students with learning disabilities demonstrate difficulty in developing a conceptual understanding of mathematical topics. Researchers recommend using visual models to support student learning of the concepts and skills necessary to complete abstract and symbolic mathematical problems. Virtual manipulatives (i.e., interactive visual models)…

  4. Math Is Like a Lion Hunting a Sleeping Gazelle: Preservice Elementary Teachers' Metaphors of Mathematics

    Science.gov (United States)

    Latterell, Carmen M.; Wilson, Janelle L.

    2016-01-01

    Preservice elementary teachers hold a variety of beliefs about mathematics and mathematics learning, which influence their teaching. Previous research has shown that preservice elementary teachers believe that mathematics is doing arithmetic. However, it is unclear if preservice elementary teachers truly believe that mathematics is only…

  5. Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-efficacy Beliefs towards Mathematics and Mathematics Teaching

    OpenAIRE

    Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

    2017-01-01

    The purpose of the research is to investigate the relationships betweenself-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacybeliefs toward mathematics teaching, mathematics teaching anxiety variables andtesting the relationships between these variables with structural equationmodel. The sample of the research, which was conducted in accordance withrelational survey model, consists of 380 university students, who studied atthe department of Elementary Mathematics Educ...

  6. The Affective Dimensions of Mathematical Difficulties in Schoolchildren

    Directory of Open Access Journals (Sweden)

    Morena Lebens

    2011-01-01

    Full Text Available Mathematical difficulties (MDs are frequently characterised by cognitive deficits such as ineffective problem solving strategies and a lack of computational fluency. The established literature indicates that mathematical achievement is not only a function of cognitive factors but it also points to the importance of affective factors for the development of mathematical achievement. In the light of this evidence, the exploration of children's affective responses towards mathematics becomes a central issue. Whereas previous studies tended to research affective motivational constructs such as self-efficacy in isolation from other related constructs, the literature suffers from a shortage of research on the relationship between different affective motivational variables and their impact on mathematical achievement in different age and achievement bands. The present paper aims to address this aim by employing a newly developed instrument to measure affective motivational variables. Overall, the present findings support the assumption that children of average ability are less influenced by affective factors than children with mathematical difficulties.

  7. Mathematical physics classical mechanics

    CERN Document Server

    Knauf, Andreas

    2018-01-01

    As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.

  8. Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety.

    Science.gov (United States)

    Devine, Amy; Fawcett, Kayleigh; Szűcs, Dénes; Dowker, Ann

    2012-07-09

    Mathematics anxiety (MA), a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population. Some research has indicated that MA negatively affects mathematics performance and that girls may report higher levels of MA than boys. On the other hand some research has indicated that boys' mathematics performance is more negatively affected by MA than girls' performance is. The aim of the current study was to measure girls' and boys' mathematics performance as well as their levels of MA while controlling for test anxiety (TA) a construct related to MA but which is typically not controlled for in MA studies. Four-hundred and thirty three British secondary school children in school years 7, 8 and 10 completed customised mental mathematics tests and MA and TA questionnaires. No gender differences emerged for mathematics performance but levels of MA and TA were higher for girls than for boys. Girls and boys showed a positive correlation between MA and TA and a negative correlation between MA and mathematics performance. TA was also negatively correlated with mathematics performance, but this relationship was stronger for girls than for boys. When controlling for TA, the negative correlation between MA and performance remained for girls only. Regression analyses revealed that MA was a significant predictor of performance for girls but not for boys. Our study has revealed that secondary school children experience MA. Importantly, we controlled for TA which is typically not controlled for in MA studies. Girls showed higher levels of MA than boys and high levels of MA were related to poorer levels of mathematics performance. As well as potentially having a detrimental effect on 'online' mathematics performance, past research has shown that high levels of MA can have negative consequences for later mathematics education. Therefore MA warrants attention in the mathematics classroom, particularly because

  9. Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety

    Science.gov (United States)

    2012-01-01

    Background Mathematics anxiety (MA), a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population. Some research has indicated that MA negatively affects mathematics performance and that girls may report higher levels of MA than boys. On the other hand some research has indicated that boys’ mathematics performance is more negatively affected by MA than girls’ performance is. The aim of the current study was to measure girls’ and boys’ mathematics performance as well as their levels of MA while controlling for test anxiety (TA) a construct related to MA but which is typically not controlled for in MA studies. Methods Four-hundred and thirty three British secondary school children in school years 7, 8 and 10 completed customised mental mathematics tests and MA and TA questionnaires. Results No gender differences emerged for mathematics performance but levels of MA and TA were higher for girls than for boys. Girls and boys showed a positive correlation between MA and TA and a negative correlation between MA and mathematics performance. TA was also negatively correlated with mathematics performance, but this relationship was stronger for girls than for boys. When controlling for TA, the negative correlation between MA and performance remained for girls only. Regression analyses revealed that MA was a significant predictor of performance for girls but not for boys. Conclusions Our study has revealed that secondary school children experience MA. Importantly, we controlled for TA which is typically not controlled for in MA studies. Girls showed higher levels of MA than boys and high levels of MA were related to poorer levels of mathematics performance. As well as potentially having a detrimental effect on ‘online’ mathematics performance, past research has shown that high levels of MA can have negative consequences for later mathematics education. Therefore MA warrants attention in

  10. Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety

    Directory of Open Access Journals (Sweden)

    Devine Amy

    2012-07-01

    Full Text Available Abstract Background Mathematics anxiety (MA, a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population. Some research has indicated that MA negatively affects mathematics performance and that girls may report higher levels of MA than boys. On the other hand some research has indicated that boys’ mathematics performance is more negatively affected by MA than girls’ performance is. The aim of the current study was to measure girls’ and boys’ mathematics performance as well as their levels of MA while controlling for test anxiety (TA a construct related to MA but which is typically not controlled for in MA studies. Methods Four-hundred and thirty three British secondary school children in school years 7, 8 and 10 completed customised mental mathematics tests and MA and TA questionnaires. Results No gender differences emerged for mathematics performance but levels of MA and TA were higher for girls than for boys. Girls and boys showed a positive correlation between MA and TA and a negative correlation between MA and mathematics performance. TA was also negatively correlated with mathematics performance, but this relationship was stronger for girls than for boys. When controlling for TA, the negative correlation between MA and performance remained for girls only. Regression analyses revealed that MA was a significant predictor of performance for girls but not for boys. Conclusions Our study has revealed that secondary school children experience MA. Importantly, we controlled for TA which is typically not controlled for in MA studies. Girls showed higher levels of MA than boys and high levels of MA were related to poorer levels of mathematics performance. As well as potentially having a detrimental effect on ‘online’ mathematics performance, past research has shown that high levels of MA can have negative consequences for later mathematics education

  11. An Evaluation of the Instructional System in Mathematics: 1977-1978.

    Science.gov (United States)

    Frechtling, Joy A.; And Others

    The results of an evaluation of various aspects of the Instructional System in Mathematics (ISM) are presented. ISM is an objectives-based, computer-supported, management system which builds upon a previously developed mathematics curriculum. Questionnaires to school-based personnel and students, in-school observations, and interviews, were used…

  12. Mathematical intuitionism

    CERN Document Server

    Dragalin, A G

    1988-01-01

    This monograph is intended to present the most important methods of proof theory in intuitionistic logic, assuming the reader to have mastered an introductory course in mathematical logic. The book starts with purely syntactical methods based on Gentzen's cut-elimination theorem, followed by intuitionistic arithmetic where Kleene's realizability method plays a central role. The author then studies algebraic models and completeness theorems for them. After giving a survey on the principles of intuitionistic analysis, the last part of the book presents the cut-elimination theorem in intuitionistic simple theory of types with an extensionality rule.

  13. European Conference on Numerical Mathematics and Advanced Applications

    CERN Document Server

    Manguoğlu, Murat; Tezer-Sezgin, Münevver; Göktepe, Serdar; Uğur, Ömür

    2016-01-01

    The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), held every 2 years, provides a forum for discussing recent advances in and aspects of numerical mathematics and scientific and industrial applications. The previous ENUMATH meetings took place in Paris (1995), Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011) and Lausanne (2013). This book presents a selection of invited and contributed lectures from the ENUMATH 2015 conference, which was organised by the Institute of Applied Mathematics (IAM), Middle East Technical University, Ankara, Turkey, from September 14 to 18, 2015. It offers an overview of central recent developments in numerical analysis, computational mathematics, and applications in the form of contributions by leading experts in the field.

  14. What's Past is Prologue: Relations Between Early Mathematics Knowledge and High School Achievement.

    Science.gov (United States)

    Watts, Tyler W; Duncan, Greg J; Siegler, Robert S; Davis-Kean, Pamela E

    2014-10-01

    Although previous research has established the association between early-grade mathematics knowledge and later mathematics achievement, few studies have measured mathematical skills prior to school entry, nor have they investigated the predictive power of early gains in mathematics ability. The current paper relates mathematical skills measured at 54 months to adolescent mathematics achievement using multi-site longitudinal data. We find that preschool mathematics ability predicts mathematics achievement through age 15, even after accounting for early reading, cognitive skills, and family and child characteristics. Moreover, we find that growth in mathematical ability between age 54 months and first grade is an even stronger predictor of adolescent mathematics achievement. These results demonstrate the importance of pre-kindergarten mathematics knowledge and early math learning for later achievement.

  15. Knots and surfaces a guide to discovering mathematics

    CERN Document Server

    Farmer, David W

    1995-01-01

    In most mathematics textbooks, the most exciting part of mathematics-the process of invention and discovery-is completely hidden from the reader. The aim of Knots and Surfaces is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequi

  16. A Multi-Method Investigation of Mathematics Motivation for Elementary Age Students

    Science.gov (United States)

    Linder, Sandra M.; Smart, Julie B.; Cribbs, Jennifer

    2015-01-01

    This paper presents the results of a multi-method study examining elementary students with high self-reported levels of mathematics motivation. Second- through fifth-grade students at a Title One school in the southeastern United States completed the Elementary Mathematics Motivation Instrument (EMMI), which examines levels of mathematics…

  17. Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-Efficacy Beliefs towards Mathematics and Mathematics Teaching

    Science.gov (United States)

    Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

    2017-01-01

    The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…

  18. Complete modeling and software implementation of a virtual solar hydrogen hybrid system

    International Nuclear Information System (INIS)

    Pedrazzi, S.; Zini, G.; Tartarini, P.

    2010-01-01

    A complete mathematical model and software implementation of a solar hydrogen hybrid system has been developed and applied to real data. The mathematical model has been derived from sub-models taken from literature with appropriate modifications and improvements. The model has been implemented as a stand-alone virtual energy system in a model-based, multi-domain software environment. A test run has then been performed on typical residential user data-sets over a year-long period. Results show that the virtual hybrid system can bring about complete grid independence; in particular, hydrogen production balance is positive (+1.25 kg) after a year's operation with a system efficiency of 7%.

  19. Cognitive and Emotional Math Problems Largely Dissociate: Prevalence of Developmental Dyscalculia and Mathematics Anxiety

    OpenAIRE

    Devine, A; Hill, F; Carey, E; Szucs, Denes

    2017-01-01

    © 2017 APA, all rights reserved). A negative correlation between math anxiety and mathematics performance is frequently reported. Thus, some may assume that high levels of mathematics anxiety are associated with poor mathematical understanding. However, no previous research has clearly measured the association between mathematics anxiety and mathematical learning disability. To fill this gap, here we investigated the comorbidity of developmental dyscalculia (a selective, serious deficit in ma...

  20. The semantic system is involved in mathematical problem solving.

    Science.gov (United States)

    Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

    2018-02-01

    Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

  1. Advanced Training in Mathematics Schools

    Indian Academy of Sciences (India)

    Mail the completed forms to: Prof. E K Narayanan, Department of Mathematics, Indian Institute of Science, Bangalore. 560012, Tel: 080-22933270,22932711 Fax: 80-23600146, Email: atm@math.iisc.ernet.in so as to reach before 20 April 2006. List of selected candidates will be posted on the websites on 24th April 2006.

  2. Processes involved in solving mathematical problems

    Science.gov (United States)

    Shahrill, Masitah; Putri, Ratu Ilma Indra; Zulkardi, Prahmana, Rully Charitas Indra

    2018-04-01

    This study examines one of the instructional practices features utilized within the Year 8 mathematics lessons in Brunei Darussalam. The codes from the TIMSS 1999 Video Study were applied and strictly followed, and from the 183 mathematics problems recorded, there were 95 problems with a solution presented during the public segments of the video-recorded lesson sequences of the four sampled teachers. The analyses involved firstly, identifying the processes related to mathematical problem statements, and secondly, examining the different processes used in solving the mathematical problems for each problem publicly completed during the lessons. The findings revealed that for three of the teachers, their problem statements coded as `using procedures' ranged from 64% to 83%, while the remaining teacher had 40% of his problem statements coded as `making connections.' The processes used when solving the problems were mainly `using procedures', and none of the problems were coded as `giving results only'. Furthermore, all four teachers made use of making the relevant connections in solving the problems given to their respective students.

  3. Completing Algebra II in High School: Does It Increase College Access and Success?

    Science.gov (United States)

    Kim, Jeongeun; Kim, Jiyun; DesJardins, Stephen L.; McCall, Brian P.

    2015-01-01

    Noting the benefits of mathematics in students' future educational attainment and labor market success, there is considerable interest in high school requirements in terms of course-taking in mathematics at the national, state, and school district level. Previous research indicates that taking advanced math courses in high school leads to positive…

  4. The image of mathematics held by Irish post-primary students

    Science.gov (United States)

    Lane, Ciara; Stynes, Martin; O'Donoghue, John

    2014-08-01

    The image of mathematics held by Irish post-primary students was examined and a model for the image found was constructed. Initially, a definition for 'image of mathematics' was adopted with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. Research focused on students studying ordinary level mathematics for the Irish Leaving Certificate examination - the final examination for students in second-level or post-primary education. Students were aged between 15 and 18 years. A questionnaire was constructed with both quantitative and qualitative aspects. The questionnaire survey was completed by 356 post-primary students. Responses were analysed quantitatively using Statistical Package for the Social Sciences (SPSS) and qualitatively using the constant comparative method of analysis and by reviewing individual responses. Findings provide an insight into Irish post-primary students' images of mathematics and offer a means for constructing a theoretical model of image of mathematics which could be beneficial for future research.

  5. Mathematical Modelling of Unmanned Aerial Vehicles

    Directory of Open Access Journals (Sweden)

    Saeed Sarwar

    2013-04-01

    Full Text Available UAVs (Unmanned Arial Vehicleis UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard autopilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an autopilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design autopilot for UAV

  6. Mathematical modelling of unmanned aerial vehicles

    International Nuclear Information System (INIS)

    Sarwar, S.; Rehman, S.U.

    2013-01-01

    UAVs (Unmanned Aerial Vehicles) UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard auto pilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an auto pilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom) equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design auto pilot for UAV. (author)

  7. The contribution of spatial ability to mathematics achievement in middle childhood.

    Science.gov (United States)

    Gilligan, Katie A; Flouri, Eirini; Farran, Emily K

    2017-11-01

    Strong spatial skills are associated with success in science, technology, engineering, and mathematics (STEM) domains. Although there is convincing evidence that spatial skills are a reliable predictor of mathematical achievement in preschool children and in university students, there is a lack of research exploring associations between spatial and mathematics achievement during the primary school years. To address this question, this study explored associations between mathematics and spatial skills in children aged 5 and 7years. The study sample included 12,099 children who participated in both Wave 3 (mean age=5; 02 [years; months]) and Wave 4 (mean age=7; 03) of the Millennium Cohort Study. Measures included a standardised assessment of mathematics and the Pattern Construction subscale of the British Ability Scales II to assess intrinsic-dynamic spatial skills. Spatial skills at 5 and 7years of age explained a significant 8.8% of the variation in mathematics achievement at 7years, above that explained by other predictors of mathematics, including gender, socioeconomic status, ethnicity, and language skills. This percentage increased to 22.6% without adjustment for language skills. This study expands previous findings by using a large-scale longitudinal sample of primary school children, a population that has been largely omitted from previous research exploring associations between spatial ability and mathematics achievement. The finding that early and concurrent spatial skills contribute to mathematics achievement at 7years of age highlights the potential of spatial skills as a novel target in the design of mathematics interventions for children in this age range. Crown Copyright © 2017. Published by Elsevier Inc. All rights reserved.

  8. Greek mathematical thought and the origin of algebra

    CERN Document Server

    Klein, Jacob

    1992-01-01

    Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th-16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science - in which the symbolic ""form"" of a mathematical statement is completely inseparable from its ""content"" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

  9. Factorization of cp-rank-3 completely positive matrices

    Czech Academy of Sciences Publication Activity Database

    Brandts, J.; Křížek, Michal

    2016-01-01

    Roč. 66, č. 3 (2016), s. 955-970 ISSN 0011-4642 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : completely positive matrix * cp-rank * factorization Subject RIV: BA - General Mathematics Impact factor: 0.364, year: 2016 http://hdl.handle.net/10338.dmlcz/145882

  10. Mathematics related anxiety: Mathematics bogeyman or not?

    Directory of Open Access Journals (Sweden)

    Videnović Marina

    2011-01-01

    Full Text Available Data of the PISA 2003 survey indicate high levels of mathematics anxiety of students in Serbia. More than half of our students worry whether they will have difficulties in mathematics class or whether they will earn poor marks. Aims of this study therefore are: examining relationship between math anxiety and achievement at mathematics literacy scale; establishing possible predictors of math anxiety and identification of students' groups in relations to their relationship towards mathematics as a subject. Mathematics anxiety is statistically negatively correlated with school achievement and achievement at mathematics literacy scale. Socio-demographic factors, motivational and cognitive aspects related to learning mathematics, perception of school and classroom climate explain 40% variance of mathematics anxiety. Based on students' relationship towards mathematics they cam be divided into three groups; while dimensions that apart them are uninterested-interested in mathematics and presence-absence of anxiety. The group displaying anxiety scores lowest among the three. Applying qualitative analysis students' and teachers' attitudes on specific issues related to teaching and learning mathematics was examined.

  11. Raising girls’ participation in A-level mathematics: initial findings from ‘good practice’ case studies

    OpenAIRE

    Smith, C.; Golding, J.

    2015-01-01

    Fewer girls than boys in England participate in post-compulsory mathematics and the recent increase in popularity of Mathematics and Further Mathematics (FM) at age 16 has not changed the gender balance. Previous studies have shown the significance to girls of their mathematics lessons and teachers, of discursive co-constructions of masculinity and mathematics, of the range of careers associated with mathematics and science, and family ‘science capital’. This study identifie...

  12. Teachers' Mathematics as Mathematics-at-Work

    Science.gov (United States)

    Bednarz, Nadine; Proulx, Jérôme

    2017-01-01

    Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…

  13. Adaptation of abbreviated mathematics anxiety rating scale for engineering students

    Science.gov (United States)

    Nordin, Sayed Kushairi Sayed; Samat, Khairul Fadzli; Sultan, Al Amin Mohamed; Halim, Bushra Abdul; Ismail, Siti Fatimah; Mafazi, Nurul Wirdah

    2015-05-01

    Mathematics is an essential and fundamental tool used by engineers to analyse and solve problems in their field. Due to this, most engineering education programs involve a concentration of study in mathematics courses whereby engineering students have to take mathematics courses such as numerical methods, differential equations and calculus in the first two years and continue to do so until the completion of the sequence. However, the students struggled and had difficulties in learning courses that require mathematical abilities. Hence, this study presents the factors that caused mathematics anxiety among engineering students using Abbreviated Mathematics Anxiety Rating Scale (AMARS) through 95 students of Universiti Teknikal Malaysia Melaka (UTeM). From 25 items in AMARS, principal component analysis (PCA) suggested that there are four mathematics anxiety factors, namely experiences of learning mathematics, cognitive skills, mathematics evaluation anxiety and students' perception on mathematics. Minitab 16 software was used to analyse the nonparametric statistics. Kruskal-Wallis Test indicated that there is a significant difference in the experience of learning mathematics and mathematics evaluation anxiety among races. The Chi-Square Test of Independence revealed that the experience of learning mathematics, cognitive skills and mathematics evaluation anxiety depend on the results of their SPM additional mathematics. Based on this study, it is recommended to address the anxiety problems among engineering students at the early stage of studying in the university. Thus, lecturers should play their part by ensuring a positive classroom environment which encourages students to study mathematics without fear.

  14. An investigation of elementary preservice teachers’ self-efficacy for teaching mathematics

    Directory of Open Access Journals (Sweden)

    Rebecca McMahon Giles

    2016-12-01

    Full Text Available Research has consistently shown that teacher efficacy is related to a variety of desirable student outcomes, thus, making teacher efficacy an important factor in high quality mathematics instruction. The purpose of this study was to determine elementary preservice teachers’ self-efficacy beliefs related to teaching mathematics. Forty-one participants from a single university responded to the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI after completing a constructivist-based elementary mathematics methods course prior to student teaching. The MTEBI is 21-item survey using a 5-point, forced choice Likert-like scale to provide an individual's perceptions of mathematics teaching efficacy beliefs on two subscales—Personal Mathematics Teaching Efficacy Belief (PMTE and Mathematics Teaching Outcome Expectancy (MTOE. Responses on the PMTE subscale (Mean = 51.08, SD=5.171 indicate that the respondents’ personal mathematics teach efficacy is positive. Participants’ responses (Mean = 29.32, SD = 3.29 on the MTOE subscale indicate positive expectations of students' mathematics learning. Attending to preservice teacher efficacy is worthy of examination. Teacher preparation programs must identify opportunities to positively impact mathematics teaching efficacy of preservice teachers.

  15. The Context of the History of Mathematics as Previous Organizer O Contexto da História da Matemática como Organizador Prévio

    OpenAIRE

    José Messildo Viana Nunes; Saddo Ag Almouloud; Renato Borges Guerra

    2010-01-01

    This article consists of a reflection on the possibility of using the History of the Mathematics as a pedagogical resource for introduction of mathematical concepts, allied to the David Ausubel’s theory of significant learning. This overlap can help us in the elaboration/organization of didactic sequences that can favor the construction of the mathematical knowledge by the pupil himself. In this case, we use some examples from Euclidean Geometry as a reference to present our conception on how...

  16. Accounting for primitive terms in mathematics

    Directory of Open Access Journals (Sweden)

    D.F.M. Strauss

    2005-07-01

    Full Text Available The philosophical problem of unity and diversity entails a challenge to the rationalist aim to define everything. Definitions of this kind surface in various academic disciplines in formulations like uniqueness, irreducibility, and what has acquired the designation “primitive terms”. Not even the most “exact” disciplines, such as mathematics, can avoid the implications entailed in giving an account of such primitive terms. A mere look at the historical development of mathematics highlights the fact that alternative perspectives prevailed – from the arithmeticism of Pythagoreanism, the eventual geometrisation of mathematics after the discovery of incommensurability up to the revival of arithmeticism in the mathematics of Cauchy, Weierstrass, Dedekind and Cantor (with the later orientation of Frege, who completed the circle by returning to the view that mathematics essentially is geometry. An assessment of logicism and axiomatic formalism is followed by looking at the primitive meaning of wholeness (and the whole-parts relation. With reference to the views of Hilbert, Weyl and Bernays the article concludes by suggesting that in opposition to arithmeticism and geometricism an alternative option ought to be pursued – one in which both the uniqueness and mutual coherence between the aspects of number and space are acknowledged.

  17. Accelerating Mathematics Achievement Using Heterogeneous Grouping

    Science.gov (United States)

    Burris, Carol Corbett; Heubert, Jay P.; Levin, Henry M.

    2006-01-01

    This longitudinal study examined the effects of providing an accelerated mathematics curriculum in heterogeneously grouped middle school classes in a diverse suburban school district. A quasi-experimental cohort design was used to evaluate subsequent completion of advanced high school math courses as well as academic achievement. Results showed…

  18. Mathematical Modeling Activities as a Useful Tool for Values Education

    Science.gov (United States)

    Doruk, Bekir Kursat

    2012-01-01

    Values education is crucial since it is one of the factors to reach success in education in broader sense and in mathematics education in particular sense. It is also important for educating next generations of societies. However, previous research showed that expected importance for values education was not given in Mathematics courses. In a few…

  19. Understanding the Influence of Two Mathematics Textbooks on Prospective Secondary Teachers' Knowledge

    Science.gov (United States)

    Davis, Jon D.

    2009-01-01

    This study examines the influence of reading and planning from two differently organized mathematics textbooks on prospective high school mathematics teachers' pedagogical content knowledge and content knowledge of exponential functions. The teachers completed a pretest and two posttests. On the pretest, the teachers possessed an incomplete…

  20. Closing the Gap: First Year Success in College Mathematics at an HBCU

    Science.gov (United States)

    Harrington, Melissa A.; Lloyd, Andrew; Smolinski, Tomasz; Shahin, Mazen

    2016-01-01

    At our Historically-Black University, about 89% of first-year students place into developmental mathematics, negatively impacting retention and degree completion. In 2012, an NSF-funded learning enrichment project began offering the introductory and developmental mathematics courses on-line over the summer to incoming science, technology,…

  1. Theological Metaphors in Mathematics

    Directory of Open Access Journals (Sweden)

    Krajewski Stanisław

    2016-03-01

    Full Text Available Examples of possible theological influences upon the development of mathematics are indicated. The best known connection can be found in the realm of infinite sets treated by us as known or graspable, which constitutes a divine-like approach. Also the move to treat infinite processes as if they were one finished object that can be identified with its limits is routine in mathematicians, but refers to seemingly super-human power. For centuries this was seen as wrong and even today some philosophers, for example Brian Rotman, talk critically about “theological mathematics”. Theological metaphors, like “God’s view”, are used even by contemporary mathematicians. While rarely appearing in official texts they are rather easily invoked in “the kitchen of mathematics”. There exist theories developing without the assumption of actual infinity the tools of classical mathematics needed for applications (For instance, Mycielski’s approach. Conclusion: mathematics could have developed in another way. Finally, several specific examples of historical situations are mentioned where, according to some authors, direct theological input into mathematics appeared: the possibility of the ritual genesis of arithmetic and geometry, the importance of the Indian religious background for the emergence of zero, the genesis of the theories of Cantor and Brouwer, the role of Name-worshipping for the research of the Moscow school of topology. Neither these examples nor the previous illustrations of theological metaphors provide a certain proof that religion or theology was directly influencing the development of mathematical ideas. They do suggest, however, common points and connections that merit further exploration.

  2. Examining Fourth-Grade Mathematics Writing: Features of Organization, Mathematics Vocabulary, and Mathematical Representations

    Science.gov (United States)

    Hebert, Michael A.; Powell, Sarah R.

    2016-01-01

    Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…

  3. What’s Past is Prologue: Relations Between Early Mathematics Knowledge and High School Achievement

    Science.gov (United States)

    Watts, Tyler W.; Duncan, Greg J.; Siegler, Robert S.; Davis-Kean, Pamela E.

    2015-01-01

    Although previous research has established the association between early-grade mathematics knowledge and later mathematics achievement, few studies have measured mathematical skills prior to school entry, nor have they investigated the predictive power of early gains in mathematics ability. The current paper relates mathematical skills measured at 54 months to adolescent mathematics achievement using multi-site longitudinal data. We find that preschool mathematics ability predicts mathematics achievement through age 15, even after accounting for early reading, cognitive skills, and family and child characteristics. Moreover, we find that growth in mathematical ability between age 54 months and first grade is an even stronger predictor of adolescent mathematics achievement. These results demonstrate the importance of pre-kindergarten mathematics knowledge and early math learning for later achievement. PMID:26806961

  4. The complete works of Gabrio Piola commented English translation

    CERN Document Server

    Maier, Giulio; Perego, Umberto; Andreaus, Ugo; Esposito, Raffaele; Forest, Samuel

    2014-01-01

    Gabrio Piola works had an enormous impact on the development of applied mathematics and continuum mechanics. An excellent scientific committee who took it upon themselves to translate his complete works. In a second step, they commented  Piola’s work and compared it to modern theories in mechanics in order to stress Piola’s impact on modern science and proofs that he has set milestones in applied mathematics. This book presents Piola's original Italian texts together with is translations and their comments. It shows impressively that Gabrio Piola’s work must still be regarded as a modern theory.

  5. Student comprehension of mathematics through astronomy

    Science.gov (United States)

    Search, Robert

    The purpose of this study is to examine how knowledge of astronomy can enhance college-level learning situations involving mathematics. The fundamental symbiosis between mathematics and astronomy was established early in the 17th century when Johannes Kepler deduced the 3 basic laws of planetary motion. This mutually harmonious relationship between these sciences has been reinforced repeatedly in history. In the early 20th century, for example, astronomer Arthur Eddington used photographic evidence from a 1919 solar eclipse to verify Einstein's mathematical theory of relativity. This study was conducted in 5 undergraduate mathematics classes over the course of 2 years. An introductory course in ordinary differential equations, taught in Spring Semester 2013, involved 4 students. A similar course in Spring Semester 2014 involved 6 students, a Summer Semester 2014 Calculus II course involved 2 students, and a Summer 2015 Astronomy course involved 8 students. The students were asked to use Kepler's astronomical evidence to deduce mathematical laws normally encountered on an undergraduate level. They were also asked to examine the elementary mathematical aspects involved in a theoretical trajectory to the planet Neptune. The summer astronomy class was asked to draw mathematical conclusions about large numbers from the recent discoveries concerning the dwarf planet Pluto. The evidence consists primarily of videotaped PowerPoint presentations conducted by the students in both differential equations classes, along with interviews and tests given in all the classes. All presentations were transcribed and examined to determine the effect of astronomy as a generator of student understanding of mathematics. An analysis of the data indicated two findings: definite student interest in a subject previously unknown to most of them and a desire to make the mathematical connection to celestial phenomena.

  6. A Cognitive Analysis of Students’ Mathematical Problem Solving Ability on Geometry

    Science.gov (United States)

    Rusyda, N. A.; Kusnandi, K.; Suhendra, S.

    2017-09-01

    The purpose of this research is to analyze of mathematical problem solving ability of students in one of secondary school on geometry. This research was conducted by using quantitative approach with descriptive method. Population in this research was all students of that school and the sample was twenty five students that was chosen by purposive sampling technique. Data of mathematical problem solving were collected through essay test. The results showed the percentage of achievement of mathematical problem solving indicators of students were: 1) solve closed mathematical problems with context in math was 50%; 2) solve the closed mathematical problems with the context beyond mathematics was 24%; 3) solving open mathematical problems with contexts in mathematics was 35%; And 4) solving open mathematical problems with contexts outside mathematics was 44%. Based on the percentage, it can be concluded that the level of achievement of mathematical problem solving ability in geometry still low. This is because students are not used to solving problems that measure mathematical problem solving ability, weaknesses remember previous knowledge, and lack of problem solving framework. So the students’ ability of mathematical problems solving need to be improved with implement appropriate learning strategy.

  7. Teaching Mathematical Modeling in Mathematics Education

    Science.gov (United States)

    Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

    2016-01-01

    Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

  8. Mathematics anxiety in secondary students in England.

    Science.gov (United States)

    Chinn, Steve

    2009-02-01

    Whatever the changes that are made to the mathematics curriculum in England, there will always remain a problem with mathematics anxiety. Maths anxiety is rarely facilitative. This study examined aspects of mathematics in secondary schools and how students rated them as sources of anxiety. Over 2000 students in independent and mainstream schools in England completed a 20-item questionnaire designed to investigate maths anxiety levels. The same questionnaire was given to over 440 dyslexic males in specialist schools within the same age range. The results showed that examinations and tests create high levels of anxiety in approximately 4% of students. The results suggest that certain aspects and topics in the maths curriculum, such as long division, cause similar levels of anxiety for students in all year groups in secondary schools.

  9. Mathematical Properties Relevant to Geomagnetic Field Modeling

    DEFF Research Database (Denmark)

    Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

    2010-01-01

    be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers.......The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...

  10. Mathematical Properties Relevant to Geomagnetic Field Modeling

    DEFF Research Database (Denmark)

    Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

    2014-01-01

    be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focused. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers....... The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...

  11. A Case of Learning Mathematics the Hard Way as a Teaching Assistant

    OpenAIRE

    Drake, Patricia S

    2005-01-01

    This paper develops early data from a qualitative longitudinal study of the first cohort of five students making the transition from teaching assistant in secondary school to specialist teacher of secondary mathematics. Data from a second cohort of four women and one man starting in 2003 is less complete, but used as appropriate. Bernstein's work on subject classification frames an argument that this student group navigates simultaneously two mathematics discourses: hard university mathematic...

  12. Mathematical Modeling and Pure Mathematics

    Science.gov (United States)

    Usiskin, Zalman

    2015-01-01

    Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

  13. The Effects of Remedial Mathematics on the Learning of Economics

    DEFF Research Database (Denmark)

    Lagerlöf, Johan N. M.; Seltzer, Andrew J.

    2009-01-01

    The authors examined the effects of remedial mathematics on performance in university-level economics courses using a natural experiment. They studied exam results prior and subsequent to the implementation of a remedial mathematics course that was compulsory for a subset of students...... and unavailable for the others, controlling for background variables. They found that, consistent with previous studies, the level of and performance in secondary school mathematics have strong predictive power on students' performances at university-level economics. However, they found relatively little evidence...

  14. The Completeness Theorem of Gödel - An Introduction to ...

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 7. The Completeness Theorem of Gödel - An Introduction to Mathematical Logic. S M Srivastava. General Article Volume 6 Issue 7 July 2001 pp 29-41. Fulltext. Click here to view fulltext PDF. Permanent link:

  15. Linking Preservice Teachers' Mathematics Self-Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

    Science.gov (United States)

    Bates, Alan B.; Latham, Nancy; Kim, Jin-ah

    2011-01-01

    This study examined preservice teachers' mathematics self-efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self-Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs…

  16. Parallel Boltzmann machines : a mathematical model

    NARCIS (Netherlands)

    Zwietering, P.J.; Aarts, E.H.L.

    1991-01-01

    A mathematical model is presented for the description of parallel Boltzmann machines. The framework is based on the theory of Markov chains and combines a number of previously known results into one generic model. It is argued that parallel Boltzmann machines maximize a function consisting of a

  17. Elementary and Advanced Mathematic thinking as human activity in permanent evolution.

    Directory of Open Access Journals (Sweden)

    Mauricio Penagos

    2017-01-01

    Full Text Available The objective of this text is to present a reflection and analysis about the processes in the development of fundamental and advanced mathematical thinking as a human activity. Traditionally, mathematics education has had two barriers to overcome: First, advanced mathematical thinking is only shown at a determined age and therefore it must be addressed in university level courses. Second, the teachers of this discipline regularly introduce mathematics to students as a body of complete and irrefutable knowledge shared by a scientific community. The task of the student is to learn it, do demonstrations and reproduce this knowledge in a given period of time. Mathematical entities or objects that in occasions have taken centuries to build. In contrast with the true sense of education of this discipline that must be to empower in the students the development of mathematical thinking.

  18. Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Mathematics Examinations

    Science.gov (United States)

    Darlington, Ellie

    2014-01-01

    This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…

  19. A mathematics vocabulary questionnaire for use in the intermediate phase

    Directory of Open Access Journals (Sweden)

    Marthie van der Walt

    2008-11-01

    Full Text Available Teachers and psychologists need an instrument to assess learners' language proficiency in mathematics to enable them to plan and evaluate interventions and to facilitate best practice in mathematics classrooms. We describe the development of a mathematics vocabulary questionnaire to measure learners' language proficiency in mathematics in the intermediate phase. It covers all the steps from designing the preliminary questionnaire to standardising the final instrument. A sample of 1 103 Grades 4 to 7 Afrikaans-, English- and Tswana-speaking learners in North West Province completed the Mathematics Vocabulary questionnaire (Primary (MV(P, consisting of 12 items. We analysed the data by calculating discrimination values, performing a factor analysis, determining reliability coefficients, and investigating item bias by language, gender, and grade. We concluded that there was strong evidence of validity and reliability for the MV(P.

  20. A cephalometric study to determine the plane of occlusion in completely edentulous patients.

    Science.gov (United States)

    Hindocha, Amit D; Vartak, Vikas N; Bhandari, Aruna J; Dudani, Mohit T

    2013-01-01

    Determination of the plane of occlusion in completely edentulous patients with the help of the ala-tragus line (Camper's plane) may be questioned. An attempt to devise an alternative method to determine the orientation of the plane of occlusion was made. Cephalometric analysis was used to identify whether a correlation exists between the plane of occlusion of dentulous Indian individuals and other stable cranial landmarks. A negative correlation was found to exist between the occlusal Plane-FH plane angle and the porion-nasion-anterior nasal spine (PoNANS) angle. From the derived mathematical correlation, it was concluded that the angulation of the occlusal plane in completely edentulous subjects may be determined by taking a cephalogram at the diagnostic stage. Further, the clinical applicability of the derived mathematical formula (while determining the plane of occlusion) was tested on completely edentulous patients.

  1. Using Mathematics Literature with Prospective Secondary Mathematics Teachers

    Science.gov (United States)

    Jett, Christopher C.

    2014-01-01

    Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…

  2. The Effectiveness of MURDER Cooperative Model towards Students' Mathematics Reasoning Ability and Self Concept of Ten Grade

    Directory of Open Access Journals (Sweden)

    Sofan Tri Prasetiyo

    2017-08-01

    Full Text Available The purpose of this research was to know the effectiveness of MURDER cooperative model towards students’ mathematics reasoning ability and self concept of ten grade. Population of this research were students of MIA ten grade Senior High School 1 Kebumen in the academic year 2016/1017. Sampling technique using simple random sampling technique. The data collected by the method of documentation, test methods, observation methods, and questionnaire methods. The analyzed of data are used completeness test and average different test. The results showed that: (1 mathematics reasoning ability of students that following MURDER cooperative model have completed individual and classical study completeness; (2 mathematics reasoning ability of students that following MURDER cooperative model better than mathematics reasoning ability of students that following ekspository learning; (3 self concept of students that following MURDER cooperative model better than self concept of students that following ekspository learning.

  3. Elements of the history of mathematics

    CERN Document Server

    Bourbaki, Nicolas

    1994-01-01

    This work gathers together, without substantial modification, the major­ ity of the historical Notes which have appeared to date in my Elements de M atMmatique. Only the flow has been made independent of the Elements to which these Notes were attached; they are therefore, in principle, accessible to every reader who possesses a sound classical mathematical background, of undergraduate standard. Of course, the separate studies which make up this volume could not in any way pretend to sketch, even in a summary manner, a complete and con­ nected history of the development of Mathematics up to our day. Entire parts of classical mathematics such as differential Geometry, algebraic Geometry, the Calculus of variations, are only mentioned in passing; others, such as the theory of analytic functions, that of differential equations or partial differ­ ential equations, are hardly touched on; all the more do these gaps become more numerous and more important as the modern era is reached. It goes without saying that t...

  4. Mathematics in computed tomography and related techniques

    International Nuclear Information System (INIS)

    Sawicka, B.

    1992-01-01

    The mathematical basis of computed tomography (CT) was formulated in 1917 by Radon. His theorem states that the 2-D function f(x,y) can be determined at all points from a complete set of its line integrals. Modern methods of image reconstruction include three approaches: algebraic reconstruction techniques with simultaneous iterative reconstruction or simultaneous algebraic reconstruction; convolution back projection; and the Fourier transform method. There is no one best approach. Because the experimental data do not strictly satisfy theoretical models, a number of effects have to be taken into account; in particular, the problems of beam geometry, finite beam dimensions and distribution, beam scattering, and the radiation source spectrum. Tomography with truncated data is of interest, employing mathematical approximations to compensate for the unmeasured projection data. Mathematical techniques in image processing and data analysis are also extensively used. 13 refs

  5. Core skills assessment to improve mathematical competency

    Science.gov (United States)

    Carr, Michael; Bowe, Brian; Fhloinn, Eabhnat Ní

    2013-12-01

    Many engineering undergraduates begin third-level education with significant deficiencies in their core mathematical skills. Every year, in the Dublin Institute of Technology, a diagnostic test is given to incoming first-year students, consistently revealing problems in basic mathematics. It is difficult to motivate students to address these problems; instead, they struggle through their degree, carrying a serious handicap of poor core mathematical skills, as confirmed by exploratory testing of final year students. In order to improve these skills, a pilot project was set up in which a 'module' in core mathematics was developed. The course material was basic, but 90% or higher was required to pass. Students were allowed to repeat this module throughout the year by completing an automated examination on WebCT populated by a question bank. Subsequent to the success of this pilot with third-year mechanical engineering students, the project was extended to five different engineering programmes, across three different year-groups. Full results and analysis of this project are presented, including responses to interviews carried out with a selection of the students involved.

  6. Doing Mathematics with Purpose: Mathematical Text Types

    Science.gov (United States)

    Dostal, Hannah M.; Robinson, Richard

    2018-01-01

    Mathematical literacy includes learning to read and write different types of mathematical texts as part of purposeful mathematical meaning making. Thus in this article, we describe how learning to read and write mathematical texts (proof text, algorithmic text, algebraic/symbolic text, and visual text) supports the development of students'…

  7. Mathematical foundations of transport theory

    International Nuclear Information System (INIS)

    Ershov, Yu.I.; Shikhov, S.B.

    1985-01-01

    Foundations of mathematical transport theory are presented. Definitions and theorems of functional analysis are given. Linear kinetic equation of neutron transport in multiplication media is derived. A model of neutron interaction with nuclei of medium determining completely the coefficient properties in transport equation is described. Non-stationary problems regarding and without regard of d=e layed neutrons are analyzed. Results of solving Cauchy problem are discussed

  8. Equations in mathematical physics a practical course

    CERN Document Server

    Pikulin, Victor P

    2001-01-01

    This handbook is addressed to students of technology institutf's where a course on mathematical physics of relatively reduced volume is offered, as well as to engineers and scientists. The aim of the handbook is to treat (demonstrate) the basic methods for solving the simplest problems of classical mathematical physics. The most basic among the methods considered hrre i8 the superposition method. It allows one, based on particular linearly indepmdent HolutionH (solution "atoms"), to obtain the solution of a given problem. To that end the "Hupply" of solution atoms must be complete. This method is a development of the well-known method of particular solutions from the theory of ordinar~' differelltial equations. In contrast to the case of ordinary differential equations, where the number of linearly independent 80lutions is always finite, for a linear partial differrntial equation a complete "supply" of solution atoms is always infinite. This infinite set of Holutions may be discrete (for example, for regular ...

  9. Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

    Science.gov (United States)

    Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

    2016-01-01

    Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

  10. Enhancing Science and Mathematics Education for Child Care Providers and Preschool Teachers.

    Science.gov (United States)

    White, Jennifer Meux; Hosoume, Kimi

    The Lawrence Hall of Science (LHS), University of California at Berkeley has completed a 3-year project to develop a science and mathematics education course and science curriculum for early childhood educators. This project was in response to the need for improving the science and mathematics knowledge and teaching skills of adults who work with…

  11. An introduction to the mathematical theory of dynamic materials

    CERN Document Server

    Lurie, Konstantin A

    2017-01-01

    Mathematical treatment to properties of dynamic materials, material substances whose properties are variable in space and time are examined in this book. This new edition emphasizes the differences between material optimization techniques in statics and dynamics. Systems with one spatial coordinate and time are used to illustrate essentials of temporal property change in this setting and prompt forthcoming extensions and technical improvements. Since the release of the first edition, a number of new results have created a more complete picture of unusual effects hidden in spatio-temporal material geometry. This renewed look has revealed a conceptually new mechanism of relaxation of material optimization problems in dynamics, which has led to additional resources for optimization previously concealed in the property layouts. Dynamic materials are studied in this book from the following perspectives: ability to appear in dissimilar implementations, universality as formations that are thermodynamically open, and...

  12. Matrix Mathematics Theory, Facts, and Formulas (Second Edition)

    CERN Document Server

    Bernstein, Dennis S

    2011-01-01

    When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices. Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminat

  13. Creating symmetry the artful mathematics of wallpaper patterns

    CERN Document Server

    Farris, Frank A

    2015-01-01

    This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks-a sort of potato-stamp method-Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics. Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, who

  14. Mapping Variation in Children's Mathematical Reasoning: The Case of "What Else Belongs?"

    Science.gov (United States)

    Vale, Colleen; Widjaja, Wanty; Herbert, Sandra; Bragg, Leicha A.; Loong, Esther Yoon-Kin

    2017-01-01

    Explaining appears to dominate primary teachers' understanding of mathematical reasoning when it is not confused with problem solving. Drawing on previous literature of mathematical reasoning, we generate a view of the critical aspects of reasoning that may assist primary teachers when designing and enacting tasks to elicit and develop…

  15. Manifold Shape : from Differential Geometry to Mathematical Morphology

    NARCIS (Netherlands)

    Roerdink, J.B.T.M.

    1994-01-01

    Much progress has been made in extending Euclidean mathematical morphology to more complex structures such as complete lattices or spaces with a non-commutative symmetry group. Such generalizations are important for practical situations such as translation and rotation invariant pattern recognition

  16. COMPLETE SEPARATION OF THE VERTICAL AND HORIZONTAL INDEPENDENT COMPONENTS OF THE FLIGHT IN POLICOPTER UAV NAU PKF "AURORA" AND MATHEMATICAL MODEL OF THIS FLIGHT

    Directory of Open Access Journals (Sweden)

    Volodymyr Kharchenko

    2017-07-01

    Full Text Available Purpose: This article presents a mathematical model and the experimental results of automatic flights of the policopter UAV NAU PKF "Aurora" of oktacopter scheme with additional elektroimpeler engines of horizontal thrust. Methods: UAV NAU PKF "Aurora" is developed for experimental flights in manual, semi-automatic and unmanned modes. The uniqueness and scientific novelty of data of flight testes is in a complete separation and isolation of vertical and horizontal components of the flight, which enables a fundamentally new way of moving of vehicle in the aerial space. This approach gives a ability to obtain all advantages and to eliminate disadvantages of helicopter and airplane in fundamentally new aircraft by structure and by function – namely in the policopter flyer with additional independent engines of the lateral thrust. Results: Obtained a new experimental data that allowed to better understand the nature of the physical forces, providing the flight of the policopter. Discussion: Revised a physical basis of the airscrew (propeller, namely on the example of flight of the policopter proved that most of the thrust of the propeller provided by the mechanical impulse (kinetic energy Ек=mv2/2 by the impulse, that a airscrew receives at his collisions with air molecules,but not by the gradient of air pressure below and above the airscrew. Is put forward a hypothesis of gravitational nature of the flight and introduced the notion of "functional antigravity", that a force completely identical in function and opposite on the direction of the force of gravity (gravity force. Deduced a mathematical formula of "functionally antigravitational" transport, namely:G·M·m/R2 = mI·v2/2 – for the flights of the aircraft with a mass m over universal astronomical body with a mass M, and m·g = mI·v2/2 – for the flights of the aircraft with mass m over a planet Earth.

  17. Probability elements of the mathematical theory

    CERN Document Server

    Heathcote, C R

    2000-01-01

    Designed for students studying mathematical statistics and probability after completing a course in calculus and real variables, this text deals with basic notions of probability spaces, random variables, distribution functions and generating functions, as well as joint distributions and the convergence properties of sequences of random variables. Includes worked examples and over 250 exercises with solutions.

  18. Mathematics Anxiety and Statistics Anxiety. Shared but Also Unshared Components and Antagonistic Contributions to Performance in Statistics

    Science.gov (United States)

    Paechter, Manuela; Macher, Daniel; Martskvishvili, Khatuna; Wimmer, Sigrid; Papousek, Ilona

    2017-01-01

    In many social science majors, e.g., psychology, students report high levels of statistics anxiety. However, these majors are often chosen by students who are less prone to mathematics and who might have experienced difficulties and unpleasant feelings in their mathematics courses at school. The present study investigates whether statistics anxiety is a genuine form of anxiety that impairs students' achievements or whether learners mainly transfer previous experiences in mathematics and their anxiety in mathematics to statistics. The relationship between mathematics anxiety and statistics anxiety, their relationship to learning behaviors and to performance in a statistics examination were investigated in a sample of 225 undergraduate psychology students (164 women, 61 men). Data were recorded at three points in time: At the beginning of term students' mathematics anxiety, general proneness to anxiety, school grades, and demographic data were assessed; 2 weeks before the end of term, they completed questionnaires on statistics anxiety and their learning behaviors. At the end of term, examination scores were recorded. Mathematics anxiety and statistics anxiety correlated highly but the comparison of different structural equation models showed that they had genuine and even antagonistic contributions to learning behaviors and performance in the examination. Surprisingly, mathematics anxiety was positively related to performance. It might be that students realized over the course of their first term that knowledge and skills in higher secondary education mathematics are not sufficient to be successful in statistics. Part of mathematics anxiety may then have strengthened positive extrinsic effort motivation by the intention to avoid failure and may have led to higher effort for the exam preparation. However, via statistics anxiety mathematics anxiety also had a negative contribution to performance. Statistics anxiety led to higher procrastination in the structural

  19. Mathematics Anxiety and Statistics Anxiety. Shared but Also Unshared Components and Antagonistic Contributions to Performance in Statistics.

    Science.gov (United States)

    Paechter, Manuela; Macher, Daniel; Martskvishvili, Khatuna; Wimmer, Sigrid; Papousek, Ilona

    2017-01-01

    In many social science majors, e.g., psychology, students report high levels of statistics anxiety. However, these majors are often chosen by students who are less prone to mathematics and who might have experienced difficulties and unpleasant feelings in their mathematics courses at school. The present study investigates whether statistics anxiety is a genuine form of anxiety that impairs students' achievements or whether learners mainly transfer previous experiences in mathematics and their anxiety in mathematics to statistics. The relationship between mathematics anxiety and statistics anxiety, their relationship to learning behaviors and to performance in a statistics examination were investigated in a sample of 225 undergraduate psychology students (164 women, 61 men). Data were recorded at three points in time: At the beginning of term students' mathematics anxiety, general proneness to anxiety, school grades, and demographic data were assessed; 2 weeks before the end of term, they completed questionnaires on statistics anxiety and their learning behaviors. At the end of term, examination scores were recorded. Mathematics anxiety and statistics anxiety correlated highly but the comparison of different structural equation models showed that they had genuine and even antagonistic contributions to learning behaviors and performance in the examination. Surprisingly, mathematics anxiety was positively related to performance. It might be that students realized over the course of their first term that knowledge and skills in higher secondary education mathematics are not sufficient to be successful in statistics. Part of mathematics anxiety may then have strengthened positive extrinsic effort motivation by the intention to avoid failure and may have led to higher effort for the exam preparation. However, via statistics anxiety mathematics anxiety also had a negative contribution to performance. Statistics anxiety led to higher procrastination in the structural

  20. Mathematics Anxiety and Statistics Anxiety. Shared but Also Unshared Components and Antagonistic Contributions to Performance in Statistics

    Directory of Open Access Journals (Sweden)

    Manuela Paechter

    2017-07-01

    Full Text Available In many social science majors, e.g., psychology, students report high levels of statistics anxiety. However, these majors are often chosen by students who are less prone to mathematics and who might have experienced difficulties and unpleasant feelings in their mathematics courses at school. The present study investigates whether statistics anxiety is a genuine form of anxiety that impairs students' achievements or whether learners mainly transfer previous experiences in mathematics and their anxiety in mathematics to statistics. The relationship between mathematics anxiety and statistics anxiety, their relationship to learning behaviors and to performance in a statistics examination were investigated in a sample of 225 undergraduate psychology students (164 women, 61 men. Data were recorded at three points in time: At the beginning of term students' mathematics anxiety, general proneness to anxiety, school grades, and demographic data were assessed; 2 weeks before the end of term, they completed questionnaires on statistics anxiety and their learning behaviors. At the end of term, examination scores were recorded. Mathematics anxiety and statistics anxiety correlated highly but the comparison of different structural equation models showed that they had genuine and even antagonistic contributions to learning behaviors and performance in the examination. Surprisingly, mathematics anxiety was positively related to performance. It might be that students realized over the course of their first term that knowledge and skills in higher secondary education mathematics are not sufficient to be successful in statistics. Part of mathematics anxiety may then have strengthened positive extrinsic effort motivation by the intention to avoid failure and may have led to higher effort for the exam preparation. However, via statistics anxiety mathematics anxiety also had a negative contribution to performance. Statistics anxiety led to higher procrastination in

  1. The effects of noise over the complete space of diffusion tensor shape.

    Science.gov (United States)

    Gahm, Jin Kyu; Kindlmann, Gordon; Ennis, Daniel B

    2014-01-01

    Diffusion tensor magnetic resonance imaging (DT-MRI) is a technique used to quantify the microstructural organization of biological tissues. Multiple images are necessary to reconstruct the tensor data and each acquisition is subject to complex thermal noise. As such, measures of tensor invariants, which characterize components of tensor shape, derived from the tensor data will be biased from their true values. Previous work has examined this bias, but over a narrow range of tensor shape. Herein, we define the mathematics for constructing a tensor from tensor invariants, which permits an intuitive and principled means for building tensors with a complete range of tensor shape and salient microstructural properties. Thereafter, we use this development to evaluate by simulation the effects of noise on characterizing tensor shape over the complete space of tensor shape for three encoding schemes with different SNR and gradient directions. We also define a new framework for determining the distribution of the true values of tensor invariants given their measures, which provides guidance about the confidence the observer should have in the measures. Finally, we present the statistics of tensor invariant estimates over the complete space of tensor shape to demonstrate how the noise sensitivity of tensor invariants varies across the space of tensor shape as well as how the imaging protocol impacts measures of tensor invariants. Copyright © 2013 Elsevier B.V. All rights reserved.

  2. Child development at 5 years of age predicted mathematics ability and schooling outcomes in Malawian adolescents.

    Science.gov (United States)

    Gandhi, Mihir; Teivaanmaki, Tiina; Maleta, Kenneth; Duan, Xiaolian; Ashorn, Per; Cheung, Yin Bun

    2013-01-01

    This study aimed to examine the association between child development at 5 years of age and mathematics ability and schooling outcomes at 12 years of age in Malawian children. A prospective cohort study looking at 609 rural Malawian children. Outcome measures were percentage of correctly answered mathematics questions, highest school grade completed and number of times repeating school grades at 12 years of age. A child development summary score obtained at 5 years of age was the main exposure variable. Regression analyses were used to estimate the association and adjust for confounders. Sensitivity analysis was performed by handling losses to follow-up with multiple imputation (MI) method. The summary score was positively associated with percentage of correctly answered mathematics questions (p = 0.057; p = 0.031 MI) and with highest school grade completed (p = 0.096; p = 0.070 MI), and negatively associated with number of times repeating school grades (p = 0.834; p = 0.339 MI). Fine motor score at 5 years was independently associated with the mathematic score (p = 0.032; p = 0.011 MI). The association between child development and mathematics ability did not depend on school attendance. Child development at 5 years of age showed signs of positive association with mathematics ability and possibly with highest school grade completed at 12 years of age. © 2012 The Author(s)/Acta Paediatrica © 2012 Foundation Acta Paediatrica.

  3. Visual short term memory related brain activity predicts mathematical abilities.

    Science.gov (United States)

    Boulet-Craig, Aubrée; Robaey, Philippe; Lacourse, Karine; Jerbi, Karim; Oswald, Victor; Krajinovic, Maja; Laverdière, Caroline; Sinnett, Daniel; Jolicoeur, Pierre; Lippé, Sarah

    2017-07-01

    Previous research suggests visual short-term memory (VSTM) capacity and mathematical abilities are significantly related. Moreover, both processes activate similar brain regions within the parietal cortex, in particular, the intraparietal sulcus; however, it is still unclear whether the neuronal underpinnings of VSTM directly correlate with mathematical operation and reasoning abilities. The main objective was to investigate the association between parieto-occipital brain activity during the retention period of a VSTM task and performance in mathematics. The authors measured mathematical abilities and VSTM capacity as well as brain activity during memory maintenance using magnetoencephalography (MEG) in 19 healthy adult participants. Event-related magnetic fields (ERFs) were computed on the MEG data. Linear regressions were used to estimate the strength of the relation between VSTM related brain activity and mathematical abilities. The amplitude of parieto-occipital cerebral activity during the retention of visual information was related to performance in 2 standardized mathematical tasks: mathematical reasoning and calculation fluency. The findings show that brain activity during retention period of a VSTM task is associated with mathematical abilities. Contributions of VSTM processes to numerical cognition should be considered in cognitive interventions. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

  4. An Introduction to Equilibrium Thermodynamics: A Rational Approach to Its Teaching. Part 1: Notation and Mathematics.

    Science.gov (United States)

    Williams, Donald F.; Glasser, David

    1991-01-01

    Introduces and develops mathematical notation to assist undergraduate students in overcoming conceptual difficulties involving the underlying mathematics of state functions, which tend to be different from functions encountered by students in previous mathematical courses, because of the need to manipulate special types of partial derivatives and…

  5. A mathematical medley fifty easy pieces on mathematics

    CERN Document Server

    Szpiro, George G

    2010-01-01

    Szpiro's book provides a delightful, well-written, eclectic selection of mathematical tidbits that makes excellent airplane reading for anyone with an interest in mathematics, regardless of their mathematical background. Excellent gift material. -Keith Devlin, Stanford University, author of The Unfinished Game and The Language of Mathematics It is great to have collected in one volume the many varied, insightful and often surprising mathematical stories that George Szpiro has written in his mathematical columns for the newspapers through the years. -Marcus du Sautoy, Oxford University, author

  6. The language of mathematics telling mathematical tales

    CERN Document Server

    Barton, Bill

    2008-01-01

    Everyday mathematical ideas are expressed differently in different languages. This book probes those differences and explores their implications for mathematics education, arguing for alternatives to how we teach and learn mathematics.

  7. The students’ mathematical argumentation in geometry

    Science.gov (United States)

    Sukirwan; Darhim; Herman, T.; Prahmana, R. C. I.

    2017-12-01

    The main objective of this research is to analyze the student's mathematical argumentation when dealing with geometry. The method is used qualitative method with grounded theory to know how the students provide an explanation or an answer against claims so that the quality of the vernacular students will be drawn up with clear from how students compose a series of arguments. The results showed that there were still many students basically experiencing constraints in argumentation, but the quality of the reasoning appears to be a variation of the argument appeared, include: inductive, algebra, visual and perceptual. In addition, the starting point of the students composes a series of arguments generally starts from claims that arise in a matter. Proof of claim further builds upon the relationship between the characteristics of data with mathematical objects that appear in the acquired mathematical knowledge from previous students. Relationship spelled out in a series of statements and reasons which support the claims through the fourth argument.

  8. Mathematics Anxiety, Working Memory, and Mathematics Performance in Secondary-School Children.

    Science.gov (United States)

    Passolunghi, Maria C; Caviola, Sara; De Agostini, Ruggero; Perin, Chiara; Mammarella, Irene C

    2016-01-01

    Mathematics anxiety (MA) has been defined as "a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of math problems in a wide variety of ordinary life and academic situations." Previous studies have suggested that a notable proportion of children in primary and secondary school suffer from MA, which is negatively correlated with calculation skills. The processing efficiency and attentional control theories suggest that working memory (WM) also plays an important part in such anxious feelings. The present study aimed to analyze the academic achievement and cognitive profiles of students with high math anxiety (HMA) and low math anxiety (LMA). Specifically, 32 students with HMA and 34 with LMA matched for age, gender, generalized anxiety, and vocabulary attending sixth to eighth grades were selected from a larger sample. The two groups were tested on reading decoding, reading comprehension, mathematics achievement, and on verbal short-term memory and WM. Our findings showed that HMA students were weak in several measures of mathematics achievement, but not in reading and writing skills, and that students with HMA reported lower scores on short-term memory and WM performances (with associated difficulties in inhibiting irrelevant information) than children with LMA. In addition, a logistic regression showed that weaknesses in inhibitory control and fact retrieval were the strongest variables for classifying children as having HMA or LMA.

  9. Mathematics Anxiety, Working Memory and Mathematics Performance in Secondary-School Children

    Directory of Open Access Journals (Sweden)

    Maria Chiara ePassolunghi

    2016-02-01

    Full Text Available Mathematics anxiety (MA has been defined as a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of math problems in a wide variety of ordinary life and academic situations. Previous studies have suggested that a notable proportion of children in primary and secondary school suffer from MA, which is negatively correlated with calculation skills. The processing efficiency and attentional control theories suggest that working memory (WM also plays an important part in such anxious feelings.The present study aimed to analyze the academic achievement and cognitive profiles of students with high math anxiety (HMA and low math anxiety (LMA. Specifically, 32 students with HMA and 34 with LMA matched for age, gender, generalized anxiety, and vocabulary attending sixth to eighth grades were selected from a larger sample. The two groups were tested on reading decoding, reading comprehension, mathematics achievement, and on verbal short-term memory and WM. Our findings showed that HMA students were weak in several measures of mathematics achievement, but not in reading and writing skills, and that students with HMA reported lower scores on short-term memory and WM performances (with associated difficulties in inhibiting irrelevant information than children with LMA. In addition, a logistic regression showed that weaknesses in inhibitory control and fact retrieval were the strongest variables for classifying children as having HMA or LMA.

  10. Simple example of definitions of truth, validity, consistency, and completeness in quantum mechanics

    International Nuclear Information System (INIS)

    Benioff, P.

    1999-01-01

    Besides their use for efficient computation, quantum computers and quantum robots form a base for studying quantum systems that create valid physical theories using mathematics and physics. If quantum mechanics is universally applicable, then quantum mechanics must describe its own validation by these quantum systems. An essential part of this process is the development of a coherent theory of mathematics and quantum-mechanics together. It is expected that such a theory will include a coherent combination of mathematical logical concepts with quantum mechanics. That this might be possible is shown here by defining truth, validity, consistency, and completeness for a quantum-mechanical version of a simple (classical) expression enumeration machine described by Smullyan. Some of the expressions are chosen as sentences denoting the presence or absence of other expressions in the enumeration. Two of the sentences are self-referential. It is seen that, for an interpretation based on a Feynman path sum over expression paths, truth, consistency, and completeness for the quantum system have different properties than for the classical system. For instance, the truth of a sentence S is defined only on those paths containing S. It is undefined elsewhere. Also S and its negation can both be true provided they appear on separate paths. This satisfies the definition of consistency. The definitions of validity and completeness connect the dynamics of the system to the truth of the sentences. It is proved that validity implies consistency. It is seen that the requirements of validity and maximal completeness strongly restrict the allowable dynamics for the quantum system. Aspects of the existence of a valid, maximally complete dynamics are discussed. An exponentially efficient quantum computer is described that is also valid and complete for the set of sentences considered here. copyright 1999 The American Physical Society

  11. Mathematical Modelling Approach in Mathematics Education

    Science.gov (United States)

    Arseven, Ayla

    2015-01-01

    The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

  12. Mathematics Underground

    Science.gov (United States)

    Luther, Kenneth H.

    2012-01-01

    Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

  13. Mathematical bridges

    CERN Document Server

    Andreescu, Titu; Tetiva, Marian

    2017-01-01

    Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...

  14. Exploring mathematics anxiety and attitude: Mathematics students' experiences

    Science.gov (United States)

    Sahri, Nurul Ashikin; Kamaruzaman, Wan Nur Farahdalila Wan; Jamil, Jastini Mohd.; Shaharanee, Izwan Nizal Mohd.

    2017-11-01

    A quantitative and correlational, survey methods were used to investigate the relationships among mathematical anxiety and attitude toward student's mathematics performance. Participants were 100 students volunteer to enroll in undergraduate Industrial Statistics, Decision Sciences and Business Mathematics at one of northern university in Malaysia. Survey data consisted of demographic items and Likert scale items. The collected data was analyzed by using the idea of correlation and regression analysis. The results indicated that there was a significant positive relationship between students' attitude and mathematics anxiety. Results also indicated that a substantial positive effect of students' attitude and mathematics anxiety in students' achievement. Further study can be conducted on how mathematical anxiety and attitude toward mathematics affects can be used to predict the students' performance in the class.

  15. A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers

    Science.gov (United States)

    Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa

    2012-01-01

    This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…

  16. Executive functioning predicts reading, mathematics, and theory of mind during the elementary years.

    Science.gov (United States)

    Cantin, Rachelle H; Gnaedinger, Emily K; Gallaway, Kristin C; Hesson-McInnis, Matthew S; Hund, Alycia M

    2016-06-01

    The goal of this study was to specify how executive functioning components predict reading, mathematics, and theory of mind performance during the elementary years. A sample of 93 7- to 10-year-old children completed measures of working memory, inhibition, flexibility, reading, mathematics, and theory of mind. Path analysis revealed that all three executive functioning components (working memory, inhibition, and flexibility) mediated age differences in reading comprehension, whereas age predicted mathematics and theory of mind directly. In addition, reading mediated the influence of executive functioning components on mathematics and theory of mind, except that flexibility also predicted mathematics directly. These findings provide important details about the development of executive functioning, reading, mathematics, and theory of mind during the elementary years. Copyright © 2016 Elsevier Inc. All rights reserved.

  17. Logic and discrete mathematics a concise introduction : solutions manual

    CERN Document Server

    Conradie, Willem; Robinson, Claudette

    2015-01-01

    Solutions manual to accompany Logic and Discrete Mathematics: A Concise Introduction This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in this accompanying solutions manual.

  18. On Mathematical Understanding: Perspectives of Experienced Chinese Mathematics Teachers

    Science.gov (United States)

    Cai, Jinfa; Ding, Meixia

    2017-01-01

    Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers' views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result…

  19. Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics

    Science.gov (United States)

    Wang, Youjun

    2009-01-01

    In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…

  20. Theoretical Mathematics

    Science.gov (United States)

    Stöltzner, Michael

    Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.

  1. Exploring Differential Effects of Mathematics Courses on Mathematics Achievement

    Science.gov (United States)

    Ma, Xin; McIntyre, Laureen J.

    2005-01-01

    Using data from the Longitudinal Study of Mathematics Participation (N = 1,518 students from 34 schools), we investigated the effects of pure and applied mathematics courses on mathematics achievement, controlling for prior mathematics achievement. Results of multilevel modelling showed that the effects of pure mathematics were significant after…

  2. Mathematics Curriculum, the Philosophy of Mathematics and its ...

    African Journals Online (AJOL)

    It is my observation that the current school mathematics curriculum in Ethiopia is not producing competent mathematics students. Many mathematicians in Ethiopia and other part of the world have often expressed grief that the majority of students do not understand mathematical concepts, or do not see why mathematical ...

  3. Mathematics, the Computer, and the Impact on Mathematics Education.

    Science.gov (United States)

    Tooke, D. James

    2001-01-01

    Discusses the connection between mathematics and the computer; mathematics curriculum; mathematics instruction, including teachers learning to use computers; and the impact of the computer on learning mathematics. (LRW)

  4. Finite Mathematics and Discrete Mathematics: Is There a Difference?

    Science.gov (United States)

    Johnson, Marvin L.

    Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

  5. Using Mental Imagery Processes for Teaching and Research in Mathematics and Computer Science

    Science.gov (United States)

    Arnoux, Pierre; Finkel, Alain

    2010-01-01

    The role of mental representations in mathematics and computer science (for teaching or research) is often downplayed or even completely ignored. Using an ongoing work on the subject, we argue for a more systematic study and use of mental representations, to get an intuition of mathematical concepts, and also to understand and build proofs. We…

  6. Underprepared Students' Performance on Algebra in a Double-Period High School Mathematics Program

    Science.gov (United States)

    Martinez, Mara V.; Bragelman, John; Stoelinga, Timothy

    2016-01-01

    The primary goal of the Intensified Algebra I (IA) program is to enable mathematically underprepared students to successfully complete Algebra I in 9th grade and stay on track to meet increasingly rigorous high school mathematics graduation requirements. The program was designed to bring a range of both cognitive and non-cognitive supports to bear…

  7. Tools of the trade introduction to advanced mathematics

    CERN Document Server

    Sally, Jr, Paul J

    2008-01-01

    This book provides a transition from the formula-full aspects of the beginning study of college level mathematics to the rich and creative world of more advanced topics. It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics. Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such

  8. Mathematical Intelligence and Mathematical Creativity: A Causal Relationship

    Science.gov (United States)

    Tyagi, Tarun Kumar

    2017-01-01

    This study investigated the causal relationship between mathematical creativity and mathematical intelligence. Four hundred thirty-nine 8th-grade students, age ranged from 11 to 14 years, were included in the sample of this study by random cluster technique on which mathematical creativity and Hindi adaptation of mathematical intelligence test…

  9. Number line estimation strategies in children with mathematical learning difficulties measured by eye tracking

    NARCIS (Netherlands)

    van 't Noordende, Jaccoline E|info:eu-repo/dai/nl/369862422; van Hoogmoed, Anne H|info:eu-repo/dai/nl/314839496; Schot, Willemijn D; Kroesbergen, Evelyn H|info:eu-repo/dai/nl/241607949

    INTRODUCTION: Number line estimation is one of the skills related to mathematical performance. Previous research has shown that eye tracking can be used to identify differences in the estimation strategies children with dyscalculia and children with typical mathematical development use on number

  10. Number line estimation strategies in children with mathematical learning difficulties measured by eye tracking

    NARCIS (Netherlands)

    van’t Noordende, Jaccoline E.; van Hoogmoed, Anne H.; Schot, Willemijn D.; Kroesbergen, Evelyn H.

    2016-01-01

    Introduction: Number line estimation is one of the skills related to mathematical performance. Previous research has shown that eye tracking can be used to identify differences in the estimation strategies children with dyscalculia and children with typical mathematical development use on number

  11. Number sense and mathematics: Which, when and how?

    Science.gov (United States)

    Tosto, Maria G; Petrill, Stephen A; Malykh, Sergey; Malki, Karim; Haworth, Claire M A; Mazzocco, Michele M M; Thompson, Lee; Opfer, John; Bogdanova, Olga Y; Kovas, Yulia

    2017-10-01

    Individual differences in number sense correlate with mathematical ability and performance, although the presence and strength of this relationship differs across studies. Inconsistencies in the literature may stem from heterogeneity of number sense and mathematical ability constructs. Sample characteristics may also play a role as changes in the relationship between number sense and mathematics may differ across development and cultural contexts. In this study, 4,984 16-year-old students were assessed on estimation ability, one aspect of number sense. Estimation was measured using 2 different tasks: number line and dot-comparison. Using cognitive and achievement data previously collected from these students at ages 7, 9, 10, 12, and 14, the study explored for which of the measures and when in development these links are observed, and how strong these links are and how much these links are moderated by other cognitive abilities. The 2 number sense measures correlated modestly with each other (r = .22), but moderately with mathematics at age 16. Both measures were also associated with earlier mathematics; but this association was uneven across development and was moderated by other cognitive abilities. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

  12. The complete cosmicomics

    CERN Document Server

    Calvino, Italo

    2014-01-01

    The definitive edition of Calvino’s cosmicomics, bringing together all of these enchanting stories—including some never before translated—in one volume for the first time. In Italo Calvino’s cosmicomics, primordial beings cavort on the nearby surface of the moon, play marbles with atoms, and bear ecstatic witness to Earth’s first dawn. Exploring natural phenomena and the origins of the universe, these beloved tales relate complex scientific concepts to our common sensory, emotional, human world. Now, The Complete Cosmicomics brings together all of the cosmicomic stories for the first time. Containing works previously published in Cosmicomics, t zero, and Numbers in the Dark, this single volume also includes seven previously uncollected stories, four of which have never been published in translation in the United States. This “complete and definitive collection” (Evening Standard) reconfirms the cosmicomics as a crowning literary achievement and makes them available to new generations of reader...

  13. Mathematics Instruction for Students with Emotional and Behavioral Disorders: A Best-Evidence Synthesis

    Science.gov (United States)

    Ralston, Nicole C.; Benner, Gregory J.; Tsai, Shu-Fei; Riccomini, Paul J.; Nelson, J. Ron

    2014-01-01

    The authors report findings of a best-evidence synthesis of the effects of mathematics instruction on the mathematics skills of students with emotional and behavioral disorders. The goal of the synthesis was to extend previous research by (a) detailing independent variables, instructional components, and outcome measures for each study; (b)…

  14. Engineering Physics and Mathematics Division progress report for period ending December 31, 1994

    International Nuclear Information System (INIS)

    Sincovec, R.F.

    1995-07-01

    This report provides a record of the research activities of the Engineering Physics and Mathematics Division for the period January 1, 1993, through December 31, 1994. This report is the final archival record of the EPM Division. On October 1, 1994, ORELA was transferred to Physics Division and on January 1, 1995, the Engineering Physics and Mathematics Division and the Computer Applications Division reorganized to form the Computer Science and Mathematics Division and the Computational Physics and Engineering Division. Earlier reports in this series are identified on the previous pages, along with the progress reports describing ORNL's research in the mathematical sciences prior to 1984 when those activities moved into the Engineering Physics and Mathematics Division

  15. Engineering Physics and Mathematics Division progress report for period ending December 31, 1994

    Energy Technology Data Exchange (ETDEWEB)

    Sincovec, R.F.

    1995-07-01

    This report provides a record of the research activities of the Engineering Physics and Mathematics Division for the period January 1, 1993, through December 31, 1994. This report is the final archival record of the EPM Division. On October 1, 1994, ORELA was transferred to Physics Division and on January 1, 1995, the Engineering Physics and Mathematics Division and the Computer Applications Division reorganized to form the Computer Science and Mathematics Division and the Computational Physics and Engineering Division. Earlier reports in this series are identified on the previous pages, along with the progress reports describing ORNL`s research in the mathematical sciences prior to 1984 when those activities moved into the Engineering Physics and Mathematics Division.

  16. Learning Mathematics for Teaching Mathematics: Non-Specialist Teachers' Mathematics Teacher Identity

    Science.gov (United States)

    Crisan, Cosette; Rodd, Melissa

    2017-01-01

    A non-specialist teacher of mathematics is a school teacher who qualified to teach in a subject other than mathematics yet teaches mathematics to students in secondary school. There is an emerging interest internationally in this population, a brief report of which is given in the paper. Because of concerns about the quality of non-specialists'…

  17. Crossroads in the History of Mathematics and Mathematics Education. The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education

    Science.gov (United States)

    Sriraman, Bharath, Ed.

    2012-01-01

    The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at…

  18. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2011-01-01

    The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

  19. Preoperative screening: value of previous tests.

    Science.gov (United States)

    Macpherson, D S; Snow, R; Lofgren, R P

    1990-12-15

    To determine the frequency of tests done in the year before elective surgery that might substitute for preoperative screening tests and to determine the frequency of test results that change from a normal value to a value likely to alter perioperative management. Retrospective cohort analysis of computerized laboratory data (complete blood count, sodium, potassium, and creatinine levels, prothrombin time, and partial thromboplastin time). Urban tertiary care Veterans Affairs Hospital. Consecutive sample of 1109 patients who had elective surgery in 1988. At admission, 7549 preoperative tests were done, 47% of which duplicated tests performed in the previous year. Of 3096 previous results that were normal as defined by hospital reference range and done closest to the time of but before admission (median interval, 2 months), 13 (0.4%; 95% CI, 0.2% to 0.7%), repeat values were outside a range considered acceptable for surgery. Most of the abnormalities were predictable from the patient's history, and most were not noted in the medical record. Of 461 previous tests that were abnormal, 78 (17%; CI, 13% to 20%) repeat values at admission were outside a range considered acceptable for surgery (P less than 0.001, frequency of clinically important abnormalities of patients with normal previous results with those with abnormal previous results). Physicians evaluating patients preoperatively could safely substitute the previous test results analyzed in this study for preoperative screening tests if the previous tests are normal and no obvious indication for retesting is present.

  20. Mathematical Literacy: A new literacy or a new mathematics?

    Directory of Open Access Journals (Sweden)

    Renuka Vithal

    2006-10-01

    Full Text Available Mathematical Literacy is a ‘hot’ topic at present in most countries, whether it is referred to by that name, or in some cases as Numeracy, or Quantitative Literacy, or Matheracy, or as some part of Ethnomathematics, or related to Mathematics in Society. Questions continue to be asked about what is meant by mathematics in any concept of Mathematical Literacy and the use of the very word ‘Literacy’ in its association with Mathematics has been challenged. Its importance, however, lies in changing our perspective on mathematics teaching, away from the elitism so often associated with much mathematics education, and towards a more equitable, accessible and genuinely educational ideal.

  1. The Relationship between Handedness and Mathematics Is Non-linear and Is Moderated by Gender, Age, and Type of Task

    Science.gov (United States)

    Sala, Giovanni; Signorelli, Michela; Barsuola, Giulia; Bolognese, Martina; Gobet, Fernand

    2017-01-01

    The relationship between handedness and mathematical ability is still highly controversial. While some researchers have claimed that left-handers are gifted in mathematics and strong right-handers perform the worst in mathematical tasks, others have more recently proposed that mixed-handers are the most disadvantaged group. However, the studies in the field differ with regard to the ages and the gender of the participants, and the type of mathematical ability assessed. To disentangle these discrepancies, we conducted five studies in several Italian schools (total participants: N = 2,314), involving students of different ages (six to seventeen) and a range of mathematical tasks (e.g., arithmetic and reasoning). The results show that (a) linear and quadratic functions are insufficient for capturing the link between handedness and mathematical ability; (b) the percentage of variance in mathematics scores explained by handedness was larger than in previous studies (between 3 and 10% vs. 1%), and (c) the effect of handedness on mathematical ability depended on age, type of mathematical tasks, and gender. In accordance with previous research, handedness does represent a correlate of achievement in mathematics, but the shape of this relationship is more complicated than has been argued so far. PMID:28649210

  2. The Relationship of Mathematics Anxiety and Mathematical Knowledge to the Learning of Mathematical Pedagogy by Preservice Elementary Teachers.

    Science.gov (United States)

    Battista, Michael T.

    1986-01-01

    Examined how preservice elementary teachers' (N=38) mathematical knowledge and mathematics anxiety affect their success in a mathematics methods course. Also examined the hypothesis that a mathematics methods course can reduce the mathematics anxiety of these teachers. One finding is that mathematics anxiety does not inhibit their learning of…

  3. Mathematics education for social justice

    Science.gov (United States)

    Suhendra

    2016-02-01

    Mathematics often perceived as a difficult subject with many students failing to understand why they learn mathematics. This situation has been further aggravated by the teaching and learning processes used, which is mechanistic without considering students' needs. The learning of mathematics tends to be just a compulsory subject, in which all students have to attend its classes. Social justice framework facilitates individuals or groups as a whole and provides equitable approaches to achieving equitable outcomes by recognising disadvantage. Applying social justice principles in educational context is related to how the teachers treat their students, dictates that all students the right to equal treatment regardless of their background and completed with applying social justice issues integrated with the content of the subject in order to internalise the principles of social justice simultaneously the concepts of the subject. The study examined the usefulness of implementing the social justice framework as a means of improving the quality of mathematics teaching in Indonesia involved four teacher-participants and their mathematics classes. The study used action research as the research methodology in which the teachers implemented and evaluated their use of social justice framework in their teaching. The data were collected using multiple research methods while analysis and interpretation of the data were carried out throughout the study. The findings of the study indicated that there were a number of challengesrelated to the implementation of the social justice framework. The findings also indicated that, the teachers were provided with a comprehensive guide that they could draw on to make decisions about how they could improve their lessons. The interactions among students and between the teachers and the students improved, they became more involved in teaching and learning process. Using social justice framework helped the teachers to make mathematics more

  4. Beyond the Given: Stretching Mathematical Thinking through Journaling

    Science.gov (United States)

    Hamdan, May

    2017-01-01

    This paper reflects on a teaching experiment and presents details of a pedagogical technique where students periodically write down their clearest interpretation of the conditions imposed on various discrete mathematical subjects they are learning in class. Through iterations, students generate a more complete understanding of the material, one…

  5. The Empathizing-Systemizing Theory, Social Abilities, and Mathematical Achievement in Children.

    Science.gov (United States)

    Escovar, Emily; Rosenberg-Lee, Miriam; Uddin, Lucina Q; Menon, Vinod

    2016-03-14

    The Empathizing-Systemizing (E-S) theory describes a profile of traits that have been linked to autism spectrum disorders, and are thought to encompass a continuum that includes typically developing (TD) individuals. Although systemizing is hypothesized to be related to mathematical abilities, empirical support for this relationship is lacking. We examine the link between empathizing and systemizing tendencies and mathematical achievement in 112 TD children (57 girls) to elucidate how socio-cognitive constructs influence early development of mathematical skills. Assessment of mathematical achievement included standardized tests designed to examine calculation skills and conceptual mathematical reasoning. Empathizing and systemizing were assessed using the Combined Empathy Quotient-Child (EQ-C) and Systemizing Quotient-Child (SQ-C). Contrary to our hypothesis, we found that mathematical achievement was not related to systemizing or the discrepancy between systemizing and empathizing. Surprisingly, children with higher empathy demonstrated lower calculation skills. Further analysis using the Social Responsiveness Scale (SRS) revealed that the relationship between EQ-C and mathematical achievement was mediated by social ability rather than autistic behaviors. Finally, social awareness was found to play a differential role in mediating the relationship between EQ-C and mathematical achievement in girls. These results identify empathy, and social skills more generally, as previously unknown predictors of mathematical achievement.

  6. Completion pancreatectomy and islet cell autotransplantation as salvage therapy for patients failing previous operative interventions for chronic pancreatitis.

    Science.gov (United States)

    Wilson, Gregory C; Sutton, Jeffrey M; Smith, Milton T; Schmulewitz, Nathan; Salehi, Marzieh; Choe, Kyuran A; Levinsky, Nick C; Brunner, John E; Abbott, Daniel E; Sussman, Jeffrey J; Edwards, Michael J; Ahmad, Syed A

    2015-10-01

    Traditional decompressive and/or pancreatic resection procedures have been the cornerstone of operative therapy for refractory abdominal pain secondary to chronic pancreatitis. Management of patients that fail these traditional interventions represents a clinical dilemma. Salvage therapy with completion pancreatectomy and islet cell autotransplantation (CPIAT) is an emerging treatment option for this patient population; however, outcomes after this procedure have not been well-studied. All patients undergoing CPIAT after previous decompressive and/or pancreatic resection for the treatment of chronic pancreatitis at our institution were identified for inclusion in this single-center observational study. Study end points included islet yield, narcotic requirements, glycemic control, and quality of life (QOL). QOL was assessed using the Short Form (SF)-36 health questionnaire. Sixty-four patients underwent CPIAT as salvage therapy. The median age at time of CPIAT was 38 years (interquartile range [IQR], 14.7-65.4). The most common etiology of chronic pancreatitis was idiopathic pancreatitis (66%; n = 42) followed by genetically linked pancreatitis (9%; n = 6) and alcoholic pancreatitis (8%; n = 5). All of these patients had previously undergone prior limited pancreatic resection or decompressive procedure. The majority of patients (50%; n = 32) underwent prior pancreaticoduodenectomy, whereas the remainder had undergone distal pancreatectomy (17%; n = 11), Frey (13%; n = 8), Puestow (13%; n = 8), or Berne (8%; n = 5) procedures. Median time from initial surgical intervention to CPIAT was 28.1 months (IQR, 13.6-43.0). All of these patients underwent a successful CPIAT. Mean operative time was 502.2 minutes with average hospital duration of stay of 13 days. Islet cell isolation was feasible despite previous procedures with a mean islet yield of 331,304 islet cell equivalents, which totaled an islet cell autotransplantation of 4,737 ± 492 IEQ/kg body weight. Median

  7. Introduction of the Thematic Issue on the Interplay of Physics and Mathematics

    DEFF Research Database (Denmark)

    Avelar Sotomaior Karam, Ricardo

    2015-01-01

    for the students. They have a hard time understanding where mathematical concepts come from and why physics has little to do with their experiential world. This problem demands a systematic research effort from experts in different fields, especially the ones who aim at informing educational practices......Since their beginnings Physics (natural philosophy) and mathematics have been deeply interrelated, and this mutual influence has played an essential role in both their developments. However, the image typically found in educational contexts is often quite different. In physics education......, it is usual to find mathematics being seen as a mere tool to describe and calculate, whereas in mathematics education, physics is commonly viewed as a possible context for the application of mathematical concepts that were previously defined abstractly. This dichotomy creates significant learning problems...

  8. Mathematical modelling

    DEFF Research Database (Denmark)

    Blomhøj, Morten

    2004-01-01

    Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...

  9. Investigating students' perceptions of graduate learning outcomes in mathematics

    Science.gov (United States)

    King, Deborah; Varsavsky, Cristina; Belward, Shaun; Matthews, Kelly

    2017-11-01

    The purpose of this study is to explore the perceptions mathematics students have of the knowledge and skills they develop throughout their programme of study. It addresses current concerns about the employability of mathematics graduates by contributing much needed insight into how degree programmes are developing broader learning outcomes for students majoring in mathematics. Specifically, the study asked students who were close to completing a mathematics major (n = 144) to indicate the extent to which opportunities to develop mathematical knowledge along with more transferable skills (communication to experts and non-experts, writing, working in teams and thinking ethically) were included and assessed in their major. Their perceptions were compared to the importance they assign to each of these outcomes, their own assessment of improvement during the programme and their confidence in applying these outcomes. Overall, the findings reveal a pattern of high levels of students' agreement that these outcomes are important, but evidence a startling gap when compared to students' perceptions of the extent to which many of these - communication, writing, teamwork and ethical thinking - are actually included and assessed in the curriculum, and their confidence in using such learning.

  10. Discrete Mathematics and the Secondary Mathematics Curriculum.

    Science.gov (United States)

    Dossey, John

    Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…

  11. Internal consistency reliability and validity of the Arabic translation of the Mathematics Teaching Efficacy Beliefs Instrument.

    Science.gov (United States)

    Alkhateeb, Haitham M

    2004-06-01

    The Arabic translation of the Mathematics Teaching Efficacy Beliefs was completed by 144 undergraduate students (M age=20.6) in Jordan. The findings support the internal reliability of the Arabic translation of the Mathematics Teaching Efficacy Beliefs as well as its construct validity.

  12. Reoperative sentinel lymph node biopsy after previous mastectomy.

    Science.gov (United States)

    Karam, Amer; Stempel, Michelle; Cody, Hiram S; Port, Elisa R

    2008-10-01

    Sentinel lymph node (SLN) biopsy is the standard of care for axillary staging in breast cancer, but many clinical scenarios questioning the validity of SLN biopsy remain. Here we describe our experience with reoperative-SLN (re-SLN) biopsy after previous mastectomy. Review of the SLN database from September 1996 to December 2007 yielded 20 procedures done in the setting of previous mastectomy. SLN biopsy was performed using radioisotope with or without blue dye injection superior to the mastectomy incision, in the skin flap in all patients. In 17 of 20 patients (85%), re-SLN biopsy was performed for local or regional recurrence after mastectomy. Re-SLN biopsy was successful in 13 of 20 patients (65%) after previous mastectomy. Of the 13 patients, 2 had positive re-SLN, and completion axillary dissection was performed, with 1 having additional positive nodes. In the 11 patients with negative re-SLN, 2 patients underwent completion axillary dissection demonstrating additional negative nodes. One patient with a negative re-SLN experienced chest wall recurrence combined with axillary recurrence 11 months after re-SLN biopsy. All others remained free of local or axillary recurrence. Re-SLN biopsy was unsuccessful in 7 of 20 patients (35%). In three of seven patients, axillary dissection was performed, yielding positive nodes in two of the three. The remaining four of seven patients all had previous modified radical mastectomy, so underwent no additional axillary surgery. In this small series, re-SLN was successful after previous mastectomy, and this procedure may play some role when axillary staging is warranted after mastectomy.

  13. Bringing Reality into Calculus Classrooms: Mathematizing a Real-life Problem Simulated in a Virtual Environment

    Directory of Open Access Journals (Sweden)

    Olga V. Shipulina

    2013-01-01

    Full Text Available The study explores how students, who had completed the AP calculus course, mathematized the optimal navigation real-life problem simulated in the Second Life Virtual Environment. The particular research interest was to investigate whether/how students’ empirical activity in VE influences the way of their mathematizing.

  14. The universe in zero words the story of mathematics as told through equations

    CERN Document Server

    Mackenzie, Dana

    2012-01-01

    Most popular books about science, and even about mathematics, tiptoe around equations as if they were something to be hidden from the reader's tender eyes. Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics--the universal language of science--keep the masterpieces of the subject hidden behind a veil? The Universe in Zero Words tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society--from the elementary

  15. Cross Coursing in Mathematics: Physical Modelling in Differential Equations Crossing to Discrete Dynamical Systems

    Science.gov (United States)

    Winkel, Brian

    2012-01-01

    We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course. This situation crosses falling body modelling in an upper level differential equations course into a modest discrete dynamical systems unit of a first-year mathematics course. (Contains 1 figure.)

  16. Meeting in mathematics

    DEFF Research Database (Denmark)

    Mogensen, Arne; Georgiev, Vladimir; Ulovec, Andreas

    To encourage many more young people to appreciate the real nature and spirit of mathematics and possibly to be enrolled in mathematics study it is important to involve them in doing mathematics (not just learning about mathematics). This goal could be achieved if mathematics teachers are prepared...... to identify and work with mathematically gifted students (without loosing the rest). The book offers chapters on gifted students, mathematical competences and other issues....

  17. Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

    Science.gov (United States)

    Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

    2015-01-01

    Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806

  18. International note: Are Emirati parents' attitudes toward mathematics linked to their adolescent children's attitudes toward mathematics and mathematics achievement?

    Science.gov (United States)

    Areepattamannil, Shaljan; Khine, Myint Swe; Melkonian, Michael; Welch, Anita G; Al Nuaimi, Samira Ahmed; Rashad, Fatimah F

    2015-10-01

    Drawing on data from the 2012 Program for International Student Assessment (PISA) and employing multilevel modeling as an analytic strategy, this study examined the relations of adolescent children's perceptions of their parents' attitudes towards mathematics to their own attitudes towards mathematics and mathematics achievement among a sample of 5116 adolescents from 384 schools in the United Arab Emirates. The results of this cross-sectional study revealed that adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children not only to study but also for their career tended to report higher levels of intrinsic and instrumental motivation to learn mathematics, mathematics self-concept and self-efficacy, and mathematics work ethic. Moreover, adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children's career tended to report positive intentions and behaviors toward mathematics. However, adolescents who perceived that their parents considered mathematics was important for their children's career tended to report higher levels of mathematics anxiety. Finally, adolescents who perceived that their parents considered mathematics was important for their children to study performed significantly better on the mathematics assessment than did their peers whose parents disregarded the importance of learning mathematics. Copyright © 2015 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.

  19. Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

    Directory of Open Access Journals (Sweden)

    Yinghui Lai

    Full Text Available Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA and mathematical metacognition on word problem solving (WPS. We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56 with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA, typical achieving (TA, low achieving (LA, and mathematical learning difficulty (MLD. Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA than the TA and HA children, but not in mathematical evaluation anxiety (MEA. MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

  20. Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

    Science.gov (United States)

    Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

    2015-01-01

    Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

  1. On the Nature and Role of Peer Review in Mathematics.

    Science.gov (United States)

    Andersen, Line Edslev

    2017-01-01

    For the past three decades, peer review practices have received much attention in the literature. But although this literature covers many research fields, only one previous systematic study has been devoted to the practice of peer review in mathematics, namely a study by Geist, Löwe, and Van Kerkhove from 2010. This lack of attention may be due to a view that peer review in mathematics is more reliable, and therefore less interesting as an object of study, than peer review in other fields. In fact, Geist, Löwe, and Van Kerkhove argue that peer review in mathematics is relatively reliable. At the same time, peer review in mathematics differs from peer review in most, if not all, other fields in that papers submitted to mathematical journals are usually only reviewed by a single referee. Furthermore, recent empirical studies indicate that the referees do not check the papers line by line. I argue that, in spite of this, mathematical practice in general and refereeing practices in particular are such that the common practice of mathematical journals of using just one referee is justified from the point of view of proof validity assessment. The argument is based on interviews I conducted with seven mathematicians.

  2. Mathematics without boundaries surveys in pure mathematics

    CERN Document Server

    Pardalos, Panos

    2014-01-01

    The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the  latest information.

  3. Pre-Service Teachers' Mathematics Self-Efficacy and Mathematics Teaching Self-Efficacy

    Science.gov (United States)

    Zuya, Habila Elisha; Kwalat, Simon Kevin; Attah, Bala Galle

    2016-01-01

    Pre-service mathematics teachers' mathematics self-efficacy and mathematics teaching self-efficacy were investigated in this study. The purpose was to determine the confidence levels of their self-efficacy in mathematics and mathematics teaching. Also, the study was aimed at finding whether their mathematics self-efficacy and teaching…

  4. Mathematics Teachers' Perceptions of Their Students' Mathematical Competence: Relations to Mathematics Achievement, Affect, and Engagement in Singapore and Australia

    Science.gov (United States)

    Areepattamannil, Shaljan; Kaur, Berinderjeet

    2013-01-01

    This study, drawing on data from the Trends in International Mathematics and Science Study (TIMSS) 2011, examined whether mathematics teachers' perceptions of their students' mathematical competence were related to mathematics achievement, affect toward mathematics, and engagement in mathematics lessons among Grade 8 students in Singapore and…

  5. Influence of mathematical models in design of PV-Diesel systems

    International Nuclear Information System (INIS)

    Dufo-Lopez, Rodolfo; Bernal-Agustin, Jose L.

    2008-01-01

    This paper presents a study of the influence of mathematical models in the optimal design of PV-Diesel systems. For this purpose, a design tool developed by the authors, which allows obtaining the most cost effective design of a PV-Diesel system through the genetic algorithm technique, has been used. The mathematical models of some elements of the hybrid system have been improved in comparison to those usually employed in hybrid systems design programs. Furthermore, a more complete general control strategy has been developed, one that also takes into account more characteristics than those usually considered in this kind of design. Several designs have been made, evaluating the effect on the results of the different mathematical models and the novel strategy that can be considered

  6. Mathematics education a spectrum of work in mathematical sciences departments

    CERN Document Server

    Hsu, Pao-sheng; Pollatsek, Harriet

    2016-01-01

    Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences. This book is intended to inform the readership of the breadth of the work and to encourage discussion of its val...

  7. Developing teaching material based on realistic mathematics andoriented to the mathematical reasoning and mathematical communication

    Directory of Open Access Journals (Sweden)

    Fitria Habsah

    2017-05-01

    Full Text Available This research aims to produce mathematics textbook for grade VII junior high school students based on realistic mathematics and oriented to the mathematical reasoning and mathematical communication. The quality is determined based on Nieveen criteria, including validity, practicality, and effectiveness.This study was a research and development and used Borg & Gall model. The subject of this research were the students of SMPN 2 Pujon-Kabupaten Malang, that is 30 students in an experimental class (using the developed textbook and 29 students in a control class (using BSE book from the government. The teaching material was categorized valid if the expert's judgment at least is categorized as “good”. The teaching material was categorized practical if both of teachers and students assessment at least categorized as “good”. The teaching material was categorized effectively if minimum 75% of student scores at least is categorized as “good” for the mathematical reasoning test and mathematical communication test. This research resulted in a valid, practical, and effective teaching material. The resulted of the validation show that material teaching is valid. The resulted of teachers and students assessment show that the product is practical. The tests scores show that the product is effective. Percentage of students who categorized at least as “good” is 83,33% for the mathematical reasoning and 86,67% for the mathematical communication. The resulted of statistic test shows that the product more effective than the BSE book from the government in terms of mathematical reasoning and mathematical communication.

  8. Mathematics and Science Learning Opportunities in Preschool Classrooms

    Science.gov (United States)

    Piasta, Shayne B.; Pelatti, Christina Yeager; Miller, Heather Lynnine

    2014-01-01

    Research findings The present study observed and coded instruction in 65 preschool classrooms to examine (a) overall amounts and (b) types of mathematics and science learning opportunities experienced by preschool children as well as (c) the extent to which these opportunities were associated with classroom and program characteristics. Results indicated that children were afforded an average of 24 and 26 minutes of mathematics and science learning opportunities, respectively, corresponding to spending approximately 25% of total instructional time in each domain. Considerable variability existed, however, in the amounts and types of mathematics and science opportunities provided to children in their classrooms; to some extent, this variability was associated with teachers’ years of experience, teachers’ levels of education, and the socioeconomic status of children served in the program. Practice/policy Although results suggest greater integration of mathematics and science in preschool classrooms than previously established, there was considerable diversity in the amounts and types of learning opportunities provided in preschool classrooms. Affording mathematics and science experiences to all preschool children, as outlined in professional and state standards, may require additional professional development aimed at increasing preschool teachers’ understanding and implementation of learning opportunities in these two domains in their classrooms. PMID:25489205

  9. Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

    Science.gov (United States)

    Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

    2014-01-01

    Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

  10. CULTUROLOGICAL APPROACH AS METHODOLOGICAL BASIS OF MATHEMATICAL EDUCATION

    Directory of Open Access Journals (Sweden)

    Ye. A. Perminov

    2017-01-01

    Full Text Available Introduction. Today, in the era of a mathematization of science and total expansion of digital technologies, mass mathematical education becomes a necessary part of culture of every person. However, there are some serious obstacles to formation and development of general mathematical culture: insufficient understanding of its importance by society and the state; fragmentary-clipconsciousness, emerging among representatives of the younger generation under the influence of the Internet, and preventing formation of a complete picture of the modern world; traditional system of disjointed subjects and courses in school, secondary vocational and high school mathematics education; non-cognitive (automatic transferring of the approaches, principles, technologies and techniques into training which are not specific in order to master a course. Development of sociological, axiological and especially culturological aspects of mathematical methodology is required for the solution of the urgent problems of methodology in mathematical education.The aim of the publication is to discuss methodological aspects of culturological approach realization in mathematical education.Methodology and research methods. The theoretical scientific methods of the present article involve analysis and synthesis of the content of philosophical, mathematical, pedagogical, methodological literature and normative documents; comparative, culturological and logical types of analysis of mathematical education; systematic, competence-based, practice-oriented and personal-activity metho-dological approaches were used to understand the concept of mathematical education.Results and scientific novelty. The practicability and leading role of culturological approach to promoting mathematical knowledge is proved from historical, philosophical and pedagogical positions. It is stated that objective conceptualization of progressive ideas and new methods of mathematical science and mathematical

  11. Evidence for shared genetic risk between ADHD symptoms and reduced mathematics ability: a twin study.

    Science.gov (United States)

    Greven, Corina U; Kovas, Yulia; Willcutt, Erik G; Petrill, Stephen A; Plomin, Robert

    2014-01-01

    Attention-deficit/hyperactivity disorder (ADHD) symptoms and mathematics ability are associated, but little is known about the genetic and environmental influences underlying this association. Data came from more than 6,000 twelve-year-old twin pairs from the UK population-representative Twins Early Development Study. Parents rated each twin's behaviour using a DSM-IV-based 18-item questionnaire of inattentive and hyperactive-impulsive ADHD symptoms. Mathematics tests based on the UK National Curriculum were completed by each twin. The twins also completed standardised tests of reading and general cognitive ability. Multivariate twin model fitting was applied. Inattentive and hyperactive-impulsive ADHD symptoms were highly heritable (67% and 73% respectively). Mathematics ability was moderately heritable (46%). Mathematics ability and inattentiveness showed a significantly greater phenotypic correlation (r(p) = -.26) and genetic correlation (r(A) = -.41) than mathematics ability and hyperactivity-impulsivity (r(p) = -.18; r(A) = -.22). The genetic correlation between inattentiveness and mathematics ability was largely independent from hyperactivity-impulsivity, and was only partially accounted for by genetic influences related to reading and general cognitive ability. Results revealed the novel finding that mathematics ability shows significantly stronger phenotypic and genetic associations with inattentiveness than with hyperactivity-impulsivity. Genetic associations between inattentiveness and mathematics ability could only partially be accounted for by hyperactivity-impulsivity, reading and general cognitive ability. Results suggest that mathematics ability is associated with ADHD symptoms largely because it shares genetic risk factors with inattentiveness, and provide further evidence for considering inattentiveness and hyperactivity-impulsivity separately. DNA markers for ADHD symptoms (especially inattentiveness) may also be candidate risk factors for

  12. A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes

    Science.gov (United States)

    Ghazali Kamardan, M.; Sufahani, Suliadi; Othman, M. Z. M.; Che-Him, Norziha; Khalid, Kamil; Roslan, Rozaini; Ali, Maselan; Zaidi, A. M. A.

    2018-04-01

    Many researches has been done on the lateral collapse of tube. However, the previous researches only focus on cylindrical and square tubes. Then a research has been done discovering the collapse behaviour of hexagonal tube and the mathematic model of the deformation behaviour had been developed [8]. The purpose of this research is to study the lateral collapse behaviour of symmetric octagonal tubes and hence to develop a mathematical model of the collapse behaviour of these tubes. For that, a predictive mathematical model was developed and a finite element analysis procedure was conducted for the lateral collapse behaviour of symmetric octagonal tubes. Lastly, the mathematical model was verified by using the finite element analysis simulation results. It was discovered that these tubes performed different deformation behaviour than the cylindrical tube. Symmetric octagonal tubes perform 2 phases of elastic - plastic deformation behaviour patterns. The mathematical model had managed to show the fundamental of the deformation behaviour of octagonal tubes. However, further studies need to be conducted in order to further improve on the proposed mathematical model.

  13. Using Mathematics in Science: Working with Your Mathematics Department

    Science.gov (United States)

    Lyon, Steve

    2014-01-01

    Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…

  14. Mathematical foundations of the projection-operator method

    International Nuclear Information System (INIS)

    Moore, S.M.

    1979-01-01

    Mathematical foundations are determined for the projection-operator method developed by Zwanzig and Mori and used in the study of cooperative phenomena in non-equilibrium processes. It is shown that the Hilbert space of operators can be taken as the Hilbert-Schmidt class. Comments are made on the possibility of a complete formulation of quantum mechanics in terms of this Hilbert space. (author)

  15. The Aftermath of Remedial Math: Investigating the Low Rate of Certificate Completion among Remedial Math Students

    Science.gov (United States)

    Bahr, Peter Riley

    2013-01-01

    Nationally, a majority of community college students require remedial assistance with mathematics, but comparatively few students who begin the remedial math sequence ultimately complete it and achieve college-level math competency. The academic outcomes of students who begin the sequence but do not complete it are disproportionately unfavorable:…

  16. Logic, mathematics, and computer science modern foundations with practical applications

    CERN Document Server

    Nievergelt, Yves

    2015-01-01

    This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory. It also serves as an excellent independent study reference and resource for instructors. Adapted from Foundations of Logic and Mathematics: Applications to Science and Cryptography © 2002 Birkhӓuser, this second edition provides a modern introduction to the foundations of logic, mathematics, and computers science, developing the theory that demonstrates construction of all mathematics and theoretical computer science from logic and set theory.  The focus is on foundations, with specific statements of all the associated axioms and rules of logic and set theory, and  provides complete details and derivations of formal proofs. Copious references to literature that document historical development is also provided. Answers are found to many questions that usually remain unanswered: Why is the truth table for logical implication so uni...

  17. Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities.

    Science.gov (United States)

    Libertus, Melissa E; Feigenson, Lisa; Halberda, Justin

    2013-12-01

    Previous research has found a relationship between individual differences in children's precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the current study, we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of 2years. In addition, at the final time point, we tested children's informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3). We found that children's numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned nonsymbolic system of quantity representation and the system of mathematics reasoning that children come to master through instruction. Copyright © 2013 Elsevier Inc. All rights reserved.

  18. The pragmatics of mathematics education vagueness and mathematical discourse

    CERN Document Server

    Rowland, Tim

    2003-01-01

    Drawing on philosophy of language and recent linguistic theory, Rowland surveys several approaches to classroom communication in mathematics. Are students intimidated by the nature of mathematics teaching? Many students appear fearful of voicing their understanding - is fear of error part of the linguistics of mathematics? The approaches explored here provide a rationale and a method for exploring and understanding speakers'' motives in classroom mathematics talk. Teacher-student interactions in mathematics are analysed, and this provides a toolkit that teachers can use to respond to the intellectual vulnerability of their students.

  19. Mathematical Experiences and Parental Involvement of Parents Who Are and Who Are Not Mathematicians

    Science.gov (United States)

    Antolin Drešar, Darja; Lipovec, Alenka

    2017-01-01

    Previous studies suggest that parental involvement in children's mathematics education is more established for parents who feel competent in mathematics. This qualitative study aimed to gain an in-depth insight into the experiences of parental involvement of two different groups of parents: those who are mathematicians and those who are not. Data…

  20. Developing Teaching Material Based on Realistic Mathematics Andoriented to the Mathematical Reasoning and Mathematical Communication

    OpenAIRE

    Habsah, Fitria

    2017-01-01

    This research aims to produce mathematics textbook for grade VII junior high school students based on realistic mathematics and oriented to the mathematical reasoning and mathematical communication. The quality is determined based on Nieveen criteria, including validity, practicality, and effectiveness.This study was a research and development and used Borg & Gall model. The subject of this research were the students of SMPN 2 Pujon-Kabupaten Malang, that is 30 students in an experimental cla...

  1. INTERSUBJECT CONNECTIONS OF COURSE OF MATHEMATICAL LOGIC AND OTHER MATHEMATICAL COURSES AT PREPARATION OF FUTURE TEACHER OF MATHEMATICS

    Directory of Open Access Journals (Sweden)

    Yu.I. Sinko

    2012-03-01

    Full Text Available In this article the interconnections of course of mathematical logic with other mathematical courses – geometry, algebra and theory of numbers, mathematical analysis, and also with the courses of mathematics teaching methodology, history of mathematics in the system of preparation of teachers of mathematics in pedagogical Institute of higher education are analyzed. The presence of connections between the elements of the system and their quality is the important description of the pedagogical system.

  2. Mathematics Connection

    African Journals Online (AJOL)

    MATHEMATICS CONNECTION aims at providing a forum topromote the development of Mathematics Education in Ghana. Articles that seekto enhance the teaching and/or learning of mathematics at all levels of theeducational system are welcome.

  3. Bohmian mechanics. The physics and mathematics of quantum theory

    International Nuclear Information System (INIS)

    Duerr, Detlef; Teufel, Stefan

    2009-01-01

    Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)

  4. Bohmian mechanics. The physics and mathematics of quantum theory

    Energy Technology Data Exchange (ETDEWEB)

    Duerr, Detlef [Muenchen Univ. (Germany). Fakultaet Mathematik; Teufel, Stefan [Tuebingen Univ. (Germany). Mathematisches Inst.

    2009-07-01

    Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)

  5. Mathematical Modelling Plant Signalling Networks

    KAUST Repository

    Muraro, D.

    2013-01-01

    During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.

  6. Exercises and problems in mathematical methods of physics

    CERN Document Server

    Cicogna, Giampaolo

    2018-01-01

    This book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order but rather in a sequence that maximizes their educational value. Each section and subsection starts with exercises based on first definitions, followed by groups of problems devoted to intermediate and, subsequently, more elaborate situations. Some of the problems are unavoidably "routine", but others bring to the forenontrivial properties that are often omitted or barely mentioned in textbooks. There are also problems where the reader is guided to obtain important results that are usually stated in textbooks without complete proofs. In all, some 350 solved problems covering all mathematical notions useful to physics are included. While the book is intended primarily for undergraduate students of physics, students...

  7. Mathematical model of the reformer sponge iron cycle

    International Nuclear Information System (INIS)

    Fraser, S.; Hacker, V.; Evers, B.; Hierzer, J.; Besenhard, J.O.

    2003-01-01

    A mathematical model of the Reformer Sponge Iron Cycle (RESC), an innovative hydrogen production process based on redox reactions of iron ore pellets is presented. In the oxidation stage of the RESC, hydrogen is produced by blowing steam over hot iron pellets, hence oxidizing the iron. In the reduction stage, synthesis gas coming from a reformer mixed with a fraction of recycled off-gas is used to reduce the iron oxide pellets (wuestite and/or magnetite) back into iron again. A mathematical model of the complete RESC was developed and verified with experimental data. The model is based on calculations of the equilibrium gas concentrations for reformer and Sponge Iron Reactor (SIR). The current model computes mass fluxes, molar fluxes, partial pressures and variations of the respective throughout the complete cycle. The recycle rate, determining the fraction of SIR off-gas recycled and added to the input gas stream was subsequently optimized in order to maximize the amount of iron oxide reduced for a certain input gas flow. (author)

  8. University Students' Metacognitive Failures in Mathematical Proving Investigated Based on the Framework of Assimilation and Accommodation

    Science.gov (United States)

    Huda, Nizlel; Subanji; Nusantar, Toto; Susiswo; Sutawidjaja, Akbar; Rahardjo, Swasono

    2016-01-01

    This study aimed to determine students' metacognitive failure in Mathematics Education Program of FKIP in Jambi University investigated based on assimilation and accommodation Mathematical framework. There were 35 students, five students did not answer the question, three students completed the questions correctly and 27 students tried to solve…

  9. Engineering Physics and Mathematics Division progress report for period ending March 31, 1991

    International Nuclear Information System (INIS)

    1991-10-01

    The primary purpose of this report is to provide an archival record of the activities of the Engineering Physics and Mathematics Division during the period September 1, 1989 through March 31, 1991. Earlier reports in this series are identified on the previous pages, along with the progress reports describing ORNL's research on the mathematical sciences prior to 1984 when those activities moved into the division. As in previous reports, our research is described through abstracts of journal articles, technical reports, and presentations. Summary lists of publications and presentations, staff additions and departures, scientific and professional activities of division staff, and technical conferences organized and sponsored by the division are included as appendices. The report is organized following the division of our research among four sections and information centers. These research areas are: Mathematical Sciences; Nuclear Data Measurement and Evaluations; Intelligent Systems; Nuclear Analysis and Shielding; and Engineering Physics Information Center

  10. Contributions of executive function and spatial skills to preschool mathematics achievement.

    Science.gov (United States)

    Verdine, Brian N; Irwin, Casey M; Golinkoff, Roberta Michnick; Hirsh-Pasek, Kathryn

    2014-10-01

    Early mathematics achievement is highly predictive of later mathematics performance. Here we investigated the influence of executive function (EF) and spatial skills, two generalizable skills often overlooked in mathematics curricula, on mathematics performance in preschoolers. Children (N=44) of varying socioeconomic status (SES) levels were assessed at 3 years of age on a new assessment of spatial skill (Test of Spatial Assembly, TOSA) and a vocabulary measure (Peabody Picture Vocabulary Test, PPVT). The same children were tested at 4 years of age on the Beery Test of Visual-Motor Integration (VMI) as well as on measures of EF and mathematics. The TOSA was created specifically as an assessment for 3-year-olds, allowing the investigation of links among spatial, EF, and mathematical skills earlier than previously possible. Results of a hierarchical regression indicate that EF and spatial skills predict 70% of the variance in mathematics performance without an explicit math test, EF is an important predictor of math performance as prior research suggested, and spatial skills uniquely predict 27% of the variance in mathematics skills. Additional research is needed to understand whether EF is truly malleable and whether EF and spatial skills may be leveraged to support early mathematics skills, especially for lower SES children who are already falling behind in these skill areas by 3 and 4 years of age. These findings indicate that both skills are part of an important foundation for mathematics performance and may represent pathways for improving school readiness for mathematics. Copyright © 2014 Elsevier Inc. All rights reserved.

  11. VEDIC MATHEMATICS

    Directory of Open Access Journals (Sweden)

    Sead Rešić

    2015-09-01

    Full Text Available It is very difficult to motivate students when it comes to a school subject like Mathematics. Teachers spend a lot of time trying to find something that will arouse interest in students. It is particularly difficult to find materials that are motivating enough for students that they eagerly wait for the next lesson. One of the solutions may be found in Vedic Mathematics. Traditional methods of teaching Mathematics create fear of this otherwise interesting subject in the majority of students. Fear increases failure. Often the traditional, conventional mathematical methods consist of very long lessons which are difficult to understand. Vedic Mathematics is an ancient system that is very flexible and encourages the development of intuition and innovation. It is a mental calculating tool that does not require a calculator because the calculator is embedded in each of us. Starting from the above problems of fear and failure in Mathematics, the goal of this paper is to do research with the control and the experimental group and to compare the test results. Two tests should be done for each of the groups. The control group would do the tests in the conventional way. The experimental group would do the first test in a conventional manner and then be subjected to different treatment, that is to say, be taught on the basis of Vedic Mathematics. After that, the second group would do the second test according to the principles of Vedic Mathematics. Expectations are that after short lectures on Vedic mathematics results of the experimental group would improve and that students will show greater interest in Mathematics.

  12. The Applied Mathematics for Power Systems (AMPS)

    Energy Technology Data Exchange (ETDEWEB)

    Chertkov, Michael [Los Alamos National Laboratory

    2012-07-24

    Increased deployment of new technologies, e.g., renewable generation and electric vehicles, is rapidly transforming electrical power networks by crossing previously distinct spatiotemporal scales and invalidating many traditional approaches for designing, analyzing, and operating power grids. This trend is expected to accelerate over the coming years, bringing the disruptive challenge of complexity, but also opportunities to deliver unprecedented efficiency and reliability. Our Applied Mathematics for Power Systems (AMPS) Center will discover, enable, and solve emerging mathematics challenges arising in power systems and, more generally, in complex engineered networks. We will develop foundational applied mathematics resulting in rigorous algorithms and simulation toolboxes for modern and future engineered networks. The AMPS Center deconstruction/reconstruction approach 'deconstructs' complex networks into sub-problems within non-separable spatiotemporal scales, a missing step in 20th century modeling of engineered networks. These sub-problems are addressed within the appropriate AMPS foundational pillar - complex systems, control theory, and optimization theory - and merged or 'reconstructed' at their boundaries into more general mathematical descriptions of complex engineered networks where important new questions are formulated and attacked. These two steps, iterated multiple times, will bridge the growing chasm between the legacy power grid and its future as a complex engineered network.

  13. Grade 9 Pilot Test. Mathematics. June 1988 = 9e Annee Test Pilote. Mathematiques. Juin 1988.

    Science.gov (United States)

    Alberta Dept. of Education, Edmonton.

    This pilot test for ninth grade mathematics is written in both French and English. The test consists of 75 multiple-choice items. Students are given 90 minutes to complete the examination and the use of a calculator is highly recommended. The test content covers a wide range of mathematical topics including: decimals; exponents; arithmetic word…

  14. The Magic of Mathematics Discovering the Spell of Mathematics

    CERN Document Server

    Pappas, Theoni

    2011-01-01

    Delves into the world of ideas, explores the spell mathematics casts on our lives, and helps you discover mathematics where you least expect it. Be spellbound by the mathematical designs found in nature. Learn how knots may untie the mysteries of life. Be mesmerized by the computer revolution. Discover how the hidden forces of mathematics hold architectural structures together connect your telephone calls help airplanes get off the ground solve the mysteries of the living cell. See how some artists use a mathematical palette in their works and how many writers draw upon the wealth of its ideas

  15. Modeling eBook acceptance: A study on mathematics teachers

    Science.gov (United States)

    Jalal, Azlin Abd; Ayub, Ahmad Fauzi Mohd; Tarmizi, Rohani Ahmad

    2014-12-01

    The integration and effectiveness of eBook utilization in Mathematics teaching and learning greatly relied upon the teachers, hence the need to understand their perceptions and beliefs. The eBook, an individual laptop completed with digitized textbook sofwares, were provided for each students in line with the concept of 1 student:1 laptop. This study focuses on predicting a model on the acceptance of the eBook among Mathematics teachers. Data was collected from 304 mathematics teachers in selected schools using a survey questionnaire. The selection were based on the proportionate stratified sampling. Structural Equation Modeling (SEM) were employed where the model was tested and evaluated and was found to have a good fit. The variance explained for the teachers' attitude towards eBook is approximately 69.1% where perceived usefulness appeared to be a stronger determinant compared to perceived ease of use. This study concluded that the attitude of mathematics teachers towards eBook depends largely on the perception of how useful the eBook is on improving their teaching performance, implying that teachers should be kept updated with the latest mathematical application and sofwares to use with the eBook to ensure positive attitude towards using it in class.

  16. Cluster algebras in mathematical physics

    International Nuclear Information System (INIS)

    Francesco, Philippe Di; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

    2014-01-01

    This special issue of Journal of Physics A: Mathematical and Theoretical contains reviews and original research articles on cluster algebras and their applications to mathematical physics. Cluster algebras were introduced by S Fomin and A Zelevinsky around 2000 as a tool for studying total positivity and dual canonical bases in Lie theory. Since then the theory has found diverse applications in mathematics and mathematical physics. Cluster algebras are axiomatically defined commutative rings equipped with a distinguished set of generators (cluster variables) subdivided into overlapping subsets (clusters) of the same cardinality subject to certain polynomial relations. A cluster algebra of rank n can be viewed as a subring of the field of rational functions in n variables. Rather than being presented, at the outset, by a complete set of generators and relations, it is constructed from the initial seed via an iterative procedure called mutation producing new seeds successively to generate the whole algebra. A seed consists of an n-tuple of rational functions called cluster variables and an exchange matrix controlling the mutation. Relations of cluster algebra type can be observed in many areas of mathematics (Plücker and Ptolemy relations, Stokes curves and wall-crossing phenomena, Feynman integrals, Somos sequences and Hirota equations to name just a few examples). The cluster variables enjoy a remarkable combinatorial pattern; in particular, they exhibit the Laurent phenomenon: they are expressed as Laurent polynomials rather than more general rational functions in terms of the cluster variables in any seed. These characteristic features are often referred to as the cluster algebra structure. In the last decade, it became apparent that cluster structures are ubiquitous in mathematical physics. Examples include supersymmetric gauge theories, Poisson geometry, integrable systems, statistical mechanics, fusion products in infinite dimensional algebras, dilogarithm

  17. Using Writing in Mathematics to Deepen Student Learning

    Science.gov (United States)

    Urquhart, Vicki

    2009-01-01

    Writing is the ability to compose text effectively for different purposes and audiences. When many of us reflect on our own school experiences, we recall writing in English and history classes, but not in mathematics. Math classes previously relied on skill-building and conceptual understanding activities. Today, teachers are realizing that…

  18. University mathematics teachers' views on the required reasoning in calculus exams

    OpenAIRE

    Bergqvist, Ewa

    2012-01-01

    Students often use imitative reasoning, i.e. copy algorithms or recall facts, when solving mathematical tasks. Research show that this type of imitative reasoning might weaken the students' understanding of the underlying mathematical concepts. In a previous study, the author classified tasks from 16 final exams from introductory calculus courses at Swedish universities. The results showed that it was possible to pass 15 of the exams, and solve most of the tasks, using imitative reasoning. Th...

  19. Interest in mathematics and science among students having high mathematics aptitude

    Science.gov (United States)

    Ely, Jane Alice

    The study investigates why men and women differ in their interest in mathematics and science and in the pursuit of careers in mathematics and science. The most persistent gender differential in educational standard testing is the scores in mathematics achievement. The mean Scholastic Aptitude Test (Mathematics) scores for women are consistently below that of men by about 40 points. One result of this gender differential in mathematics is that few women entertain a career requiring a robust knowledge of higher mathematics (i.e. engineering, computing, or the physical sciences). A large body of literature has been written attempting to explain why this is happening. Biological, cultural, structural and psychological explanations have been suggested and empirically examined. Controlling for mathematical ability is one method of sorting out these explanations. Eliminating mathematical ability as a factor, this dissertation reports the results of a study of men and women college students who all had high mathematics ability. Thus, any differences we found among them would have to be a result of other variables. Using a Mathematics Placement Exam and the SAT-M, forty-two students (12 males and 30 females) with high scores in both were interviewed. Student were asked about their experiences in high school and college mathematics, their career choices, and their attitudes toward mathematics. The findings, that there were no gender differences in the course selection, attitudes towards mathematics, and career choice, differed from my initial expectations. This negative finding suggests that women with high ability in mathematics are just as likely as men to pursue interests in mathematics and related courses in college and in selecting careers.

  20. Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

    Directory of Open Access Journals (Sweden)

    María F. Ayllón

    2016-04-01

    Full Text Available This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas, flexibility (range of ideas, novelty (unique idea and elaboration (idea development. These factors contribute, among others, to the fact that schoolchildren are competent in mathematics. The problem solving and posing are a very powerful evaluation tool that shows the mathematical reasoning and creative level of a person. Creativity is part of the mathematics education and is a necessary ingredient to perform mathematical assignments. This contribution presents some important research works about problem posing and solving related to the development of mathematical knowledge and creativity. To that end, it is based on various beliefs reflected in the literature with respect to notions of creativity, problem solving and posing.

  1. Mathematical thinking styles of undergraduate students and their achievement in mathematics

    Science.gov (United States)

    Risnanosanti

    2017-08-01

    The main purpose of this study is to analyze the role of mathematical thinking styles in students' achievement in mathematics. On the basis of this study, it is also to generate recommendation for classroom instruction. The two specific aims are; first to observe students' mathematical thinking styles during problem solving, the second to asses students' achievement in mathematics. The data were collected by using Mathematical Thinking Styles questionnaires and test of students' achievement in mathematics. The subject in this study was 35 students from third year at mathematics study program of Muhammadiyah University of Bengkulu in academic year 2016/2017. The result of this study was that the students have three mathematical thinking styles (analytic, visual, and integrated), and the students who have analytic styles have better achievement than those who have visual styles in mathematics.

  2. An introduction to the mathematics of biology with computer algebra models

    CERN Document Server

    Yeargers, Edward K; Herod, James V

    1996-01-01

    Biology is a source of fascination for most scientists, whether their training is in the life sciences or not. In particular, there is a special satisfaction in discovering an understanding of biology in the context of another science like mathematics. Fortunately there are plenty of interesting (and fun) problems in biology, and virtually all scientific disciplines have become the richer for it. For example, two major journals, Mathematical Biosciences and Journal of Mathematical Biology, have tripled in size since their inceptions 20-25 years ago. The various sciences have a great deal to give to one another, but there are still too many fences separating them. In writing this book we have adopted the philosophy that mathematical biology is not merely the intrusion of one science into another, but has a unity of its own, in which both the biology and the math­ ematics should be equal and complete, and should flow smoothly into and out of one another. We have taught mathematical biology with this philosophy...

  3. Quotable Quotes in Mathematics

    Science.gov (United States)

    Lo, Bruce W. N.

    1983-01-01

    As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)

  4. Unfinished Student Answer in PISA Mathematics Contextual Problem

    Science.gov (United States)

    Lutfianto, Moch.; Zulkardi; Hartono, Yusuf

    2013-01-01

    Solving mathematics contextual problems is one way that can be used to enable students to have the skills needed to live in the 21st century. Completion contextual problem requires a series of steps in order to properly answer the questions that are asked. The purpose of this study was to determine the steps performed students in solving…

  5. Erlotinib-induced rash spares previously irradiated skin

    International Nuclear Information System (INIS)

    Lips, Irene M.; Vonk, Ernest J.A.; Koster, Mariska E.Y.; Houwing, Ronald H.

    2011-01-01

    Erlotinib is an epidermal growth factor receptor inhibitor prescribed to patients with locally advanced or metastasized non-small cell lung carcinoma after failure of at least one earlier chemotherapy treatment. Approximately 75% of the patients treated with erlotinib develop acneiform skin rashes. A patient treated with erlotinib 3 months after finishing concomitant treatment with chemotherapy and radiotherapy for non-small cell lung cancer is presented. Unexpectedly, the part of the skin that had been included in his previously radiotherapy field was completely spared from the erlotinib-induced acneiform skin rash. The exact mechanism of erlotinib-induced rash sparing in previously irradiated skin is unclear. The underlying mechanism of this phenomenon needs to be explored further, because the number of patients being treated with a combination of both therapeutic modalities is increasing. The therapeutic effect of erlotinib in the area of the previously irradiated lesion should be assessed. (orig.)

  6. Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication

    Science.gov (United States)

    Kaya, Defne; Aydin, Hasan

    2016-01-01

    Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…

  7. Understanding in mathematics

    CERN Document Server

    Sierpinska, Anna

    1994-01-01

    The concept of understanding in mathematics with regard to mathematics education is considered in this volume, the main problem for mathematics teachers being how to facilitate their students'' understanding of the mathematics being taught.

  8. Figures of thought mathematics and mathematical texts

    CERN Document Server

    Reed, David

    2003-01-01

    Examines the ways in which mathematical works can be read as texts, examines their textual strategiesand demonstrates that such readings provide a rich source of philosophical debate regarding mathematics.

  9. Mathematical foundation of the optimization-based fluid animation method

    DEFF Research Database (Denmark)

    Erleben, Kenny; Misztal, Marek Krzysztof; Bærentzen, Jakob Andreas

    2011-01-01

    We present the mathematical foundation of a fluid animation method for unstructured meshes. Key contributions not previously treated are the extension to include diffusion forces and higher order terms of non-linear force approximations. In our discretization we apply a fractional step method to ...

  10. Predicting Success in College Mathematics from High School Mathematics Preparation

    OpenAIRE

    Shepley, Richard A.

    1983-01-01

    The purpose of this study was to develop a model to predict the college mathematics courses a freshman could expect to pass by considering their high school mathematics preparation. The high school information that was used consisted of the student's sex, the student's grade point average in mathematics, the highest level of high school mathematics courses taken, and the number of mathematics courses taken in high school. The high school sample was drawn from graduated Seniors in the State...

  11. The (Mathematical) Modeling Process in Biosciences.

    Science.gov (United States)

    Torres, Nestor V; Santos, Guido

    2015-01-01

    In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.

  12. The growth of mathematical knowledge --- introduction of convex bodies

    DEFF Research Database (Denmark)

    Carter, Jessica M H Grund; Hoff Kjeldsen, Tinne

    2012-01-01

    The article addresses the topic of the growth of mathematicalknowledge with a special focus on the question: How are mathematical objects introduced to mathematical practice? It takes as starting point a proposal made in a previous paper which is based on a case study on the introduction of Riemann......, which makes new definitions possible. This proposal is tested on a case study on Minkowski’s introduction of convexbodies. The conclusion is that the proposal holds also for this example. In both cases we notice that in a first stage is a close connection between the new object and the objects...

  13. Mathematical Chemistry

    OpenAIRE

    Trinajstić, Nenad; Gutman, Ivan

    2002-01-01

    A brief description is given of the historical development of mathematics and chemistry. A path leading to the meeting of these two sciences is described. An attempt is made to define mathematical chemistry, and journals containing the term mathematical chemistry in their titles are noted. In conclusion, the statement is made that although chemistry is an experimental science aimed at preparing new compounds and materials, mathematics is very useful in chemistry, among other things, to produc...

  14. Mathematical E-Learning: State of the Art and Experiences at the Open University of Catalonia

    Science.gov (United States)

    Juan, A.; Huertas, A.; Steegmann, C.; Corcoles, C.; Serrat, C.

    2008-01-01

    In this article we present a review of the state of the art in mathematical e-learning and some personal experiences on this area developed during the last eleven years at the Open University of Catalonia (UOC), a completely online university located in Spain. The article discusses important aspects related to online mathematics courses offered in…

  15. Elementary Pre-Service Teachers' Mathematics Anxiety and Mathematics Teaching Anxiety

    Science.gov (United States)

    Haciomeroglu, Guney

    2014-01-01

    The present study examined the structure of elementary pre-service teachers' mathematics anxiety and mathematics teaching anxiety by asking whether the two systems of anxiety are related. The Turkish Mathematics Anxiety Rating Scale Short Version and the Mathematics Teaching Anxiety Scale were administered to 260 elementary pre-service teachers.…

  16. Mathematics across cultures the history of non-Western mathematics

    CERN Document Server

    2000-01-01

    Mathematics Across Cultures: A History of Non-Western Mathematics consists of essays dealing with the mathematical knowledge and beliefs of cultures outside the United States and Europe. In addition to articles surveying Islamic, Chinese, Native American, Aboriginal Australian, Inca, Egyptian, and African mathematics, among others, the book includes essays on Rationality, Logic and Mathematics, and the transfer of knowledge from East to West. The essays address the connections between science and culture and relate the mathematical practices to the cultures which produced them. Each essay is well illustrated and contains an extensive bibliography. Because the geographic range is global, the book fills a gap in both the history of science and in cultural studies. It should find a place on the bookshelves of advanced undergraduate students, graduate students, and scholars, as well as in libraries serving those groups.

  17. Should I take Further Mathematics? Physics undergraduates’ experiences of post-compulsory Mathematics

    Science.gov (United States)

    Bowyer, Jessica; Darlington, Ellie

    2017-01-01

    It is essential that physics undergraduates are appropriately prepared for the mathematical demands of their course. This study investigated physics students’ perceptions of post-compulsory mathematics as preparation for their degree course. 494 physics undergraduates responded to an online questionnaire about their experiences of A-level Mathematics and Further Mathematics. The findings suggest that physics undergraduates would benefit from studying Further Mathematics and specialising in mechanics during their A-level studies. As both A-level Mathematics and Further Mathematics are being reformed, universities should look closely at the benefits of Further Mathematics as preparation for their physics courses and either increase their admissions requirements, or recommend that students take Further Mathematics.

  18. New Avenues for History in Mathematics Education: Mathematical Competencies and Anchoring

    DEFF Research Database (Denmark)

    Jankvist, U. T.; Kjeldsen, T. H.

    2011-01-01

    . The first scenario occurs when history is used as a ‘tool’ for the learning and teaching of mathematics, the second when history of mathematics as a ‘goal’ is pursued as an integral part of mathematics education. We introduce a multiple-perspective approach to history, and suggest that research on history......The paper addresses the apparent lack of impact of ‘history in mathematics education’ in mathematics education research in general, and proposes new avenues for research. We identify two general scenarios of integrating history in mathematics education that each gives rise to different problems...... in mathematics education follows one of two different avenues in dealing with these scenarios. The first is to focus on students’ development of mathematical competencies when history is used a tool for the learning of curriculum-dictated mathematical in-issues. A framework for this is described. Secondly, when...

  19. Slope across the Curriculum: Principles and Standards for School Mathematics and Common Core State Standards

    Science.gov (United States)

    Nagle, Courtney; Moore-Russo, Deborah

    2014-01-01

    This article provides an initial comparison of the Principles and Standards for School Mathematics and the Common Core State Standards for Mathematics by examining the fundamental notion of slope. Each set of standards is analyzed using eleven previously identified conceptualizations of slope. Both sets of standards emphasize Functional Property,…

  20. Mathematical methods in quantum and statistical mechanics

    International Nuclear Information System (INIS)

    Fishman, L.

    1977-01-01

    The mathematical structure and closed-form solutions pertaining to several physical problems in quantum and statistical mechanics are examined in some detail. The J-matrix method, introduced previously for s-wave scattering and based upon well-established Hilbert Space theory and related generalized integral transformation techniques, is extended to treat the lth partial wave kinetic energy and Coulomb Hamiltonians within the context of square integrable (L 2 ), Laguerre (Slater), and oscillator (Gaussian) basis sets. The theory of relaxation in statistical mechanics within the context of the theory of linear integro-differential equations of the Master Equation type and their corresponding Markov processes is examined. Several topics of a mathematical nature concerning various computational aspects of the L 2 approach to quantum scattering theory are discussed

  1. Mathematical psychology.

    Science.gov (United States)

    Batchelder, William H

    2010-09-01

    Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.

  2. Mathematical marriages: intercourse between mathematics and Semiotic choice.

    Science.gov (United States)

    Wagner, Roy

    2009-04-01

    This paper examines the interaction between Semiotic choices and the presentation and solution of a family of contemporary mathematical problems centred around the so-called 'stable marriage problem'. I investigate how a socially restrictive choice of signs impacts mathematical production both in terms of problem formation and of solutions. I further note how the choice of gendered language ends up constructing a reality, which duplicates the very structural framework that it imported into mathematical analysis in the first place. I go on to point out some semiotic lines of flight from this interlocking grip of mathematics and gendered language.

  3. The Benefits of Fine Art Integration into Mathematics in Primary School

    Directory of Open Access Journals (Sweden)

    Anja Brezovnik

    2015-09-01

    Full Text Available The main purpose of the article is to research the effects of the integration of fine art content into mathematics on students at the primary school level. The theoretical part consists of the definition of arts integration into education, a discussion of the developmental process of creative mathematical thinking, an explanation of the position of art and mathematics in education today, and a summary of the benefits of arts integration and its positive effects on students. The empirical part reports on the findings of a pedagogical experiment involving two different ways of teaching fifth-grade students: the control group was taught mathematics in a traditional way, while the experimental group was taught with the integration of fine art content into the mathematics lessons. At the end of the teaching periods, four mathematics tests were administered in order to determine the difference in knowledge between the control group and the experimental group. The results of our study confirmed the hypotheses, as we found positive effects of fine art integration into mathematics, with the experimental group achieving higher marks in the mathematics tests than the control group. Our results are consistent with the findings of previous research and studies, which have demonstrated and confirmed that long-term participation in fine art activities offers advantages related to mathematical reasoning, such as intrinsic motivation, visual imagination and reflection on how to generate creative ideas.

  4. The Relation between Parental Involvement and Math Anxiety: Implications for Mathematics Achievement

    Science.gov (United States)

    Roberts, Steven O.; Vukovic, Rose K.

    2011-01-01

    Previous research served as the platform for this study's research question: Does math anxiety mediate the relation between parental involvement and mathematics achievement? The primary purpose of this study was to examine this mediation model in a sample of at-risk second graders. Due to previous research, the investigators hypothesized that math…

  5. Structural Equation Model to Validate: Mathematics-Computer Interaction, Computer Confidence, Mathematics Commitment, Mathematics Motivation and Mathematics Confidence

    Science.gov (United States)

    Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe

    2016-01-01

    Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…

  6. Impact of a required pharmaceutical calculations course on mathematics ability and knowledge retention.

    Science.gov (United States)

    Hegener, Michael A; Buring, Shauna M; Papas, Elizabeth

    2013-08-12

    To assess doctor of pharmacy (PharmD) students' mathematics ability by content area before and after completing a required pharmaceutical calculations course and to analyze changes in scores. A mathematics skills assessment was administered to 2 cohorts of pharmacy students (class of 2013 and 2014) before and after completing a pharmaceutical calculations course. The posttest was administered to the second cohort 6 months after completing the course to assess knowledge retention. Both cohorts performed significantly better on the posttest (cohort 1, 13% higher scores; cohort 2, 15.9% higher scores). Significant improvement on posttest scores was observed in 6 of the 10 content areas for cohorts 1 and 2. Both cohorts scored lower in percentage calculations on the posttest than on the pretest. A required, 1-credit-hour pharmaceutical calculations course improved PharmD students' overall ability to perform fundamental and application-based calculations.

  7. High rate of complete responses to immune checkpoint inhibitors in patients with relapsed or refractory Hodgkin lymphoma previously exposed to epigenetic therapy

    Directory of Open Access Journals (Sweden)

    Lorenzo Falchi

    2016-11-01

    Full Text Available Abstract Options for patients with relapsed or refractory (R/R classical Hodgkin lymphoma (cHL after brentuximab vedotin (Bv and autologous stem cell transplantation (ASCT are limited. Immune checkpoint inhibitors (ICI are active in this population but rarely induce complete response (CR. Ten patients with R/R cHL after ASCT and Bv received pembrolizumab (n = 8 or nivolumab (n = 2. Five had been previously exposed to 5-azacitidine on a phase 1 study. Among nine evaluable patients, seven (78% achieved CR, one partial response, and one reduction of tumor burden. All five patients who had received 5-azacitidine prior to ICI achieved CR, while only two of four who did not receive prior 5-azacitidine achieved CR. At a median follow-up of 9.9 months [0.5–14.3], eight patients are alive and five are still receiving treatment. We documented an unprecedented CR rate after ICI in patients with R/R cHL. We hypothesize that hypomethylating agents might have an immune priming effect and enhance the efficacy of ICI.

  8. Building Knowledge Structures by Testing Helps Children With Mathematical Learning Difficulty.

    Science.gov (United States)

    Zhang, Yiyun; Zhou, Xinlin

    2016-01-01

    Mathematical learning difficulty (MLD) is prevalent in the development of mathematical abilities. Previous interventions for children with MLD have focused on number sense or basic mathematical skills. This study investigated whether mathematical performance of fifth grade children with MLD could be improved by developing knowledge structures by testing using a web-based curriculum learning system. A total of 142 children with MLD were recruited; half of the children were in the experimental group (using the system), and the other half were in the control group (not using the system). The children were encouraged to use the web-based learning system at home for at least a 15-min session, at least once a week, for one and a half months. The mean accumulated time of testing on the system for children in the experimental group was 56.2 min. Children in the experimental group had significantly higher scores on their final mathematical examination compared to the control group. The results suggest that web-based curriculum learning through testing that promotes the building of knowledge structures for a mathematical course was helpful for children with MLD. © Hammill Institute on Disabilities 2014.

  9. ACER: A framework on the use of mathematics in upper-division physics

    Science.gov (United States)

    Caballero, Marcos D.; Wilcox, Bethany R.; Pepper, Rachel E.; Pollock, Steven J.

    2013-01-01

    At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics, electromagnetism, and quantum mechanics. Unsurprisingly, a number of difficulties are related to students' use of mathematical tools (e.g., approximation methods). Previous work has documented a number of challenges that students must overcome to use mathematical tools fluently in introductory physics (e.g., mapping meaning onto mathematical symbols). We have developed a theoretical framework to facilitate connecting students' difficulties to challenges with specific mathematical and physical concepts. In this paper, we motivate the need for this framework and demonstrate its utility for both researchers and course instructors by applying it to frame results from interview data on students' use of Taylor approximations.

  10. Live Lectures or Online Videos: Students' Resource Choices in a First-Year University Mathematics Module

    Science.gov (United States)

    Howard, Emma; Meehan, Maria; Parnell, Andrew

    2018-01-01

    In "Maths for Business", a mathematics module for non-mathematics specialists, students are given the choice of completing the module content via short online videos, live lectures or a combination of both. In this study, we identify students' specific usage patterns with both of these resources and discuss their reasons for the…

  11. Mathematics

    CERN Document Server

    Eringen, A Cemal

    2013-01-01

    Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th

  12. The materiality of mathematics: presenting mathematics at the blackboard.

    Science.gov (United States)

    Greiffenhagen, Christian

    2014-09-01

    Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. © London School of Economics and Political Science 2014.

  13. Complete Heart Block with Diastolic Heart Failure and Pulmonary Edema Secondary to Enlarging Previously Diagnosed Thrombosed Aneurysm of Sinus of Valsalva in a Patient with History of Autosomal Dominant Polycystic Kidney Disease

    Directory of Open Access Journals (Sweden)

    Sherif Ali Eltawansy

    2015-01-01

    Full Text Available Autosomal dominant polycystic kidney disease (ADPKD is associated with vascular aneurysms that can affect any part of the vascular tree, like ascending aorta or coronary arteries. Sinus of Valsalva is known as an anatomical dilation at the root of aorta above the aortic valve and very few cases show aneurysm at that site in patients with ADPKD. Sinus of Valsalva aneurysm (SVA can present with rupture and acute heart failure and infective endocarditis or could be asymptomatic accidentally discovered during cardiac catheterization. We report a case of a 76-year-old male with a unique constellation of cardiovascular anomalies associated with ADPKD. Patient was previously diagnosed with aneurysms affecting ascending aorta, sinus of Valsalva, and coronary arteries. Several years later, he came with complete heart block which was discovered later to be secondary to enlargement of his previously diagnosed thrombosed SVA. His case was complicated with acute heart failure and pulmonary edema. Conclusion. Patients with ADPKD can present with extrarenal manifestations. In our case, aneurysm at sinus of Valsalva was progressively enlarging and presented with complete heart block.

  14. Engineering Physics and Mathematics Division progress report for period ending March 31, 1991

    Energy Technology Data Exchange (ETDEWEB)

    1991-10-01

    The primary purpose of this report is to provide an archival record of the activities of the Engineering Physics and Mathematics Division during the period September 1, 1989 through March 31, 1991. Earlier reports in this series are identified on the previous pages, along with the progress reports describing ORNL's research on the mathematical sciences prior to 1984 when those activities moved into the division. As in previous reports, our research is described through abstracts of journal articles, technical reports, and presentations. Summary lists of publications and presentations, staff additions and departures, scientific and professional activities of division staff, and technical conferences organized and sponsored by the division are included as appendices. The report is organized following the division of our research among four sections and information centers. These research areas are: Mathematical Sciences; Nuclear Data Measurement and Evaluations; Intelligent Systems; Nuclear Analysis and Shielding; and Engineering Physics Information Center.

  15. Rainforest Mathematics

    Science.gov (United States)

    Kilpatrick, Jeremy

    2014-01-01

    This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…

  16. Mathematical scandals

    CERN Document Server

    Pappas, Theoni

    1997-01-01

    In this highly readable volume of vignettes of mathematical scandals and gossip, Theoni Pappas assembles 29 fascinating stories of intrigue and the bizarre ? in short, the human background of the history of mathematics. Might a haberdasher have changed Einstein's life? Why was the first woman mathematician murdered? How come there's no Nobel Prize in mathematics?Mathematics is principally about numbers, equations, and solutions, all of them precise and timeless. But, behind this arcane matter lies the sometimes sordid world of real people, whose rivalries and deceptions

  17. Mathematics beliefs and instructional strategies in achievement of elementary-school students in Japan: results from the TIMSS 2003 assessment.

    Science.gov (United States)

    House, J Daniel

    2007-04-01

    Recent findings concerning mathematics assessment indicate that students in Japan consistently score above international averages. Researchers have examined specific mathematics beliefs and instructional strategies associated with mathematics achievement for students in Japan. This study examined relationships among self-beliefs, classroom instructional strategies, and mathematics achievement for a large national sample of students (N=4,207) from the TIMSS 2003 international sample of fourth graders in Japan. Several significant relationships between mathematics beliefs and test scores were found; a number of classroom teaching strategies were also significantly associated with test scores. However, multiple regression using the complete set of five mathematics beliefs and five instructional strategies explained only 25.1% of the variance in mathematics achievement test scores.

  18. High school mathematics teachers' perspectives on the purposes of mathematical proof in school mathematics

    Science.gov (United States)

    Dickerson, David S.; Doerr, Helen M.

    2014-12-01

    Proof serves many purposes in mathematics. In this qualitative study of 17 high school mathematics teachers, we found that these teachers perceived that two of the most important purposes for proof in school mathematics were (a) to enhance students' mathematical understanding and (b) to develop generalized thinking skills that were transferable to other fields of endeavor. We found teachers were divided on the characteristics (or features) of proofs that would serve these purposes. Teachers with less experience tended to believe that proofs in the high school should adhere to strict standards of language and reasoning while teachers with more experience tended to believe that proofs based on concrete or visual features were well suited for high school mathematics. This study has implications for teacher preparation because it appears that there is a wide variation in how teachers think about proof. It seems likely that students would experience proof very differently merely because they were seated in different classrooms.

  19. Optimal control for mathematical models of cancer therapies an application of geometric methods

    CERN Document Server

    Schättler, Heinz

    2015-01-01

    This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.

  20. HOW MATHEMATICS TEACHERS DEVELOP THEIR PUPILS’ SELF-REGULATED LEARNING SKILLS

    Directory of Open Access Journals (Sweden)

    Iuliana Marchis

    2011-11-01

    Full Text Available Self-regulated learning skills are important in mathematical problem solving. The aim of the paper is to present a research on how mathematics teachers guide their pupils’ mathematical problem-solving activities in order to increase self-regulation. 62 teachers have filled in a questionnaire developed for this research. The results are show that more than two third of the teachers promote the methods of understanding the problem; develop pupils’ self-efficacy and self-control. But only one third of the teachers ask pupils to use different strategies for solving a problem; ask students to explain the solution to their colleagues. In case of unsuccessful problem solving only one third of the respondents ask pupils to present previous knowledge about the problem or/and recall and try different methods.

  1. Financial mathematics

    CERN Document Server

    Jothi, A Lenin

    2009-01-01

    Financial services, particularly banking and insurance services is the prominent sector for the development of a nation. After the liberalisation of financial sector in India, the scope of getting career opportunities has been widened. It is heartening to note that various universities in India have introduced professional courses on banking and insurance. A new field of applied mathematics has come into prominence under the name of Financial Mathematics. Financial mathematics has attained much importance in the recent years because of the role played by mathematical concepts in decision - m

  2. Mathematics everywhere

    CERN Document Server

    Aigner, Martin; Spain, Philip G

    2010-01-01

    Mathematics is all around us. Often we do not realize it, though. Mathematics Everywhere is a collection of presentations on the role of mathematics in everyday life, through science, technology, and culture. The common theme is the unique position of mathematics as the art of pure thought and at the same time as a universally applicable science. The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" unde

  3. Engineering mathematics

    CERN Document Server

    Stroud, K A

    2013-01-01

    A groundbreaking and comprehensive reference that's been a bestseller since it first debuted in 1970, the new seventh edition of Engineering Mathematics has been thoroughly revised and expanded. Providing a broad mathematical survey, this innovative volume covers a full range of topics from the very basic to the advanced. Whether you're an engineer looking for a useful on-the-job reference or want to improve your mathematical skills, or you are a student who needs an in-depth self-study guide, Engineering Mathematics is sure to come in handy time and time again.

  4. Skolem and pessimism about proof in mathematics.

    Science.gov (United States)

    Cohen, Paul J

    2005-10-15

    Attitudes towards formalization and proof have gone through large swings during the last 150 years. We sketch the development from Frege's first formalization, to the debates over intuitionism and other schools, through Hilbert's program and the decisive blow of the Gödel Incompleteness Theorem. A critical role is played by the Skolem-Lowenheim Theorem, which showed that no first-order axiom system can characterize a unique infinite model. Skolem himself regarded this as a body blow to the belief that mathematics can be reliably founded only on formal axiomatic systems. In a remarkably prescient paper, he even sketches the possibility of interesting new models for set theory itself, something later realized by the method of forcing. This is in contrast to Hilbert's belief that mathematics could resolve all its questions. We discuss the role of new axioms for set theory, questions in set theory itself, and their relevance for number theory. We then look in detail at what the methods of the predicate calculus, i.e. mathematical reasoning, really entail. The conclusion is that there is no reasonable basis for Hilbert's assumption. The vast majority of questions even in elementary number theory, of reasonable complexity, are beyond the reach of any such reasoning. Of course this cannot be proved and we present only plausibility arguments. The great success of mathematics comes from considering 'natural problems', those which are related to previous work and offer a good chance of being solved. The great glories of human reasoning, beginning with the Greek discovery of geometry, are in no way diminished by this pessimistic view. We end by wishing good health to present-day mathematics and the mathematics of many centuries to come.

  5. Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

    Science.gov (United States)

    Wickstrom, Megan H.

    2017-01-01

    This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…

  6. Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

    Science.gov (United States)

    Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.

    2014-01-01

    This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…

  7. Mathematics and engineering in real life through mathematical competitions

    Science.gov (United States)

    More, M.

    2018-02-01

    We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

  8. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2011-01-01

    ; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

  9. Levels of infinity selected writings on mathematics and philosophy

    CERN Document Server

    Weyl, Hermann

    2012-01-01

    This original anthology collects 11 of Weyl's less-technical writings that address the broader scope and implications of mathematics. Most have been long unavailable or not previously published in book form. Subjects include logic, topology, abstract algebra, relativity theory, and reflections on the work of Weyl's mentor, David Hilbert.

  10. Some mathematical methods of physics

    CERN Document Server

    Goertzel, Gerald

    2014-01-01

    This well-rounded, thorough treatment for advanced undergraduates and graduate students introduces basic concepts of mathematical physics involved in the study of linear systems. The text emphasizes eigenvalues, eigenfunctions, and Green's functions. Prerequisites include differential equations and a first course in theoretical physics.The three-part presentation begins with an exploration of systems with a finite number of degrees of freedom (described by matrices). In part two, the concepts developed for discrete systems in previous chapters are extended to continuous systems. New concepts u

  11. Mathematics Anxiety in Young Children: Concurrent and Longitudinal Associations with Mathematical Performance

    Science.gov (United States)

    Vukovic, Rose K.; Kieffer, Michael J.; Bailey, Sean P.; Harari, Rachel R.

    2013-01-01

    This study explored mathematics anxiety in a longitudinal sample of 113 children followed from second to third grade. We examined how mathematics anxiety related to different types of mathematical performance concurrently and longitudinally and whether the relations between mathematics anxiety and mathematical performance differed as a function of…

  12. Introducing philosophy of mathematics

    CERN Document Server

    Friend, Michele

    2014-01-01

    What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual acc

  13. On the mathematical modeling of aeolian saltation

    DEFF Research Database (Denmark)

    Jensen, Jens Ledet; Sørensen, Michael

    1983-01-01

    The development of a mathematical model for aeolian saltation is a promising way of obtaining further progress in the field of wind-blown sand. Interesting quantities can be calculated from a model defined in general terms, and a specific model is defined and compared to previously published data...... on aeolian saltation. This comparison points out the necessity of discriminating between pure and real saltation. -Authors...

  14. Developing non-routine problems for assessing students’ mathematical literacy

    Science.gov (United States)

    Murdiyani, N. M.

    2018-03-01

    The purpose of this study is to develop non-routine problems for assessing the mathematics literacy skills of students, which is valid, practical, and effective. It is based on the previous research said that Indonesian students’ mathematical literacy is still low. The results of this study can be used as a guide in developing the evaluation questions that can train students to improve the ability of solving non-routine problems in everyday life. This research type is formative evaluation that consists of preliminary, self evaluation, expert reviews, one-to-one, small group, and field test. The sample of this research is grade 8 students at one of Junior High School in Yogyakarta. This study results in mathematics literacy problems prototype consisting of level 1 to level 6 problems similar to PISA problems. This study also discusses the examples of students’ answer and their reasoning.

  15. What Did the Abbacus Teachers Really Do When They (Sometimes) Ended Up Doing Mathematics?

    DEFF Research Database (Denmark)

    Høyrup, Jens

    Italian fourteenth- and fifteenth-century abbacus algebra presents us with a number of deviations from what we would consider normal (or proper) mathematical behaviour: the invention of completely false algebraic rules for the solution of cubic and quartic equations, and of rules that pretend...... to be generally valid but in fact only hold in very special cases; and (in modern terms) an attempt to expand the multiplicative semi-group of non-negative algebraic powers into a complete group by treating roots as negative powers. In both cases, the authors of the fallacies must have known they were cheating...... mathematics as this can be extracted from the more elementary level of the abbacus treatises....

  16. Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

    Science.gov (United States)

    Lowe, James; Carter, Merilyn; Cooper, Tom

    2018-01-01

    Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

  17. DEVELOPING STUDENTS’ ABILITY OF MATHEMATICAL CONNECTION THROUGH USING OUTDOOR MATHEMATICS LEARNING

    Directory of Open Access Journals (Sweden)

    Saleh Haji

    2017-01-01

    Full Text Available The Purpose of this study is to determine the achievement and improvement of students’ mathematical connectionability through using outdoor mathematics learning. 64 students from the fifth grade of Primary School at SDN 65 and SDN 67 Bengkulu City were taken as the sample of this study. While the method of the research used in this research is experiment with quasi-experimental designs non-equivalent control group. The results of the study are as follows: (1 There is an increasing ability found in mathematical connection of students whom taught by using outdoors mathematics learning is 0,53; (2 Based on statical computation that achievement of students’ ability of mathematical connection is taught by using outdoor mathematics learning score is 71,25. It is higher than the students score 66,25 which were taught by using the conventional learning. So as to improve students’ mathematical connection, teachers are suggested to use the outdoors mathematics learning

  18. Loving + hating mathematics challenging the myths of mathematical life

    CERN Document Server

    Hersh, Reuben

    2011-01-01

    Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathema

  19. On the Failure of Standard Completeness in PiMTL for Infinite Theories

    Czech Academy of Sciences Publication Activity Database

    Horčík, Rostislav

    2007-01-01

    Roč. 158, č. 6 (2007), s. 619-624 ISSN 0165-0114 Source of funding: V - iné verejné zdroje Keywords : strong standard completeness * monoidal t-norm based logic (MTL) * basic fuzzy logic (BL) * product logic * Lukasiewicz logic * PiMTL * IMTL Subject RIV: BA - General Mathematics Impact factor: 1.373, year: 2007

  20. Mathematics beliefs and achievement of adolescent students in Japan: results from the TIMSS 1999 assessment.

    Science.gov (United States)

    House, J Daniel

    2005-12-01

    A recent study (1) of undergraduate students in a precalculus course indicated that they expressed slightly positive attitudes toward mathematics. It is important, however, to examine relationships between students' initial attitudes and achievement outcomes. The present purpose was to assess the relationship between self-beliefs and mathematics achievement for a large national sample of students from the TIMSS 1999 international sample (eighth graders) from Japan. Several significant relationships between mathematics beliefs and test scores were noted. In addition, the overall multiple regression equation that assessed the joint significance of the complete set of self-belief variables was significant (F7.65 = 159.48, p < .001) and explained 20.6% of the variance in mathematics achievement test scores.

  1. Dilemma in Teaching Mathematics

    Science.gov (United States)

    Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain

    2012-01-01

    The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…

  2. Introductory discrete mathematics

    CERN Document Server

    Balakrishnan, V K

    2010-01-01

    This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv

  3. Identifying Subtypes among Children with Developmental Coordination Disorder and Mathematical Learning Disabilities, Using Model-Based Clustering

    Science.gov (United States)

    Pieters, Stefanie; Roeyers, Herbert; Rosseel, Yves; Van Waelvelde, Hilde; Desoete, Annemie

    2015-01-01

    A relationship between motor and mathematical skills has been shown by previous research. However, the question of whether subtypes can be differentiated within developmental coordination disorder (DCD) and/or mathematical learning disability (MLD) remains unresolved. In a sample of children with and without DCD and/or MLD, a data-driven…

  4. A New Kind of Aesthetics —The Mathematical Structure of the Aesthetic

    Directory of Open Access Journals (Sweden)

    Akihiro Kubota

    2017-06-01

    Full Text Available This paper proposes a new approach to the investigation into aesthetics. Specifically, it~argues that it is possible to explain the aesthetic and its underlying dynamic relations with an~axiomatic structure (the octahedral axiom-derived category based on contemporary mathematics (namely category theory, and through this argument suggests the possibility for discussion about the mathematical structure of the aesthetic. If there were a way to describe the structure of the aesthetic with the language of mathematical structures and mathematical axioms---a~language completely devoid of arbitrariness---then we would make possible a universal argument about the essential human activity of ``the aesthetic'', and we would also gain a new method and viewpoint into the philosophy and meaning of the act of creating a work of art and artistic activities. This paper presents one mathematical structure as a foundation in constructing the science of dynamic aesthetics based on axiomatic functionalism, which is in turn based on a new interdisciplinary investigation into the generative structure of the aesthetic.

  5. Mathematics Prerequisites for Introductory Geoscience Courses: Using Technology to Help Solve the Problem

    Science.gov (United States)

    Burn, H. E.; Wenner, J. M.; Baer, E. M.

    2011-12-01

    , students completed a pretest, the assigned modules, and a posttest. Success in remediation was measured using normalized gain scores, which measures the change in score divided by the maximum possible increase: (posttest-pretest)/(1-pretest). To compare across courses, normalized gain scores were standardized. Additional analysis included disaggregating normalized gain scores by quartiles based on pretest scores. The results were supplemented by qualitative data from faculty interviews and information provided by faculty on a web form upon completion of the course. Results suggest TMYN modules remediate mathematical skills effectively, and that normalized gains tend to be higher for students in the lower quartiles on the pretest. Students indicate finding the modules helpful, though sometimes difficult. Faculty interview data triangulate these findings and provide further evidence that online, modularized remediation is an effective alternative to assigning prerequisite mathematical courses to remediate mathematical skills.

  6. Interaction between Mathematics and Physics

    Directory of Open Access Journals (Sweden)

    Hitchin, Nigel

    2007-06-01

    Full Text Available There is at the moment a highly active interface between mathematics and theoretical physics, which extends into completely new areas of both disciplines. This article, based on a round table discussion which took place as part of the activities around the 2006 International Congress of Mathematicians in Madrid, explores some of the issues involved: the differing goals and backgrounds of the two communities, today’s interactions and their precedents, the possibilities for the future and the role of mathematics itself in understanding the world in which we live.Actualmente existe una importante interfaz entre matemáticas y física teórica, que ha producido áreas completamente nuevas. Este artículo está basado en un debate en una mesa redonda organizada en el entorno del International Congress of Mathematicians en 2006 de Madrid, explora algunos de estos temas: los diferentes objetivos y pasado de ambas disciplinas, las interacciones actuales y sus precedentes, las posibilidades para el futuro y el papel de las matemáticas para entender el mundo en que vivimos.

  7. Mathematics and Engineering in Real Life through Mathematical Competitions

    Science.gov (United States)

    More, M.

    2018-01-01

    We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build…

  8. Secondary School Mathematics Teachers' Attitude in Teaching Mathematics

    OpenAIRE

    Mulugeta Atnafu

    2014-01-01

    The purpose of this study was to examine Addis Ababa secondary school mathematics teachers’ attitude in teaching mathematics. 148 mathematics teachers were selected using cluster sampling from Addis Ababa administration region. The study used survey method of data collection and it includes both quantitative and qualitative research methods. From the independent t-test, ANOVA, tukey test and regression analysis, some of the results obtained were: the majority of the secondary school mathemati...

  9. An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

    Science.gov (United States)

    Thrasher, Emily Plunkett

    2016-01-01

    The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

  10. Nonassociative Substructural Logics and Their Semilinear Extensions: Axiomatization and Completeness Properties

    Czech Academy of Sciences Publication Activity Database

    Cintula, Petr; Horčík, Rostislav; Noguera, Carles

    2013-01-01

    Roč. 6, č. 3 (2013), s. 394-423 ISSN 1755-0203 R&D Projects: GA ČR GBP202/12/G061 Grant - others:ESF/Austrian Science Foundation project(AT) I143-G15 Institutional support: RVO:67985807 ; RVO:67985556 Keywords : nonassociative full Lambek calculus * deduction theorem * standard completeness Subject RIV: BA - General Mathematics Impact factor: 0.525, year: 2013

  11. Panel Debate: Technics and technology in mathematics and mathematics education

    DEFF Research Database (Denmark)

    Misfeldt, Morten

    2015-01-01

    The use of computer technology for teaching and learning of mathematics has several consequences and does sometimes give rise to both controversies and misunderstandings. We address these problems by both a philosophical and a historical approach, investigating what it actually is that goes on when...... guidelines and conclusions regarding the use of computer technology in mathematics education....... new technologies enter mathematics as a discipline and mathematics education as a societal practice. Our analysis suggests a focus on continuities in time and place in the sense that it is necessary to understand the history of “tool use” in mathematics and the various ways that scholastic and non...

  12. Improving professional IT doctorate completion rates

    Directory of Open Access Journals (Sweden)

    Oliver Kisalay Burmeister

    2015-08-01

    Full Text Available Professional doctorates in Information Technology (IT have been a relatively recent phenomenon, giving IT professionals career management choices not previously available to them. However, successful completion rates are the lowest of all disciplines. Completed doctorates rate in quality equivalent to PhDs, and retention has been identified as a major obstacle to completion. This qualitative study, involving 44 semi-structured interviews with students, supervisors and institutional support personnel, investigated the obstacles. Amongst the strategies discovered to improve completion rates were retention, student engagement with supervisors, feedback on progress, student engagement in the course, and student involvement in institutional communities of practice.

  13. Effects of Clicker Use on Calculus Students' Mathematics Anxiety

    Science.gov (United States)

    Batchelor, John

    2015-01-01

    This paper reports the results of a survey study of clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course during the Fall 2013 semester. Students in two large lecture sections of calculus completed surveys at the beginning and end of the course. One class used clickers, whereas the other class was taught…

  14. The Joy of Mathematics Discovering Mathematics All Around You

    CERN Document Server

    Pappas, Theoni

    1993-01-01

    Part of the joy of mathematics is that it is everywhere-in soap bubbles, electricity, da Vinci's masterpieces, even in an ocean wave. Written by the well-known mathematics teacher consultant, this volume's collection of over 200 clearly illustrated mathematical ideas, concepts, puzzles, and games shows where they turn up in the "real" world. You'll find out what a googol is, visit hotel infinity, read a thorny logic problem that was stumping them back in the 8th century. THE JOY OF MATHEMATICS is designed to be opened at random…it's mini essays are self-contained providing the reader

  15. Grounded Blends and Mathematical Gesture Spaces: Developing Mathematical Understandings via Gestures

    Science.gov (United States)

    Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy

    2011-01-01

    This paper examines how a person's gesture space can become endowed with mathematical meaning associated with mathematical spaces and how the resulting mathematical gesture space can be used to communicate and interpret mathematical features of gestures. We use the theory of grounded blends to analyse a case study of two teachers who used gestures…

  16. Mathematical literacy in undergraduates: role of gender, emotional intelligence and emotional self-efficacy

    Science.gov (United States)

    Tariq, Vicki N.; Qualter, Pamela; Roberts, Sian; Appleby, Yvon; Barnes, Lynne

    2013-12-01

    This empirical study explores the roles that Emotional Intelligence (EI) and Emotional Self-Efficacy (ESE) play in undergraduates' mathematical literacy, and the influence of EI and ESE on students' attitudes towards and beliefs about mathematics. A convenience sample of 93 female and 82 male first-year undergraduates completed a test of mathematical literacy, followed by an online survey designed to measure the students' EI, ESE and factors associated with mathematical literacy. Analysis of the data revealed significant gender differences. Males attained a higher mean test score than females and out-performed the females on most of the individual questions and the associated mathematical tasks. Overall, males expressed greater confidence in their mathematical skills, although both males' and females' confidence outweighed their actual mathematical proficiency. Correlation analyses revealed that males and females attaining higher mathematical literacy test scores were more confident and persistent, exhibited lower levels of mathematics anxiety and possessed higher mathematics qualifications. Correlation analyses also revealed that in male students, aspects of ESE were associated with beliefs concerning the learning of mathematics (i.e. that intelligence is malleable and that persistence can facilitate success), but not with confidence or actual performance. Both EI and ESE play a greater role with regard to test performance and attitudes/beliefs regarding mathematics amongst female undergraduates; higher EI and ESE scores were associated with higher test scores, while females exhibiting higher levels of ESE were also more confident and less anxious about mathematics, believed intelligence to be malleable, were more persistent and were learning goal oriented. Moderated regression analyses confirmed mathematics anxiety as a negative predictor of test performance in males and females, but also revealed that in females EI and ESE moderate the effects of anxiety on test

  17. Mathematics through Millenia

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    2005-01-01

    A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....

  18. Mathematics through millenia

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....

  19. Mathematical biology

    CERN Document Server

    Murray, James D

    1993-01-01

    The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...

  20. Mathematics unbound

    CERN Document Server

    Parshall, Karen Hunger

    2002-01-01

    Although today's mathematical research community takes its international character very much for granted, this "global nature" is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom the goal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians and mathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only develo...

  1. The contribution of parent-child numeracy activities to young Chinese children's mathematical ability.

    Science.gov (United States)

    Huang, Qi; Zhang, Xiao; Liu, Yingyi; Yang, Wen; Song, Zhanmei

    2017-09-01

    A growing body of recent research has shown that parent-child mathematical activities have a strong effect on children's mathematical learning. However, this research was conducted predominantly in Western societies and focused mainly on mothers' involvement in such activities. This study aimed to examine both mother-child and father-child numeracy activities in Hong Kong Chinese families and both parents' unique roles in predicting young Chinese children's mathematics ability. A sample of 104 Hong Kong Chinese children aged approximately 5 years and their mothers and fathers participated in this study. Mothers and fathers independently reported the frequency of their own numeracy activities with their children. Children were assessed individually using two measures of mathematical ability. Hierarchical regression models were used to investigate the contribution of parent-child numeracy activities to children's mathematical ability. Mothers' participation in number skill activities and fathers' participation in number game and application activities significantly predicted their children's mathematical performance even after controlling for background variables and children's language ability. This study extends previous research with a sample of Chinese kindergarten children and shows that parent-child numeracy activities are related to young children's mathematical ability. The findings highlight the important roles that mothers and fathers play in their young children's mathematical learning. © 2017 The British Psychological Society.

  2. A study of competence in mathematics and mechanics in an engineering curriculum

    Science.gov (United States)

    Munns, Andrew

    2017-11-01

    Professional bodies expect engineers to show competence in both mathematics and engineering topics such as mechanics, using their abilities in both of these to solve problems. Yet within engineering programmes there is a phenomenon known as 'The Mathematics Problem', with students not demonstrating understanding of the subject. This paper will suggest that students are constructing different concept images in engineering and mathematics, based on their perception of either the use or exchange-value for the topics. Using a mixed methods approach, the paper compares 10 different types of concept image constructed by students, which suggests that familiar procedural images are preferred in mathematics. In contrast strategic and conceptual images develop for mechanics throughout the years of the programme, implying that different forms of competence are being constructed by students between the two subjects. The paper argues that this difference is attributed to the perceived use-value of mechanics in the career of the engineer, compared to the exchange-value associated with mathematics. Questions are raised about the relevance of current definitions of competence given that some routine mathematical operations previously performed by engineers are now being replaced by technology, in the new world of work.

  3. Attitude toward mathematics among the students at Nazarbayev University Foundation Year Programme

    Science.gov (United States)

    Karjanto, N.

    2017-08-01

    This article investigates the attitude toward mathematics among the students enrolled in the Foundation Year Programme at Nazarbayev University. The study is conducted quantitatively and an inventory developed by Tapia and Marsh II is adopted in this research. The inventory consists of 40 statements on the five-point Likert scale. Gender, specialization and final high school score in mathematics are collected. The number of valid returned questionnaires is 108. There are 55 males, 53 females, 73 Mathematical-Physics (MP), 22 Biology-Chemistry (BC) and 13 International Relations-Economics (IRE) students. Generally, they have a positive attitude toward mathematics, with the score mean and standard deviation are 3.999 and 0.531 out of five, respectively. We confirm a hypothesis on a positive correlation between previous high achievement in mathematics and favorable attitude toward it. The correlation value is r = 0.300, its effect size is medium and it is extremely significant (p-value = 0.0008 0.05). There is a very significant difference between students who specialize in IRE and MP in terms of their attitude toward mathematics (F(2, 105) = 5.6848, p-value = 0.0045 < 0.01).

  4. Implementing a new mathematics curriculum: Mathematics teachers’ beliefs and practices

    OpenAIRE

    Ernest Ampadu

    2013-01-01

    Mathematics has become a ‘critical filter’ in the social, economic and professional development of individuals and forms a core component of the school curriculum in most countries. It is upon this utilitarian nature of mathematics to the individual and the society as a whole that the school mathematics curriculum has been undergoing a number of restructuring over the last three decades. In Ghana, a new mathematics curriculum was introduced in September 2007 which aims at shifting the teachin...

  5. The Present Affairs and Issues of Research on Collaborative Learning in Mathematics Education

    OpenAIRE

    松島, 充

    2014-01-01

    In this research, at first, the previous work of collaborative learning and cooperative learning was investigated on learning sciences and cognitive psychology. It is clarified the difference of interde-pendent, of the epistemology and of the subject who construct knowledge. The secondly, investigation since 1990 of the collaborative learning research in mathematics educa-tion was conducted based on eight sorts of mathematics education academic journals, and the present affairs and the issues...

  6. Mathematics for physicists

    CERN Document Server

    Martin, B R

    2015-01-01

    Mathematics for Physicists is a relatively short volume covering all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses. Early chapters deliberately overlap with senior school mathematics, to a degree that will depend on the background of the individual reader, who may quickly skip over those topics with which he or she is already familiar. The rest of the book covers the mathematics that is usually compulsory for all students in their first two years of a typical university physics degree, plus a little more. There are worked examples throughout the text, and chapter-end problem sets. Mathematics for Physicists features: * Interfaces with modern school mathematics syllabuses * All topics usually taught in the first two years of a physics degree * Worked examples throughout * Problems in every chapter, with answers to selected questions at the end of the book and full solutions on a website This text will ...

  7. First-year engineering students’ use of their mathematics textbook - opportunities and constraints

    OpenAIRE

    Randahl, Mira

    2012-01-01

    Published version of an article in the journal: Mathematics Education Research Journal. Also available from the publlisher at: http://dx.doi.org/10.1007/s13394-012-0040-9 The role of the mathematics textbook at tertiary level has received limited exposure in previous research although it is likely that students work individually and that some of this work depends on the use of the textbook. The aim of this study was to investigate the process of approaching the textbook from epistemologica...

  8. Semiotic Scaffolding in Mathematics

    DEFF Research Database (Denmark)

    Johansen, Mikkel Willum; Misfeldt, Morten

    2015-01-01

    This paper investigates the notion of semiotic scaffolding in relation to mathematics by considering its influence on mathematical activities, and on the evolution of mathematics as a research field. We will do this by analyzing the role different representational forms play in mathematical...... cognition, and more broadly on mathematical activities. In the main part of the paper, we will present and analyze three different cases. For the first case, we investigate the semiotic scaffolding involved in pencil and paper multiplication. For the second case, we investigate how the development of new...... in both mathematical cognition and in the development of mathematics itself, but mathematical cognition cannot itself be reduced to the use of semiotic scaffolding....

  9. Calculus Problem Solving Behavior of Mathematic Education Students

    Science.gov (United States)

    Rizal, M.; Mansyur, J.

    2017-04-01

    The purpose of this study is to obtain a description of the problem-solving behaviour of mathematics education students. The attainment of the purpose consisted of several stages: (1) to gain the subject from the mathematic education of first semester students, each of them who has a high, medium, and low competence of mathematic case. (2) To give two mathematical problems with different characteristics. The first problem (M1), the statement does not lead to a resolution. The second problem (M2), a statement leads to problem-solving. (3) To explore the behaviour of problem-solving based on the step of Polya (Rizal, 2011) by way of thinking aloud and in-depth interviews. The obtained data are analysed as suggested by Miles and Huberman (1994) but at first, time triangulation is done or data’s credibility by providing equivalent problem contexts and at different times. The results show that the behavioral problem solvers (mathematic education students) who are capable of high mathematic competency (ST). In understanding M1, ST is more likely to pay attention to an image first, read the texts piecemeal and repeatedly, then as a whole and more focus to the sentences that contain equations, numbers or symbols. As a result, not all information can be received well. When understanding the M2, ST can link the information from a problem that is stored in the working memory to the information on the long-term memory. ST makes planning to the solution of M1 and M2 by using a formula based on similar experiences which have been ever received before. Another case when implementing the troubleshooting plans, ST complete the M1 according to the plan, but not all can be resolved correctly. In contrast to the implementation of the solving plan of M2, ST can solve the problem according to plan quickly and correctly. According to the solving result of M1 and M2, ST conducts by reading the job based on an algorithm and reasonability. Furthermore, when SS and SR understand the

  10. TIMSS 2003: Relating dimensions of mathematics attitude to mathematics achievement

    Directory of Open Access Journals (Sweden)

    Kadijević Đorđe

    2008-01-01

    Full Text Available This study, which used a sample of 137,346 students from thirty three countries that participated in the TIMSS 2003 project in the eighth grade, examined the features of the individual and collective relations of three dimensions of mathematics attitude to mathematics achievement (MA, searching for the dimension mostly related to that achievement. The three dimensions of mathematics attitude were self-confidence in learning mathematics (SCLM, liking mathematics (LM and usefulness of mathematics (UM. By utilizing psychometrically valid and reliable measures of the three dimensions, it was found that: (1 each dimension of mathematics attitude alone was positively related to MA for almost all thirty three countries; (2 SCLM was primarily related to MA for thirty one countries; (3 when the two other dimensions were held constant, SCLM was positively related to MA for thirty three countries, LM was negatively related to MA for thirty countries, whereas UM was not related to MA for twenty one countries; (4 positive collective relationships of SCLM, LM and UM to MA considerably varied from country to country. Implications for research and practice are included.

  11. Philosophy of mathematics

    CERN Document Server

    Gabbay, Dov M; Woods, John

    2009-01-01

    One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mat

  12. Einstein's Theory A Rigorous Introduction for the Mathematically Untrained

    CERN Document Server

    Grøn, Øyvind

    2011-01-01

    This book provides an introduction to the theory of relativity and the mathematics used in its processes. Three elements of the book make it stand apart from previously published books on the theory of relativity. First, the book starts at a lower mathematical level than standard books with tensor calculus of sufficient maturity to make it possible to give detailed calculations of relativistic predictions of practical experiments. Self-contained introductions are given, for example vector calculus, differential calculus and integrations. Second, in-between calculations have been included, making it possible for the non-technical reader to follow step-by-step calculations. Thirdly, the conceptual development is gradual and rigorous in order to provide the inexperienced reader with a philosophically satisfying understanding of the theory.  Einstein's Theory: A Rigorous Introduction for the Mathematically Untrained aims to provide the reader with a sound conceptual understanding of both the special and genera...

  13. Essentials of Mathematica With Applications to Mathematics and Physics

    CERN Document Server

    Boccara, Nino

    2007-01-01

    Essentials of Mathematica: With Applications to Mathematics and Physics, based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergraduate and graduate students, teaches how to use Mathematica to solve a wide variety problems in mathematics and physics. The text assumes no previous exposure to Mathematica. It is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy-to-read Mathematica programs. It includes many detailed graphics, with instructions to students on how to achieve similar results. The aim of Essentials of Mathematica is to provide the reader with Mathematica proficiency quickly and efficiently. The first part, in which the reader learns how to use a variety of Mathematica commands, avoids long discussions and overly sophisticated techniques. The second part covers a broad range of applications in physics and applied mathematics, including negative and complex bases, the double pendulum, fractals,...

  14. Introduction to the mathematics of finance from risk management to options pricing

    CERN Document Server

    Roman, Steven

    2004-01-01

    The Mathematics of Finance has become a hot topic in applied mathematics ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for upper division undergraduate or beginning graduate students in mathematics, finance or economics. With the exception of an optional chapter on the Capital Asset Pricing Model, the book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model. The final chapter is devoted to American options. The mathematics is not watered down but is appropriate for the intended audience. No measure theory is used and only a small amount of linear algebra is required. All necessary probability theory is developed in several chapters throughout the book, on a "need-to-know" basis. No background in finance is required, sinc...

  15. Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.

    Science.gov (United States)

    Suppes, Patrick

    This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

  16. PhiMSAMP: philosophy of mathematics: sociological aspects and mathematical practice

    NARCIS (Netherlands)

    Löwe, B.; Müller, T.

    2010-01-01

    Philosophy of mathematics is moving in a new direction: away from a foundationalism in terms of formal logic and traditional ontology, and towards a broader range of approaches that are united by a focus on mathematical practice. The scientific research network PhiMSAMP (Philosophy of Mathematics:

  17. Mathematical Creativity and Mathematical Aptitude: A Cross-Lagged Panel Analysis

    Science.gov (United States)

    Tyagi, Tarun Kumar

    2016-01-01

    Cross-lagged panel correlation (CLPC) analysis has been used to identify causal relationships between mathematical creativity and mathematical aptitude. For this study, 480 8th standard students were selected through a random cluster technique from 9 intermediate and high schools of Varanasi, India. Mathematical creativity and mathematical…

  18. Representations of Mathematics, their teaching and learning: an exploratory study

    Directory of Open Access Journals (Sweden)

    Maria Margarida Graça

    2004-03-01

    Full Text Available This work describes an exploratory study, the first of the four phases of a more inclusive research, which aims at understanding the way to promote, in a Mathematics teachers’ group, a representational evolution leading to a practice that allows a Mathematical meaningful learning of Mathematics. The methodology of this study is qualitative. Data gathering was based on questioning; all the subjects of the sample (n=48 carried out a projective task (a hierarchical evocation test and answered a written individual questionnaire. Data analysis was based in a set of categories previously defined. The main purpose of this research was to identify, to characterize and to describe the representations of Mathematics, their teaching and learning, in a group of 48 subjects, from different social groups, in order to get indicators for the construction of the instruments to be used in to the next phases of the research. The main results of this study are the following: (1 we were able to identify and characterize different representations of the teaching and learning of Mathematics, in what respects its epistemological, pedagogical, emotional and sociocultural dimensions; (2 we were also able to identify limitations, difficulties and items to be included or rephrased in the instruments used.

  19. The role of mathematical models in understanding pattern formation in developmental biology.

    Science.gov (United States)

    Umulis, David M; Othmer, Hans G

    2015-05-01

    In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

  20. A synthesis of mathematical and cognitive performances of students with mathematics learning disabilities.

    Science.gov (United States)

    Shin, Mikyung; Bryant, Diane Pedrotty

    2015-01-01

    The purpose of this study was to synthesize the findings from 23 articles that compared the mathematical and cognitive performances of students with mathematics learning disabilities (LD) to (a) students with LD in mathematics and reading, (b) age- or grade-matched students with no LD, and (c) mathematical-ability-matched younger students with no LD. Overall results revealed that students with mathematics LD exhibited higher word problem-solving abilities and no significant group differences on working memory, long-term memory, and metacognition measures compared to students with LD in mathematics and reading. Findings also revealed students with mathematics LD demonstrated significantly lower performance compared to age- or grade-matched students with no LD on both mathematical and cognitive measures. Comparison between students with mathematics LD and younger students with no LD revealed mixed outcomes on mathematical measures and generally no significant group differences on cognitive measures. © Hammill Institute on Disabilities 2013.

  1. Improved methods for the mathematically controlled comparison of biochemical systems

    Directory of Open Access Journals (Sweden)

    Schwacke John H

    2004-06-01

    Full Text Available Abstract The method of mathematically controlled comparison provides a structured approach for the comparison of alternative biochemical pathways with respect to selected functional effectiveness measures. Under this approach, alternative implementations of a biochemical pathway are modeled mathematically, forced to be equivalent through the application of selected constraints, and compared with respect to selected functional effectiveness measures. While the method has been applied successfully in a variety of studies, we offer recommendations for improvements to the method that (1 relax requirements for definition of constraints sufficient to remove all degrees of freedom in forming the equivalent alternative, (2 facilitate generalization of the results thus avoiding the need to condition those findings on the selected constraints, and (3 provide additional insights into the effect of selected constraints on the functional effectiveness measures. We present improvements to the method and related statistical models, apply the method to a previously conducted comparison of network regulation in the immune system, and compare our results to those previously reported.

  2. Mathematics education practice in Nigeria: Its impact in a post-colonial era

    Science.gov (United States)

    Enime, Noble O. J.

    document in Chapter IV. The emerging themes suggested that the influence Nigerian Colonial era Mathematics Education Practice had on the independent Nigerian state is yet to completely diminish. The following are among the conclusions drawn n from the study. Student's enrollment age appeared to generally have an influence over the performance in mathematics at all levels of school. Also, students that had encouraging parents were likely to enjoy learning mathematics, while students that attended mission schools were likely to be successful in mathematics. The students whose parents were educated were likely to be successful in Mathematics.

  3. Additive and Multiplicative Effects of Working Memory and Test Anxiety on Mathematics Performance in Grade 3 Students

    Science.gov (United States)

    Korhonen, Johan; Nyroos, Mikaela; Jonsson, Bert; Eklöf, Hanna

    2018-01-01

    The aim of this study was to investigate the interplay between test anxiety and working memory (WM) on mathematics performance in younger children. A sample of 624 grade 3 students completed a test battery consisting of a test anxiety scale, WM tasks and the Swedish national examination in mathematics for grade 3. The main effects of test anxiety…

  4. Effects of Gender, Mathematics Anxiety and Achievement Motivation on College Students’ Achievement in Mathematics

    Directory of Open Access Journals (Sweden)

    Ajogbeje Oke James

    2013-07-01

    Full Text Available The urge to excel or perform maximally in mathematics varies from individual to individual because achievement motivation is often developed or learnt during socialization and learning experiences. The study examined the relationship between College of Education students’ achievement motivation and mathematics achievement, correlation coefficient between mathematics anxiety and college students’ achievement motivation as well as mathematics anxiety and mathematics achievement. The sample, 268 College of Education students offering mathematics as one of their subject combination, was selected using purposive sampling techniques. Three research instruments namely: Mathematics Anxiety Scale (MAS, Achievement Motivation Scale (AMS and Mathematics Achievement Test (MAT were used to collect data for the study. Data collected for the study were analyzed using correlational analysis and ANOVA. The results showed that a significantly low negative correlation coefficient existed between mathematics anxiety and mathematics achievement. There is a negative and significant correlation coefficient between mathematics anxiety and achievement motivation. Similarly, a positive and significant correlation coefficient also exists between achievement motivation and mathematics achievement. Based on the findings of the study, it was recommended that mathematics teachers should adopt activity based strategies and conducive learning environment in order to reduce college students’ anxieties in mathematics learning.

  5. Does the cognitive reflection test measure cognitive reflection? A mathematical modeling approach.

    Science.gov (United States)

    Campitelli, Guillermo; Gerrans, Paul

    2014-04-01

    We used a mathematical modeling approach, based on a sample of 2,019 participants, to better understand what the cognitive reflection test (CRT; Frederick In Journal of Economic Perspectives, 19, 25-42, 2005) measures. This test, which is typically completed in less than 10 min, contains three problems and aims to measure the ability or disposition to resist reporting the response that first comes to mind. However, since the test contains three mathematically based problems, it is possible that the test only measures mathematical abilities, and not cognitive reflection. We found that the models that included an inhibition parameter (i.e., the probability of inhibiting an intuitive response), as well as a mathematical parameter (i.e., the probability of using an adequate mathematical procedure), fitted the data better than a model that only included a mathematical parameter. We also found that the inhibition parameter in males is best explained by both rational thinking ability and the disposition toward actively open-minded thinking, whereas in females this parameter was better explained by rational thinking only. With these findings, this study contributes to the understanding of the processes involved in solving the CRT, and will be particularly useful for researchers who are considering using this test in their research.

  6. The Mathematics Education Debates: Preparing Students to Become Professionally Active Mathematics Teachers

    Science.gov (United States)

    Munakata, Mika

    2010-01-01

    The Mathematics Education Debate is an assignment designed for and implemented in an undergraduate mathematics methods course for prospective secondary school mathematics teachers. For the assignment, students read and analyze current research and policy reports related to mathematics education, prepare and present their positions, offer…

  7. The Use of a Bar Model Drawing to Teach Word Problem Solving to Students with Mathematics Difficulties

    Science.gov (United States)

    Morin, Lisa L.; Watson, Silvana M. R.; Hester, Peggy; Raver, Sharon

    2017-01-01

    For students with mathematics difficulties (MD), math word problem solving is especially challenging. The purpose of this study was to examine the effects of a problem-solving strategy, bar model drawing, on the mathematical problem-solving skills of students with MD. The study extended previous research that suggested that schematic-based…

  8. Mathematical modeling of reciprocating pump

    International Nuclear Information System (INIS)

    Lee, Jong Kyeom; Jung, Jun Ki; Chai, Jang Bom; Lee, Jin Woo

    2015-01-01

    A new mathematical model is presented for the analysis and diagnosis of a high-pressure reciprocating pump system with three cylinders. The kinematic and hydrodynamic behaviors of the pump system are represented by the piston displacements, volume flow rates and pressures in its components, which are expressed as functions of the crankshaft angle. The flow interaction among the three cylinders, which was overlooked in the previous models, is considered in this model and its effect on the cylinder pressure profiles is investigated. The tuning parameters in the mathematical model are selected, and their values are adjusted to match the simulated and measured cylinder pressure profiles in each cylinder in a normal state. The damage parameter is selected in an abnormal state, and its value is adjusted to match the simulated and ensured pressure profiles under the condition of leakage in a valve. The value of the damage parameter over 300 cycles is calculated, and its probability density function is obtained for diagnosis and prognosis on the basis of the probabilistic feature of valve leakage.

  9. Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

    Science.gov (United States)

    Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio

    2016-01-01

    This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…

  10. Authenticity of Mathematical Modeling

    Science.gov (United States)

    Tran, Dung; Dougherty, Barbara J.

    2014-01-01

    Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…

  11. Effects of Vigorous Intensity Physical Activity on Mathematics Test Performance

    Science.gov (United States)

    Phillips, David S.; Hannon, James C.; Castelli, Darla M.

    2015-01-01

    The effect of an acute bout of physical activity on academic performance in school-based settings is under researched. The purpose of this study was to examine associations between a single, vigorous (70-85%) bout of physical activity completed during physical education on standardized mathematics test performance among 72, eighth grade students…

  12. Using video games to combine learning and assessment in mathematics education

    Directory of Open Access Journals (Sweden)

    Kristian Juha Mikael Kiili

    2015-12-01

    Full Text Available One problem with most education systems is that learning and (summative assessment are generally treated as quite separate things in schools. We argue that video games can provide an opportunity to combine these processes in an engaging and effective way. The present study focuses on investigating the effectiveness and the assessment power of two different mathematics video games, Semideus and Wuzzit Trouble. In the current study, we validated the Semideus game as a rational number test instrument. We used it as a pre- and a post-test for a three-hour intervention in which we studied the effectiveness of Wuzzit Trouble, a game built on whole number arithmetic and designed to enhance mathematical thinking and problem solving skills. The results showed that (1 games can be used to assess mathematical knowledge validly, and (2 even short game-based interventions can be very effective. Based on the results, we argue that game-based assessment can create a more complete picture of mathematical knowledge than simply measuring students' accuracy, providing indicators of student misconceptions and conceptual change processes

  13. Pre-Service Secondary Mathematics Teachers' Reflections on Good and Bad Mathematics Teaching

    Science.gov (United States)

    Dayal, Hem Chand

    2013-01-01

    Researchers suggest that teachers' beliefs about teaching are strongly influenced by their personal experiences with mathematics. This study aimed to explore Pacific Island pre-service secondary mathematics teachers' perceptions about good and bad mathematics teachers. Thirty pre-service teachers, enrolled in a mathematics teaching methods course…

  14. The Effect of Realistic Mathematics Education Approach on Students' Achievement And Attitudes Towards Mathematics

    Directory of Open Access Journals (Sweden)

    Effandi Zakaria

    2017-02-01

    Full Text Available This study was conducted to determine the effect of Realistic Mathematics Education Approach on mathematics achievement and student attitudes towards mathematics. This study also sought determine the relationship between student achievement and attitudes towards mathematics. This study used a quasi-experimental design conducted on 61 high school students at SMA Unggul Sigli. Students were divided into two groups, the treatment group $(n = 30$ namely, the Realistic Mathematics Approach group (PMR and the control group $(n = 31$ namely, the traditional group. This study was conducted for six weeks. The instruments used in this study were the achievement test and the attitudes towards mathematics questionnaires. Data were analyzed using SPSS. To determine the difference in mean achievement and attitudes between the two groups, data were analyzed using one-way ANOVA test. The result showed significant differences between the Realistic Mathematics Approach and the traditional approach in terms of achievement. The study showed no significant difference between the Realistic Mathematics Approach and the traditional approach in term of attitudes towards mathematics. It can be concluded that the use of realistic mathematics education approach enhanced students' mathematics achievement, but not attitudes towards mathematics. The Realistic Mathematics Education Approach encourage students to participate actively in the teaching and learning of mathematics. Thus, Realistic Mathematics Education Approach is an appropriate methods to improve the quality of teaching and learning process.

  15. Experiencing mathematics what do we do, when we do mathematics?

    CERN Document Server

    Hersh, Reuben

    2014-01-01

    The question "What am I doing?" haunts many creative people, researchers, and teachers. Mathematics, poetry, and philosophy can look from the outside sometimes as ballet en pointe, and at other times as the flight of the bumblebee. Reuben Hersh looks at mathematics from the inside; he collects his papers written over several decades, their edited versions, and new chapters in his book Experiencing Mathematics, which is practical, philosophical, and in some places as intensely personal as Swann's madeleine. -Yuri Manin, Max Planck Institute, Bonn, Germany What happens when mid-career a mathemat

  16. Mathematical simulation of contaminant distribution in and around the uranium mill tailing piles, Riverton, Wyoming

    International Nuclear Information System (INIS)

    Narasimhan, T.N.; Tokunaga, T.; White, A.F.; Smith, A.R.

    1983-02-01

    As part of the Research and Development phase of the Uranium Mill Tailings Remedial Action (UMTRA) program, the Lawrence Berkeley Laboratory (LBL) has set itself the goal of explaining the physico-chemical evolution of the Riverton site on the basis of the already collected field data at the site (Tokunaga and Narasimhan, 1982, Smith and Moed, 1982; White et al., 1984). The predictive aspects as well as addressing the question of critical quantity of field data have to be considered during the design phase of the project as a joint effort between the LBL team and the construction engineers. At the present time, LBL is in the process of completing the Research and Development phase of the work. As of this writing, the development of an appropriate set of mathematical models has been completed. The computations of the soil-water regime at the upper tailings surface, involving climatological factors is nearing completion. Computations of chemical transport are still in progress. This paper is devoted to a description of the key mathematical issues, the mathematical models that are needed to address these issues and a discussion of the model results pertaining to the soil water regime at the tailings-atmosphere interface. 11 references, 3 figures

  17. Structured Matrix Completion with Applications to Genomic Data Integration.

    Science.gov (United States)

    Cai, Tianxi; Cai, T Tony; Zhang, Anru

    2016-01-01

    Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. We provide theoretical justification for the proposed SMC method and derive lower bound for the estimation errors, which together establish the optimal rate of recovery over certain classes of approximately low-rank matrices. Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several ovarian cancer genomic studies with different extent of genomic measurements, which enables us to construct more accurate prediction rules for ovarian cancer survival.

  18. Evaluation of the Effectiveness of a Tablet Computer Application (App) in Helping Students with Visual Impairments Solve Mathematics Problems

    Science.gov (United States)

    Beal, Carole R.; Rosenblum, L. Penny

    2018-01-01

    Introduction: The authors examined a tablet computer application (iPad app) for its effectiveness in helping students studying prealgebra to solve mathematical word problems. Methods: Forty-three visually impaired students (that is, those who are blind or have low vision) completed eight alternating mathematics units presented using their…

  19. Stable Same-Sex Friendships with Higher Achieving Partners Promote Mathematical Reasoning in Lower Achieving Primary School Children

    Science.gov (United States)

    DeLay, Dawn; Laursen, Brett; Kiuru, Noona; Poikkeus, Anna-Maija; Aunola, Kaisa; Nurmi, Jari-Erik

    2015-01-01

    This study is designed to investigate friend influence over mathematical reasoning in a sample of 374 children in 187 same-sex friend dyads (184 girls in 92 friendships; 190 boys in 95 friendships). Participants completed surveys that measured mathematical reasoning in the 3rd grade (approximately 9 years old) and one year later in the 4th grade (approximately 10 years old). Analyses designed for dyadic data (i.e., longitudinal Actor-Partner Interdependence Models) indicated that higher achieving friends influenced the mathematical reasoning of lower achieving friends, but not the reverse. Specifically, greater initial levels of mathematical reasoning among higher achieving partners in the 3rd grade predicted greater increases in mathematical reasoning from 3rd grade to 4th grade among lower achieving partners. These effects held after controlling for peer acceptance and rejection, task avoidance, interest in mathematics, maternal support for homework, parental education, length of the friendship, and friendship group norms on mathematical reasoning. PMID:26402901

  20. Racial Differences in Mathematics Test Scores for Advanced Mathematics Students

    Science.gov (United States)

    Minor, Elizabeth Covay

    2016-01-01

    Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be…

  1. Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

    Science.gov (United States)

    Karali, Diren; Durmus, Soner

    2015-01-01

    The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

  2. Mathematical physics applied mathematics for scientists and engineers

    CERN Document Server

    Kusse, Bruce R

    2006-01-01

    What sets this volume apart from other mathematics texts is its emphasis on mathematical tools commonly used by scientists and engineers to solve real-world problems. Using a unique approach, it covers intermediate and advanced material in a manner appropriate for undergraduate students. Based on author Bruce Kusse's course at the Department of Applied and Engineering Physics at Cornell University, Mathematical Physics begins with essentials such as vector and tensor algebra, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential and integral equations, and solutions to Laplace's equations

  3. Why do early mathematics skills predict later reading? The role of mathematical language.

    Science.gov (United States)

    Purpura, David J; Logan, Jessica A R; Hassinger-Das, Brenna; Napoli, Amy R

    2017-09-01

    A growing body of evidence indicates that the development of mathematics and literacy skills is highly related. The importance of literacy skills-specifically language-for mathematics development has been well rationalized. However, despite several prominent studies indicating that mathematics skills are highly predictive of literacy development, the reason for this relation is not well understood. The purpose of this study was to identify how and why early mathematics is predictive of early literacy development. Participants included 125 preschool children 3-5 years old (M = 4 years 3 months). Participants were assessed on mathematics, literacy, and cognitive measures in both the fall and spring of their preschool year. Mediation analyses indicated that the relation between early mathematics and literacy skills is mediated by children's mathematical language skills. These findings suggest that, in prior research identifying mathematical performance as a significant predictor of later literacy skills, mathematical performance may have acted only as a proxy measure for more complex language skills such as those assessed on a mathematical language measure. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

  4. An Invitation to Mathematics

    CERN Document Server

    Schleicher, Dierk

    2011-01-01

    This "Invitation to Mathematics" consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is

  5. The Mathematical Event: Mapping the Axiomatic and the Problematic in School Mathematics

    Science.gov (United States)

    de Freitas, Elizabeth

    2013-01-01

    Traditional philosophy of mathematics has been concerned with the nature of mathematical objects rather than events. This traditional focus on reified objects is reflected in dominant theories of learning mathematics whereby the learner is meant to acquire familiarity with ideal mathematical objects, such as number, polygon, or tangent. I argue…

  6. Magical mathematics the mathematical ideas that animate great magic tricks

    CERN Document Server

    Diaconis, Persi

    2012-01-01

    Magical Mathematics reveals the secrets of amazing, fun-to-perform card tricks--and the profound mathematical ideas behind them--that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge. For example, the Gilbreath Principle--a fantastic effect where the cards remain in control despite being shuffled--is found to share an intimate connection with the Mandelbrot set. Other card tricks link to the mathematical secrets of combinatorics, graph theory, number theory, topology, the Riemann hypothesis, and even Fermat's last theorem.

  7. Mathematical modelling

    CERN Document Server

    2016-01-01

    This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

  8. Mathematical modeling

    CERN Document Server

    Eck, Christof; Knabner, Peter

    2017-01-01

    Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.

  9. Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

    Science.gov (United States)

    E Siswono, T. Y.; Kohar, A. W.; Hartono, S.

    2017-02-01

    This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.

  10. Mathematics Connection: Contact

    African Journals Online (AJOL)

    Principal Contact. Dr. Kofi Mereku Executive Editor Department of Mathematics Education, UCE Mathematical Association of Ghana, C/o Department of Mathematics Education University College of Education of Winneba P. O. Box 25, Winneba, Ghana Phone: +233244961318. Email: dkmereku@uew.edu.gh ...

  11. Middle School Mathematics Students' Perspectives on the Study of Mathematics

    Science.gov (United States)

    Vaughn, Christy H.

    2012-01-01

    This qualitative study addressed the perceptions toward the study of mathematics by middle school students who had formerly been in a remedial mathematics program. The purpose of the study was to explore the past experiences of nine students in order to determine what is needed for them to feel successful in mathematics. The conceptual framework…

  12. Improving on the American Dream: Mathematics Pathways to Student Success

    Science.gov (United States)

    Clyburn, Gay M.

    2013-01-01

    Developmental mathematics is one of the most serious barriers to educational and economic achievement. Over 60 percent of all students entering community colleges in the United States are required to complete remedial/developmental courses as a first step towards earning associate's or bachelor's degrees. Then, to earn a degree,…

  13. Mathematics disorder

    Science.gov (United States)

    ... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...

  14. Ability Of Mathematical Reasoning in SMK 10th Grade with LAPS- Heuristic using Performance Assessment

    Directory of Open Access Journals (Sweden)

    Aulia Nur Arivina

    2017-11-01

    Full Text Available The purposes of this research are: (1 Test the learning with LAPS-Heuristic model using performance assessment on 10th grade of Trigonometry material is complete, (2 to test the difference of students' mathematical reasoning ability on 10th grade of Trigonometry material between the learning model of LAPS-Heuristic using performance assessment, LAPS-Heuristic learning model with Expository learning model, (3 test the ability of mathematical reasoning with learning model of LAPS-Heuristik on Trigonometry material of SMK on 10th grade using performance assessment is increase. This is a quantitative research. The population is students of 10th grade of SMK 10 Semarang academic year 2016/2017 and the subject of research is selected by clustering random sampling. The results show that (1 Learning by model LAPS-Heuristic using performance assessment on 10th grade of Trigonometry material is complete (2 there are differences in students' mathematical reasoning ability on 10th grade of Trigonometry materials between LAPS-Heuristic learning model using performance assessment, LAPS-Heuristic learning model, and Expository learning model, (3 The ability of mathematical reasoning with learning model of LAPS-Heuristic on Trigonometry material of SMK class X using performance assessment increased.

  15. Learning via problem solving in mathematics education

    Directory of Open Access Journals (Sweden)

    Piet Human

    2009-09-01

    Full Text Available Three forms of mathematics education at school level are distinguished: direct expository teaching with an emphasis on procedures, with the expectation that learners will at some later stage make logical and functional sense of what they have learnt and practised (the prevalent form, mathematically rigorous teaching in terms of fundamental mathematical concepts, as in the so-called “modern mathematics” programmes of the sixties, teaching and learning in the context of engaging with meaningful problems and focused both on learning to become good problem solvers (teaching for problem solving andutilising problems as vehicles for the development of mathematical knowledge andproficiency by learners (problem-centred learning, in conjunction with substantialteacher-led social interaction and mathematical discourse in classrooms.Direct expository teaching of mathematical procedures dominated in school systems after World War II, and was augmented by the “modern mathematics” movement in the period 1960-1970. The latter was experienced as a major failure, and was soon abandoned. Persistent poor outcomes of direct expository procedural teaching of mathematics for the majority of learners, as are still being experienced in South Africa, triggered a world-wide movement promoting teaching mathematics for and via problem solving in the seventies and eighties of the previous century. This movement took the form of a variety of curriculum experiments in which problem solving was the dominant classroom activity, mainly in the USA, Netherlands, France and South Africa. While initially focusing on basic arithmetic (computation with whole numbers and elementary calculus, the problem-solving movement started to address other mathematical topics (for example, elementary statistics, algebra, differential equations around the turn of the century. The movement also spread rapidly to other countries, including Japan, Singapore and Australia. Parallel with the

  16. Mathematical theory of compressible fluid flow

    CERN Document Server

    von Mises, Richard

    2004-01-01

    A pioneer in the fields of statistics and probability theory, Richard von Mises (1883-1953) made notable advances in boundary-layer-flow theory and airfoil design. This text on compressible flow, unfinished upon his sudden death, was subsequently completed in accordance with his plans, and von Mises' first three chapters were augmented with a survey of the theory of steady plane flow. Suitable as a text for advanced undergraduate and graduate students - as well as a reference for professionals - Mathematical Theory of Compressible Fluid Flow examines the fundamentals of high-speed flows, with

  17. 1st Joint India-AMS Meeting in Mathematics : History of Indian Mathematics at the AMS-India Mathematics Conference

    CERN Document Server

    Sridharan, R; Srinivas, M

    2005-01-01

    This volume consists of a collection of articles based on lectures given by scholars from India, Europe and USA at the sessions on 'History of Indian Mathematics' at the AMS-India mathematics conference in Bangalore during December 2003. These articles cover a wide spectrum of themes in Indian mathematics. They begin with the mathematics of the ancient period dealing with Vedic Prosody and Buddhist Logic, move on to the work of Brahmagupta, of Bhaskara, and that of the mathematicians of the Kerala school of the classical and medieval period, and end with the work of Ramanaujan, and Indian contributions to Quantum Statistics during the modern era. The volume should be of value to those interested in the history of mathematics.

  18. Mathematical concepts

    CERN Document Server

    Jost, Jürgen

    2015-01-01

    The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: ·         simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure ·         by itself as a first introduction to abstract mathematics ·         together with existing textbooks, to put their results into a more general perspective ·         to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detaile...

  19. Are OBE‐trained learners ready for university mathematics?

    Directory of Open Access Journals (Sweden)

    Johann Engelbrecht

    2010-09-01

    Full Text Available The 2009 intake of university students were the first to have received complete school education within the recently implemented Outcomes‐Based Education (OBE system. A feature of the matriculation examination results of these students was the exceptionally high Grade 12 marks for Mathematics. This paper addresses the question of how the 2009‐ intake of students performed at university with respect to general performance, general attributes, mathematical attributes and content related attributes. It appears that these students are better prepared with respect to personal attributes such as confidence. However, in many instances they are weaker than their predecessors with respect to mathematical and content related attributes. Yet, there are positive indications that these students adapt and improve over a semester. We make some suggestions on how to make the transition from secondary to university mathematics somewhat smoother.

  20. Intentional and Automatic Numerical Processing as Predictors of Mathematical Abilities in Primary School Children

    Directory of Open Access Journals (Sweden)

    Violeta ePina

    2015-03-01

    Full Text Available Previous studies have suggested that numerical processing relates to mathematical performance, but it seems that such relationship is more evident for intentional than for automatic numerical processing. In the present study we assessed the relationship between the two types of numerical processing and specific mathematical abilities in a sample of 109 children in grades 1 to 6. Participants were tested in an ample range of mathematical tests and also performed both a numerical and a size comparison task. The results showed that numerical processing related to mathematical performance only when inhibitory control was involved in the comparison tasks. Concretely, we found that intentional numerical processing, as indexed by the numerical distance effect in the numerical comparison task, was related to mathematical reasoning skills only when the task-irrelevant dimension (the physical size was incongruent; whereas automatic numerical processing, indexed by the congruency effect in the size comparison task, was related to mathematical calculation skills only when digits were separated by small distance. The observed double dissociation highlights the relevance of both intentional and automatic numerical processing in mathematical skills, but when inhibitory control is also involved.

  1. The Interaction of Procedural Skill, Conceptual Understanding and Working Memory in Early Mathematics Achievement

    Directory of Open Access Journals (Sweden)

    Camilla Gilmore

    2017-12-01

    Full Text Available Large individual differences in children’s mathematics achievement are observed from the start of schooling. Previous research has identified three cognitive skills that are independent predictors of mathematics achievement: procedural skill, conceptual understanding and working memory. However, most studies have only tested independent effects of these factors and failed to consider moderating effects. We explored the procedural skill, conceptual understanding and working memory capacity of 75 children aged 5 to 6 years as well as their overall mathematical achievement. We found that, not only were all three skills independently associated with mathematics achievement, but there was also a significant interaction between them. We found that levels of conceptual understanding and working memory moderated the relationship between procedural skill and mathematics achievement such that there was a greater benefit of good procedural skill when associated with good conceptual understanding and working memory. Cluster analysis also revealed that children with equivalent levels of overall mathematical achievement had differing strengths and weaknesses across these skills. This highlights the importance of considering children’s skill profile, rather than simply their overall achievement.

  2. Teaching secondary mathematics

    CERN Document Server

    Rock, David

    2013-01-01

    Solidly grounded in up-to-date research, theory and technology,?Teaching Secondary Mathematics?is a practical, student-friendly, and popular text for secondary mathematics methods courses. It provides clear and useful approaches for mathematics teachers, and shows how concepts typically found in a secondary mathematics curriculum can be taught in a positive and encouraging way. The thoroughly revised fourth edition combines this pragmatic approach with truly innovative and integrated technology content throughout. Synthesized content between the book and comprehensive companion websi

  3. Appraising Lexical Bundles in Mathematics Classroom Discourse: Obligation and Choice

    Science.gov (United States)

    Herbel-Eisenmann, Beth; Wagner, David

    2010-01-01

    Working from a large corpus of transcripts from secondary mathematics classrooms, we identify patterns of speech that encode interpersonal positioning. We extend our analysis from a previous article (Herbel-Eisenmann, Wagner & Cortes, Educ Stud Math, 2010, in press), in which we introduced a concept from corpus linguistics--a "lexical bundle,"…

  4. DISCRETE MATHEMATICS/NUMBER THEORY

    OpenAIRE

    Mrs. Manju Devi*

    2017-01-01

    Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...

  5. An interpolation problem for completely positive maps on matrix algebras: solvability and parametrization

    Czech Academy of Sciences Publication Activity Database

    Ambrozie, Calin-Grigore; Gheondea, A.

    2015-01-01

    Roč. 63, č. 4 (2015), s. 826-851 ISSN 0308-1087 R&D Projects: GA AV ČR IAA100190903 Institutional support: RVO:67985840 Keywords : Choi matrix * completely positive * density matrix Subject RIV: BA - General Mathematics Impact factor: 0.761, year: 2015 http://www.tandfonline.com/doi/abs/10.1080/03081087.2014.903253

  6. Mathematics Teaching Today

    Science.gov (United States)

    Martin, Tami S.; Speer, William R.

    2009-01-01

    This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…

  7. Do girls really experience more anxiety in mathematics?

    Science.gov (United States)

    Goetz, Thomas; Bieg, Madeleine; Lüdtke, Oliver; Pekrun, Reinhard; Hall, Nathan C

    2013-10-01

    Two studies were conducted to examine gender differences in trait (habitual) versus state (momentary) mathematics anxiety in a sample of students (Study 1: N = 584; Study 2: N = 111). For trait math anxiety, the findings of both studies replicated previous research showing that female students report higher levels of anxiety than do male students. However, no gender differences were observed for state anxiety, as assessed using experience-sampling methods while students took a math test (Study 1) and attended math classes (Study 2). The discrepant findings for trait versus state math anxiety were partly accounted for by students' beliefs about their competence in mathematics, with female students reporting lower perceived competence than male students despite having the same average grades in math. Implications for educational practices and the assessment of anxiety are discussed.

  8. Perspectives on mathematical practices bringing together philosophy of mathematics, sociology of mathematics, and mathematics education

    CERN Document Server

    van Kerkhove, Bart

    2007-01-01

    Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the ""classical"" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the ""products"" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next. The editors of this book felt the urge, first of all, to bring together the widest variety of aut

  9. Ability Of Mathematical Reasoning in SMK 10th Grade with LAPS- Heuristic using Performance Assessment

    OpenAIRE

    Aulia Nur Arivina; Masrukan Masrukan; Ardhi Prabowo

    2017-01-01

    The purposes of this research are: (1) Test the learning with LAPS-Heuristic model using performance assessment on 10th grade of Trigonometry material is complete, (2) to test the difference of students' mathematical reasoning ability on 10th grade of Trigonometry material between the learning model of LAPS-Heuristic using performance assessment, LAPS-Heuristic learning model with Expository learning model, (3) test the ability of mathematical reasoning with learning model of LAPS-Heuristik o...

  10. Mathematical models of electrical network systems theory and applications : an introduction

    CERN Document Server

    Kłos, Andrzej

    2017-01-01

    This book is for all those who are looking for a non-conventional mathematical model of electrical network systems. It presents a modern approach using linear algebra and derives various commonly unknown quantities and interrelations of network analysis. It also explores some applications of algebraic network model of and solves some examples of previously unsolved network problems in planning and operation of network systems. Complex mathematical aspects are illustrated and described in a way that is understandable for non-mathematicians. Discussing interesting concepts and practically useful methods of network analysis, it is a valuable resource for lecturers, students, engineers and research workers. .

  11. Developmental Mathematics Students: Who are They and What is Their Mathematics Self-Efficacy?

    OpenAIRE

    Baxter, Ryan; Bates, Alan; Al-Bataineh, Adel Tawfig

    2017-01-01

    The purpose of this quantitative study was to determine differences indevelopmental mathematics students’ self-efficacy within the demographic datafrom the survey. Data from a sample of 240 Intermediate Algebra students at asingle four-year university using the Mathematics Self-Efficacy Resultsindicate that males possess higher levels of mathematics self-efficacy andconfidence with their mathematical abilities than females. Students whocompleted a lower developmental mathematics course prior ...

  12. Algorithmic mathematics

    CERN Document Server

    Hougardy, Stefan

    2016-01-01

    Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.

  13. ANS acuity and mathematics ability in preschoolers from low-income homes: contributions of inhibitory control.

    Science.gov (United States)

    Fuhs, Mary Wagner; McNeil, Nicole M

    2013-01-01

    Recent findings by Libertus, Feigenson, and Halberda (2011) suggest that there is an association between the acuity of young children's approximate number system (ANS) and their mathematics ability before exposure to instruction in formal schooling. The present study examined the generalizability and validity of these findings in a sample of preschoolers from low-income homes. Children attending Head Start (N = 103) completed measures to assess ANS acuity, mathematics ability, receptive vocabulary, and inhibitory control. Results showed only a weak association between ANS acuity and mathematics ability that was reduced to non-significance when controlling for a direct measure of receptive vocabulary. Results also revealed that inhibitory control plays an important role in the relation between ANS acuity and mathematics ability. Specifically, ANS acuity accounted for significant variance in mathematics ability over and above receptive vocabulary, but only for ANS acuity trials in which surface area conflicted with numerosity. Moreover, this association became non-significant when controlling for inhibitory control. These results suggest that early mathematical experiences prior to formal schooling may influence the strength of the association between ANS acuity and mathematics ability and that inhibitory control may drive that association in young children. © 2012 Blackwell Publishing Ltd.

  14. Digital image processing mathematical and computational methods

    CERN Document Server

    Blackledge, J M

    2005-01-01

    This authoritative text (the second part of a complete MSc course) provides mathematical methods required to describe images, image formation and different imaging systems, coupled with the principle techniques used for processing digital images. It is based on a course for postgraduates reading physics, electronic engineering, telecommunications engineering, information technology and computer science. This book relates the methods of processing and interpreting digital images to the 'physics' of imaging systems. Case studies reinforce the methods discussed, with examples of current research

  15. Handbook of mathematics

    CERN Document Server

    Kuipers, L

    1969-01-01

    International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examp

  16. Relationships between Mathematics Teacher Preparation and Graduates' Analyses of Classroom Teaching

    Science.gov (United States)

    Hiebert, James; Berk, Dawn; Miller, Emily

    2017-01-01

    The purpose of this longitudinal study was to investigate the relationships between mathematics teacher preparation and graduates' analyses of classroom teaching. Fifty-three graduates from an elementary teacher preparation program completed 4 video-based, analysis-of-teaching tasks in the semester before graduation and then in each of the 3…

  17. Mathematical physics

    CERN Document Server

    Geroch, Robert

    1985-01-01

    Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the ""whys"" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle

  18. Applied mathematics

    CERN Document Server

    Logan, J David

    2013-01-01

    Praise for the Third Edition"Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference." -MAA Reviews Applied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and nat

  19. Speed mathematics

    CERN Document Server

    Handley, Bill

    2012-01-01

    This new, revised edition of the bestselling Speed Mathematics features new chapters on memorising numbers and general information, calculating statistics and compound interest, square roots, logarithms and easy trig calculations. Written so anyone can understand, this book teaches simple strategies that will enable readers to make lightning-quick calculations. People who excel at mathematics use better strategies than the rest of us; they are not necessarily more intelligent. With Speed Mathematics you'll discover methods to make maths easy and fun. This book is perfect for stud

  20. Masculinities in mathematics

    CERN Document Server

    Mendick, Heather

    2006-01-01

    The study of mathematics, with other ''gendered'' subjects such as science and engineering, usually attracts more male than female pupils. This book explores this phenomenon, addressing the important question of why more boys than girls choose to study mathematics. It illuminates what studying mathematics means for both students and teachers.

  1. Gendered Pathways: How Mathematics Ability Beliefs Shape Secondary and Postsecondary Course and Degree Field Choices

    Science.gov (United States)

    Perez-Felkner, Lara; Nix, Samantha; Thomas, Kirby

    2017-01-01

    Do mathematics ability beliefs explain gender gaps in the physical science, engineering, mathematics, and computer science fields (PEMC) and other science fields? We leverage U.S. nationally representative longitudinal data to estimate gendered differences in girls' and boys' perceptions of mathematics ability with the most difficult or challenging material. Our analyses examine the potentially interacting effects of gender and these ability beliefs on students' pathways to scientific careers. Specifically, we study how beliefs about ability with challenging mathematics influence girls' and boys' choices to pursue PEMC degrees, evaluating educational milestones over a 6-year period: advanced science course completion in secondary school and postsecondary major retention and selection. Our findings indicate even at the same levels of observed ability, girls' mathematics ability beliefs under challenge are markedly lower than those of boys. These beliefs matter over time, potentially tripling girls' chances of majoring in PEMC sciences, over and above biological science fields, all else being equal. Implications and potential interventions are discussed. PMID:28428762

  2. Manifold Shape: from Differential Geometry to Mathematical Morphology

    OpenAIRE

    Roerdink, J.B.T.M.

    1994-01-01

    Much progress has been made in extending Euclidean mathematical morphology to more complex structures such as complete lattices or spaces with a non-commutative symmetry group. Such generalizations are important for practical situations such as translation and rotation invariant pattern recognition or shape description of patterns on spherical surfaces. Also in computer vision much use is made of spherical mappings to describe the world as seen by a human or machine observer. Stimulated by th...

  3. Analysis of mathematical literacy ability based on self-efficacy in model eliciting activities using metaphorical thinking approach

    Science.gov (United States)

    Setiani, C.; Waluya, S. B.; Wardono

    2018-03-01

    The purposes of this research are: (1) to identify learning quality in Model Eliciting Activities (MEAs) using a Metaphorical Thinking (MT) approach regarding qualitative and quantitative; (2) to analyze mathematical literacy of students based on Self-Efficacy (SE). This research is mixed method concurrent embedded design with qualitative research as the primary method. The quantitative research used quasi-experimental with non-equivalent control group design. The population is VIII grade students of SMP Negeri 3 Semarang Indonesia. Quantitative data is examined by conducting completeness mean test, standard completeness test, mean differentiation test and proportional differentiation test. Qualitative data is analyzed descriptively. The result of this research shows that MEAs learning using MT approach accomplishes good criteria both quantitatively and qualitatively. Students with low self-efficacy can identify problems, but they are lack ability to arrange problem-solving strategy on mathematical literacy questions. Students with medium self-efficacy can identify information provided in issues, but they find difficulties to use math symbols in making a representation. Students with high self-efficacy are excellent to represent problems into mathematical models as well as figures by using appropriate symbols and tools, so they can arrange strategy easily to solve mathematical literacy questions.

  4. Empathic climate and learning outcomes: a study of teaching empathy in relation to mathematics learning outcomes

    OpenAIRE

    Buckley, Finian

    1993-01-01

    This study examined the influence of Empathie Teaching Climate on Mathematics Learnmg'andMathematics and General School Self-Concepts, in sateen schools in Dublin, Ireland. The study required the design development and validation of the Student-Teacher Interaction Questionnaire (STIQ), which measures specific behavioural indices of classroom Teaching Empathy. The research monitored the effects of Teaching Empathy on students (N=387) in their first year of secondary schooling, as they complete...

  5. Studies in the history of Indian mathematics

    CERN Document Server

    2010-01-01

    This volume is the outcome of a seminar on the history of mathematics held at the Chennai Mathematical Institute during January-February 2008 and contains articles based on the talks of distinguished scholars both from the West and from India. The topics covered include: (1) geometry in the oulvasatras; (2) the origins of zero (which can be traced to ideas of lopa in Paoini's grammar); (3) combinatorial methods in Indian music (which were developed in the context of prosody and subsequently applied to the study of tonal and rhythmic patterns in music); (4) a cross-cultural view of the development of negative numbers (from Brahmagupta (c. 628 CE) to John Wallis (1685 CE); (5) Kunnaka, Bhavana and Cakravala (the techniques developed by Indian mathematicians for the solution of indeterminate equations); (6) the development of calculus in India (covering the millennium-long history of discoveries culminating in the work of the Kerala school giving a complete analysis of the basic calculus of polynomial and trigon...

  6. Mathematics at University

    DEFF Research Database (Denmark)

    Winsløw, Carl

    2015-01-01

    Mathematics is studied in universities by a large number of students. At the same time it is a field of research for a (smaller) number of university teachers. What relations, if any, exist between university research and teaching of mathematics? Can research “support” teaching? What research...... and what teaching? In this presentation we propose a theoretical framework to study these questions more precisely, based on the anthropological theory of didactics. As a main application, the links between the practices of mathematical research and university mathematics teaching are examined...

  7. Mathematics in civilization

    CERN Document Server

    Resnikoff, Howard L

    2015-01-01

    Space flight, computers, lasers, and information technology ― these are but a few examples of the spectacular growth, development, and far-reaching applications of mathematics. But what of the field's past? Upon which intellectual milestones were the foundations of modern mathematics constructed? How has our comprehension of the physical universe, language, and the nature of thought itself been influenced and informed by the developments of mathematics through the ages?This lucid presentation examines how mathematics shaped and was shaped by the course of human events. In a format suited to co

  8. Mathematics in India

    CERN Document Server

    Plofker, Kim

    2009-01-01

    Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic sc

  9. Meaning in mathematics

    CERN Document Server

    2011-01-01

    Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics.

  10. The Use of the History of Mathematics in the Teaching Pre-Service Mathematics Teachers

    Science.gov (United States)

    Galante, Dianna

    2014-01-01

    Many scholars have written about using the history of mathematics in the teaching of pre-service mathematics teachers. For this study, pre-service mathematics teachers developed an electronic journal of reflections based on presentations in the history of mathematics in a secondary mathematics education course. The main purpose of the…

  11. Construction of mathematical knowledge using graphic calculators (CAS) in the mathematics classroom

    Science.gov (United States)

    Hitt, Fernando

    2011-09-01

    Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the mathematics classroom has not had the expected impact, as it has been its use in everyday life (i.e. cell phone). What about teachers' opinions? Mathematics teachers can be divided into three categories: those with a boundless overflow (enthusiasm) who want to use the technology without worrying much about the construction of mathematical concepts, those who reject outright the use of technology because they think that their use inhibits the development of mathematical skills and others that reflect on the balance that must exist between paper-pencil activities and use of technology. The mathematics teacher, by not having clear examples that support this last option about the balance of paper-pencil activities and technology, opt for one of the extreme positions outlined above. In this article, we show the results of research on a methodology based on collaborative learning (ACODESA) in the training of mathematics teachers in secondary schools and implementation of activities in an environment of paper-pencil and CAS in the mathematics classroom. We also note that with the development of technology on the use of electronic tablets and interactive whiteboards, these activities will take on greater momentum in the near future.

  12. Mathematical Perspectives

    Energy Technology Data Exchange (ETDEWEB)

    Glimm, J.

    2009-10-14

    Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.

  13. Empowering Mathematical Practices

    Science.gov (United States)

    Coomes, Jacqueline; Lee, Hyung Sook

    2017-01-01

    Mathematics teachers want to empower students as mathematical thinkers and doers (NCTM 2000). Specific ways of thinking and doing mathematics were described in the Process Standards (NCTM 2000); they were further characterized as habits of mind (Mark, Goldenberg, and Sword 2010); and more recently, they were detailed in the Common Core's Standards…

  14. Learners with learning difficulties in mathematics : attitudes, curriculum and methods of teaching mathematics

    OpenAIRE

    2012-01-01

    D.Ed. The aim of this theses is to find out whether there is any relationship between learners' attitudes and learning difficulties in mathematics: To investigate whether learning difficulties in mathematics are associated with learners' gender. To establish the nature of teachers' perceptions of the learning problem areas in the mathematics curriculum. To find out about the teachers' views on the methods of teaching mathematics, resources, learning of mathematics, extra curricular activit...

  15. Studies in Mathematics, Volume X. Applied Mathematics in the High School.

    Science.gov (United States)

    Schiffer, Max M.

    This publication contains a sequence of lectures given to high school mathematics teachers by the author. Applications of mathematics emphasized are elementary algebra, geometry, and matrix algebra. Included are: (1) an introduction concerning teaching applications of mathematics; (2) Chapter 1: Mechanics for the High School Student; (3) Chapter…

  16. Exploring Statistics Anxiety: Contrasting Mathematical, Academic Performance and Trait Psychological Predictors

    Science.gov (United States)

    Bourne, Victoria J.

    2018-01-01

    Statistics anxiety is experienced by a large number of psychology students, and previous research has examined a range of potential correlates, including academic performance, mathematical ability and psychological predictors. These varying predictors are often considered separately, although there may be shared variance between them. In the…

  17. Mathematics, anxiety, and the brain.

    Science.gov (United States)

    Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer

    2017-05-24

    Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.

  18. Mathematics for the liberal arts

    CERN Document Server

    Bindner, Donald; Hemmeter, Joe

    2014-01-01

    Presents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life. Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, including problem-solving techniques and real-world applications. This book emphasizes learning through doing, presents a practical approach, and features: A detailed explanation of why mathematical principles are true and how the mathematical processes workNumerous figures and diagrams as well as hundreds of worked example...

  19. Mathematical models of granular matter

    CERN Document Server

    Mariano, Paolo; Giovine, Pasquale

    2008-01-01

    Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.

  20. 3rd International Symposium Mathematical Progress in Expressive Image Synthesis

    CERN Document Server

    Ochiai, Hiroyuki

    2016-01-01

    “Progress in Expressive Image Synthesis” (MEIS2015), was held in Fukuoka, Japan, September 25–27, 2015. The aim of the symposium was to provide a unique venue where various issues in computer graphics (CG) application fields could be discussed by mathematicians, CG researchers, and practitioners. Through the previous symposiums MEIS2013 and MEIS2014, mathematicians as well as CG researchers have recognized that CG is a specific and practical activity derived from mathematical theories. Issues found in CG broaden the field of mathematics and vice versa, and CG visualizes mathematical theories in an aesthetic manner. In this volume, the editors aim to provoke interdisciplinary research projects through the peer-reviewed papers and poster presentations at the this year’s symposium. This book captures interactions among mathematicians, CG researchers, and practitioners sharing important, state-of-the-art issues in graphics and visual perception. The book is suitable for all CG researchers seeking open pro...

  1. Engineering mathematics

    CERN Document Server

    Bird, John

    2014-01-01

    A practical introduction to the core mathematics required for engineering study and practiceNow in its seventh edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams.John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure

  2. Preservice Elementary Mathematics Teachers' Level of Relating Mathematical Concepts in Daily Life Contexts

    Science.gov (United States)

    Akkus, Oylum

    2008-01-01

    The purpose of this study was to investigate preservice elementary mathematics teachers' ability of relating mathematical concepts and daily life context. Two research questions were set; what is the preservice elementary mathematics teachers' level of relating mathematical concepts and daily life context regarding to their education year and…

  3. Secondary Mathematics Coaching: The Components of Effective Mathematics Coaching and Implications

    Science.gov (United States)

    Bengo, Priscilla

    2016-01-01

    Mathematics coaching, which can be defined broadly as job-embedded learning for mathematics teachers with someone who can help, is being used in Canada to improve teaching practice and increase student achievement. Mathematics coaching research is quite new with little written on the components of effective coaching. The paper attempts to…

  4. Exploring rural high school learners' experience of mathematics anxiety in academic settings

    Directory of Open Access Journals (Sweden)

    Dipane Hlalele

    2012-01-01

    Full Text Available The purpose of the study was to explore rural high school learners' experience of mathematics anxiety in academic settings. Mathematics anxiety has been found to have an adverse effect on confidence, motivation and achievement. This quantitative study is exploratory and descriptive in nature. The participants were 403 learners doing mathematics in 18 rural schools in the Free State province of South Africa. Participants completed a 20-item questionnaire and 373 (92.5% questionnaires were found to contain valid responses and were analysed by a professional statistician at the University of the Free State using the Statistical Package for the Social Sciences (SPSS, Version 17.0. The questionnaire was testedfor reliability using the Cronbach alpha coefficient and was found to have a reliability score of .841, indicating an acceptable reliability coefficient. Findings reveal that all learners sometimes, often, or always experience mathematics anxiety in academic settings. It is therefore important for teachers and authorities in education to observe its prevalence and to implement strategies toward the alleviation of the effects ofmathematics anxiety.

  5. Learning higher mathematics

    CERN Document Server

    Pontrjagin, Lev Semenovič

    1984-01-01

    Lev Semenovic Pontrjagin (1908) is one of the outstanding figures in 20th century mathematics. In a long career he has made fundamental con­ tributions to many branches of mathematics, both pure and applied. He has received every honor that a grateful government can bestow. Though in no way constrained to do so, he has through the years taught mathematics courses at Moscow State University. In the year 1975 he set himself the task of writing a series of books on secondary school and beginning university mathematics. In his own words, "I wished to set forth the foundations of higher mathematics in a form that would have been accessible to myself as a lad, but making use of all my experience as a scientist and a teacher, ac­ cumulated over many years. " The present volume is a translation of the first two out of four moderately sized volumes on this theme planned by Pro­ fessor Pontrjagin. The book begins at the beginning of modern mathematics, analytic ge­ ometry in the plane and 3-dimensional space. Refin...

  6. Children's Implicit and Explicit Gender Stereotypes about Mathematics and Reading Ability

    Science.gov (United States)

    Nowicki, Elizabeth A.; Lopata, Joel

    2017-01-01

    Study objectives were to clarify children's gender-based implicit and explicit mathematics and reading stereotypes, and to determine if implicit and explicit measures were related or represented distinct constructs. One hundred and fifty-six boys and girls (mean age 11.3 years) from six elementary schools completed math or reading stereotype…

  7. Making Sense of Mathematics

    Science.gov (United States)

    Umphrey, Jan

    2011-01-01

    The National Council of Teachers of Mathematics (NCTM) is a voice and advocate for mathematics educators, working to ensure that all students receive equitable mathematics learning of the highest quality. To help teachers and school leaders understand the Common Core State Standards for Mathematics (CCSSM) and to point out how the CCSSM can be…

  8. The Computer Student Worksheet Based Mathematical Literacy for Statistics

    Science.gov (United States)

    Manoy, J. T.; Indarasati, N. A.

    2018-01-01

    The student worksheet is one of media teaching which is able to improve teaching an activity in the classroom. Indicators in mathematical literacy were included in a student worksheet is able to help the students for applying the concept in daily life. Then, the use of computers in learning can create learning with environment-friendly. This research used developmental research which was Thiagarajan (Four-D) development design. There are 4 stages in the Four-D, define, design, develop, and disseminate. However, this research was finish until the third stage, develop stage. The computer student worksheet based mathematical literacy for statistics executed good quality. This student worksheet is achieving the criteria if able to achieve three aspects, validity, practicality, and effectiveness. The subject in this research was the students at The 1st State Senior High School of Driyorejo, Gresik, grade eleven of The 5th Mathematics and Natural Sciences. The computer student worksheet products based mathematical literacy for statistics executed good quality, while it achieved the aspects for validity, practical, and effectiveness. This student worksheet achieved the validity aspects with an average of 3.79 (94.72%), and practical aspects with an average of 2.85 (71.43%). Besides, it achieved the effectiveness aspects with a percentage of the classical complete students of 94.74% and a percentage of the student positive response of 75%.

  9. Where mathematics come from how the embodied mind brings mathematics into being

    CERN Document Server

    Lakoff, George

    2001-01-01

    This book is about mathematical ideas, about what mathematics means-and why. Abstract ideas, for the most part, arise via conceptual metaphor-metaphorical ideas projecting from the way we function in the everyday physical world. Where Mathematics Comes From argues that conceptual metaphor plays a central role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms.

  10. Pluralism in mathematics a new position in philosophy of mathematics

    CERN Document Server

    Friend, Michèle

    2014-01-01

    This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy's Naturalism, Shapiro's Structuralism and Formalism. In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry. In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a stron...

  11. Learning transfer of geospatial technologies in secondary science and mathematics core areas

    Science.gov (United States)

    Nielsen, Curtis P.

    The purpose of this study was to investigate the transfer of geospatial technology knowledge and skill presented in a social sciences course context to other core areas of the curriculum. Specifically, this study explored the transfer of geospatial technology knowledge and skill to the STEM-related core areas of science and mathematics among ninth-grade students. Haskell's (2001) research on "levels of transfer" provided the theoretical framework for this study, which sought to demonstrate the experimental group's higher ability to transfer geospatial skills, higher mean assignment scores, higher post-test scores, higher geospatial skill application and deeper levels of transfer application than the control group. The participants of the study consisted of thirty ninth-graders enrolled in U.S. History, Earth Science and Integrated Mathematics 1 courses. The primary investigator of this study had no previous classroom experiences with this group of students. The participants who were enrolled in the school's existing two-section class configuration were assigned to experimental and control groups. The experimental group had ready access to Macintosh MacBook laptop computers, and the control group had ready access to Macintosh iPads. All participants in U.S. History received instruction with and were required to use ArcGIS Explorer Online during a Westward Expansion project. All participants were given the ArcGIS Explorer Online content assessment following the completion of the U.S. History project. Once the project in U.S. History was completed, Earth Science and Integrated Mathematics 1 began units of instruction beginning with a multiple-choice content pre-test created by the classroom teachers. Experimental participants received the same unit of instruction without the use or influence of ArcGIS Explorer Online. At the end of the Earth Science and Integrated Math 1 units, the same multiple-choice test was administered as the content post-test. Following the

  12. Mathematics for physical chemistry

    CERN Document Server

    Mortimer, Robert G

    2013-01-01

    Mathematics for Physical Chemistry is the ideal supplementary text for practicing chemists and students who want to sharpen their mathematics skills while enrolled in general through physical chemistry courses. This book specifically emphasizes the use of mathematics in the context of physical chemistry, as opposed to being simply a mathematics text. This 4e includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The early chapters are constructed around a sequence of mathematical topics, wit

  13. The analysis of mathematics literacy on PMRI learning with media schoology of junior high school students

    Science.gov (United States)

    Wardono; Mariani, S.

    2018-03-01

    Indonesia as a developing country in the future will have high competitiveness if its students have high mathematics literacy ability. The current reality from year to year rankings of PISA mathematics literacy Indonesian students are still not good. This research is motivated by the importance and low ability of the mathematics literacy. The purpose of this study is to: (1) analyze the effectiveness of PMRI learning with media Schoology, (2) describe the ability of students' mathematics literacy on PMRI learning with media Schoology which is reviewed based on seven components of mathematics literacy, namely communication, mathematizing, representation, reasoning, devising strategies, using symbols, and using mathematics tool. The method used in this research is the method of sequential design method mix. Techniques of data collection using observation, interviews, tests, and documentation. Data analysis techniques use proportion test, appellate test, and use descriptive analysis. Based on the data analysis, it can be concluded; (1) PMRI learning with media Schoology effectively improve the ability of mathematics literacy because of the achievement of classical completeness, students' mathematics literacy ability in PMRI learning with media Schoology is higher than expository learning, and there is increasing ability of mathematics literacy in PMRI learning with media Schoology of 30%. (2) Highly capable students attain excellent mathematics literacy skills, can work using broad thinking with appropriate resolution strategies. Students who are capable of achieving good mathematics literacy skills can summarize information, present problem-solving processes, and interpret solutions. low-ability students have reached the level of ability of mathematics literacy good enough that can solve the problem in a simple way.

  14. Secondary School Mathematics Teachers' Knowledge Levels and Use of History of Mathematics

    Science.gov (United States)

    Bütüner, Suphi Önder

    2018-01-01

    This study describes secondary school mathematics teachers' use of history of mathematics in their classes and their knowledge levels in this field. The study population included a total of 58 secondary school mathematics teachers working at the secondary schools located in Yozgat city center, and the sample included 32 mathematics teachers from…

  15. Mathematical mind-benders

    CERN Document Server

    Winkler, Peter

    2007-01-01

    Peter Winkler is at it again. Following the enthusiastic reaction to Mathematical Puzzles: A Connoisseur's Collection, Peter has compiled a new collection of elegant mathematical puzzles to challenge and entertain the reader. The original puzzle connoisseur shares these puzzles, old and new, so that you can add them to your own anthology. This book is for lovers of mathematics, lovers of puzzles, lovers of a challenge. Most of all, it is for those who think that the world of mathematics is orderly, logical, and intuitive-and are ready to learn otherwise! A pdf with errata is updated by the aut

  16. Mathematical knowledge for teaching: Making the tacit more explicit in mathematics teacher education

    Science.gov (United States)

    Abdullah, Mohd Faizal Nizam Lee; Vimalanandan, Lena

    2017-05-01

    Teaching practice during school based experiences, afford an opportunity for pre service teachers to put into practice their knowledge for teaching mathematics. Like all knowledge, Mathematical Knowledge for Teaching (MKT) is held in both tacit and explicit form, making it especially difficult to study and map during instruction. This study investigates the tacit and explicit nature of MKT held by pre service teachers in a Malaysian Teacher Education Program and how it impacts the Mathematical Quality of their instruction (MQI). This study of three mathematics pre-service teachers (PSTs), utilised videos of mathematics lessons, reflective debriefs and interviews. The findings suggest that factors such as reflecting, peer-sharing, conferencing with mentors and observing support in making tacit knowledge more explicit during planning and instruction. Implications for preparation of mathematics teachers capable of high Mathematical Quality of Instruction are also discussed.

  17. Teaching mathematics using excel

    OpenAIRE

    Bonello, Mary Rose; Camilleri, Silvana

    2004-01-01

    'Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.' (Principles and Standards for School Mathematics-NCTM April 2000)

  18. Nonconvex Model of Material Growth: Mathematical Theory

    Science.gov (United States)

    Ganghoffer, J. F.; Plotnikov, P. I.; Sokolowski, J.

    2018-06-01

    The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.

  19. Perception determinants in learning mathematics

    Science.gov (United States)

    Mokhtar, Siti Fairus; Ali, Noor Rasidah; Rashid, Nurazlina Abdul

    2015-05-01

    This article described a statistical study of students' perception in mathematics. The objective of this study is to identify factors related to perception about learning mathematics among non mathematics' student. This study also determined the relationship between of these factors among non mathematics' student. 43 items questionnaires were distributed to one hundred students in UiTM Kedah who enrolled in the Business Mathematics course. These items were measured by using a semantic scale with the following anchors: 1 = strongly disagree to 7 = strongly agree. A factor analysis of respondents were identified into five factors that influencing the students' perception in mathematics. In my study, factors identified were attitude, interest, role of the teacher, role of peers and usefulness of mathematics that may relate to the perception about learning mathematics among non mathematics' student.

  20. Construction mathematics

    CERN Document Server

    Virdi, Surinder; Virdi, Narinder Kaur

    2014-01-01

    Construction Mathematics is an introductory level mathematics text, written specifically for students of construction and related disciplines. Learn by tackling exercises based on real-life construction maths. Examples include: costing calculations, labour costs, cost of materials and setting out of building components. Suitable for beginners and easy to follow throughout. Learn the essential basic theory along with the practical necessities. The second edition of this popular textbook is fully updated to match new curricula, and expanded to include even more learning exercises. End of chapter exercises cover a range of theoretical as well as practical problems commonly found in construction practice, and three detailed assignments based on practical tasks give students the opportunity to apply all the knowledge they have gained. Construction Mathematics addresses all the mathematical requirements of Level 2 construction NVQs from City & Guilds/CITB and Edexcel courses, including the BTEC First Diploma in...

  1. Attitudes of Mathematics Teachers toward Using Smart Board in Teaching Mathematics

    Science.gov (United States)

    Muhanna, Wafa; Nejem, Khamis Mousa

    2013-01-01

    This study aimed at investigating the attitudes of mathematics teachers toward using a smart board in teaching mathematics and also to determine the effect of gender, experience, and qualification of teachers on their attitudes. The sample of this study consisted of 74 mathematics teachers--35 males and 39 females--from private schools in Amman…

  2. The role of mathematics in politics as an issue for mathematics teaching

    DEFF Research Database (Denmark)

    Sánchez, Mario; Blomhøj, Morten

    2010-01-01

    This paper presents analyses of some examples of mathematical models used in the Mexican society of today. We seek to justify why and illustrate how such examples can be included in mathematics teaching and in teacher education.......This paper presents analyses of some examples of mathematical models used in the Mexican society of today. We seek to justify why and illustrate how such examples can be included in mathematics teaching and in teacher education....

  3. Metacognition Process of Students with High Mathematics Anxiety in Mathematics Problem-Solving

    OpenAIRE

    Patrisius Afrisno Udil; Tri Atmojo Kusmayadi; Riyadi Riyadi

    2017-01-01

    This study aims to find out students’ metacognition process while solving the mathematics problem. It focuses on analyzing the metacognition process of students with high mathematics anxiety based on Polya’s problem solving phases. This study uses qualitative research with case study strategy. The subjects consist of 8 students of 7th grade selected through purposive sampling. Data in the form of Mathematics Anxiety Scale (MAS) result and recorded interview while solving mathematics problems ...

  4. Mathematics for the imagination

    CERN Document Server

    Higgins, Peter

    2002-01-01

    Mathematics for the Imagination provides an accessible and entertaining investigation into mathematical problems in the world around us. From world navigation, family trees, and calendars to patterns, tessellations, and number tricks, this informative and fun new book helps you to understand the maths behind real-life questions and rediscover your arithmetical mind.This is a follow-up to the popular Mathematics for the Curious, Peter Higgins's first investigation into real-life mathematical problems.A highly involving book which encourages the reader to enter into the spirit of mathematical ex

  5. What is mathematical logic?

    CERN Document Server

    Crossley, J N; Brickhill, CJ; Stillwell, JC

    2010-01-01

    Although mathematical logic can be a formidably abstruse topic, even for mathematicians, this concise book presents the subject in a lively and approachable fashion. It deals with the very important ideas in modern mathematical logic without the detailed mathematical work required of those with a professional interest in logic.The book begins with a historical survey of the development of mathematical logic from two parallel streams: formal deduction, which originated with Aristotle, Euclid, and others; and mathematical analysis, which dates back to Archimedes in the same era. The streams beg

  6. The nature of mathematics

    CERN Document Server

    Jourdain, Philip E B

    2007-01-01

    Anyone with an interest in mathematics will welcome the republication of this little volume by a remarkable mathematician who was also a logician, a philosopher, and an occasional writer of fiction and poetry. Originally published in 1913, and later included in the acclaimed anthology The World of Mathematics, Jourdain's survey shows how and why the methods of mathematics were developed, traces the development of mathematical science from the earliest to modern times, and chronicles the application of mathematics to natural science.Starting with the ancient Egyptians and Greeks, the author p

  7. Fundamental concepts of mathematics

    CERN Document Server

    Goodstein, R L

    Fundamental Concepts of Mathematics, 2nd Edition provides an account of some basic concepts in modern mathematics. The book is primarily intended for mathematics teachers and lay people who wants to improve their skills in mathematics. Among the concepts and problems presented in the book include the determination of which integral polynomials have integral solutions; sentence logic and informal set theory; and why four colors is enough to color a map. Unlike in the first edition, the second edition provides detailed solutions to exercises contained in the text. Mathematics teachers and people

  8. The development of mathematics

    CERN Document Server

    Bell, Eric Temple

    1945-01-01

    ""This important book . . . presents a broad account of the part played by mathematics in the evolution of civilization, describing clearly the main principles, methods, and theories of mathematics that have survived from about 4000 BC to 1940.""― BooklistIn this time-honored study, one of the 20th century's foremost scholars and interpreters of the history and meaning of mathematics masterfully outlines the development of its leading ideas, and clearly explains the mathematics involved in each. According to the author, a professor of mathematics at the California Institute of Technology from

  9. Mathematics in ancient Greece

    CERN Document Server

    Dantzig, Tobias

    2006-01-01

    More than a history of mathematics, this lively book traces mathematical ideas and processes to their sources, stressing the methods used by the masters of the ancient world. Author Tobias Dantzig portrays the human story behind mathematics, showing how flashes of insight in the minds of certain gifted individuals helped mathematics take enormous forward strides. Dantzig demonstrates how the Greeks organized their precursors' melange of geometric maxims into an elegantly abstract deductive system. He also explains the ways in which some of the famous mathematical brainteasers of antiquity led

  10. About the Code of Practice of the European Mathematical Society

    DEFF Research Database (Denmark)

    Jensen, Arne

    2013-01-01

    The Executive Committee of the European Mathematical Society created an Ethics Committee in the Spring of 2010. The first task of the Committee was to prepare a Code of Practice. This task was completed in the Spring of 2012 and went into effect on 1 November 2012. Arne Jensen, author...... of this article, is Chair of the EMS Ethics Committee...

  11. How Do Higher-Education Students Use Their Initial Understanding to Deal with Contextual Logic-Based Problems in Discrete Mathematics?

    Science.gov (United States)

    Lubis, Asrin; Nasution, Andrea Arifsyah

    2017-01-01

    Mathematical reasoning in logical context has now received much attention in the mathematics curriculum documents of many countries, including Indonesia. In Indonesia, students start formally learning about logic when they pursue to senior-high school. Before, they previously have many experiences to deal with logic, but the earlier assignments do…

  12. The Importance of Mathematics as a Prerequisite to Introductory Financial Accounting

    Science.gov (United States)

    McCarron, Karen B.; Burstein, Alan N.

    2017-01-01

    Mathematics has long served as a prerequisite to introductory financial accounting in the 4-year college business curriculum. However, 2-year colleges have been slower to adopt math as a prerequisite. Its usefulness in relation to achieving successful completion of accounting has not been demonstrated at either a 2-year or 4-year college. Using…

  13. Challenging previous conceptions of vegetarianism and eating disorders.

    Science.gov (United States)

    Fisak, B; Peterson, R D; Tantleff-Dunn, S; Molnar, J M

    2006-12-01

    The purpose of this study was to replicate and expand upon previous research that has examined the potential association between vegetarianism and disordered eating. Limitations of previous research studies are addressed, including possible low reliability of measures of eating pathology within vegetarian samples, use of only a few dietary restraint measures, and a paucity of research examining potential differences in body image and food choice motives of vegetarians versus nonvegetarians. Two hundred and fifty-six college students completed a number of measures of eating pathology and body image, and a food choice motives questionnaire. Interestingly, no significant differences were found between vegetarians and nonvegetarians in measures of eating pathology or body image. However, significant differences in food choice motives were found. Implications for both researchers and clinicians are discussed.

  14. Meaning in mathematics education

    CERN Document Server

    Valero, Paola; Hoyles, Celia; Skovsmose, Ole

    2005-01-01

    What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding the complexity of meaning in mathematics education is a matter of huge importance. There are twin directions in which discussions have developed - theoretical and practical - and this book seeks to move the debate forward along both dimensions while seeking to relate them where appropriate. A discussion of meaning can start from a theoretical examination of mathematics and how mathematicians over time have made sense of their work. However, from a more practical perspective, anybody involved in teaching mathematics is faced with the need to orchestrate the myriad of meanings derived from multiple sources that students develop of mathematical knowledge.

  15. New SUSYQM coherent states for Pöschl-Teller potentials: a detailed mathematical analysis

    Science.gov (United States)

    Bergeron, H.; Siegl, P.; Youssef, A.

    2012-06-01

    In a recent short note (Bergeron et al 2010 Europhys. Lett. 92 60003), we have presented the good properties of a new family of semi-classical states for Pöschl-Teller potentials. These states are built from a supersymmetric quantum mechanics (SUSYQM) approach and the parameters of these ‘coherent’ states are points in the classical phase space. In this paper, we develop all the mathematical aspects that have been left out of the previous paper (proof of the resolution of unity, detailed calculations of the quantized version of classical observables and mathematical study of the resulting operators: problems of domains, self-adjointness or self-adjoint extensions). Some additional questions such as asymptotic behavior are also studied. Moreover, the framework is extended to a larger class of Pöschl-Teller potentials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.

  16. New SUSYQM coherent states for Pöschl–Teller potentials: a detailed mathematical analysis

    International Nuclear Information System (INIS)

    Bergeron, H; Siegl, P; Youssef, A

    2012-01-01

    In a recent short note (Bergeron et al 2010 Europhys. Lett. 92 60003), we have presented the good properties of a new family of semi-classical states for Pöschl–Teller potentials. These states are built from a supersymmetric quantum mechanics (SUSYQM) approach and the parameters of these ‘coherent’ states are points in the classical phase space. In this paper, we develop all the mathematical aspects that have been left out of the previous paper (proof of the resolution of unity, detailed calculations of the quantized version of classical observables and mathematical study of the resulting operators: problems of domains, self-adjointness or self-adjoint extensions). Some additional questions such as asymptotic behavior are also studied. Moreover, the framework is extended to a larger class of Pöschl–Teller potentials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

  17. Changing Students Minds and Achievement in Mathematics: The Impact of a Free Online Student Course

    Directory of Open Access Journals (Sweden)

    Jo Boaler

    2018-04-01

    Full Text Available This study reports on the impact of a “massive, open, online course” (MOOC designed to change students' ideas about mathematics and their own potential and improve their mathematics achievement. Many students hold damaging fixed mindsets, believing that their intelligence is unchangeable. When students shift to a growth mindset (believing that their intelligence is malleable, their achievement increases. This study of a MOOC intervention differs from previous mindset research in three ways (1 the intervention was delivered through a free online course with the advantage of being scalable nationwide (2 the intervention infused mindset messages into mathematics, specifically targeting students' beliefs about mathematics (3 the research was conducted with a teacher randomized controlled design to estimate its effects. Results show that the treatment group who took the MOOC reported more positive beliefs about math, engaged more deeply in math in class, and achieved at significantly higher levels on standardized mathematics assessments.

  18. Philosophical dimensions in mathematics education

    CERN Document Server

    Francois, Karen

    2007-01-01

    This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in this book offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum.

  19. Women in mathematics celebrating the centennial of the Mathematical Association of America

    CERN Document Server

    Greenwald, Sarah; Jensen-Vallin, Jacqueline; Mast, Maura

    2017-01-01

    This collection of refereed papers celebrates the contributions, achievements, and progress of female mathematicians, mostly in the 20th and 21st centuries. Emerging from the themed paper session “The Contributions of Women to Mathematics: 100 Years and Counting” at MAA's 2015 MathFest, this volume contains a diverse mix of current scholarship and exposition on women and mathematics, including biographies, histories, and cultural discussions. The multiplicity of authors also ensures a wide variety of perspectives. In inspiring and informative chapters, the authors featured in this volume reflect on the accomplishments of women in mathematics, showcasing the changes in mathematical culture that resulted as more women obtained tenure-track and tenured academic positions, received prestigious awards and honors, served in leadership roles in professional societies, and became more visibly active in the mathematical community. Readers will find discussions of mathematical excellence at Girton College, Cambridg...

  20. Tanglegrams: A Reduction Tool for Mathematical Phylogenetics.

    Science.gov (United States)

    Matsen, Frederick A; Billey, Sara C; Kas, Arnold; Konvalinka, Matjaz

    2018-01-01

    Many discrete mathematics problems in phylogenetics are defined in terms of the relative labeling of pairs of leaf-labeled trees. These relative labelings are naturally formalized as tanglegrams, which have previously been an object of study in coevolutionary analysis. Although there has been considerable work on planar drawings of tanglegrams, they have not been fully explored as combinatorial objects until recently. In this paper, we describe how many discrete mathematical questions on trees "factor" through a problem on tanglegrams, and how understanding that factoring can simplify analysis. Depending on the problem, it may be useful to consider a unordered version of tanglegrams, and/or their unrooted counterparts. For all of these definitions, we show how the isomorphism types of tanglegrams can be understood in terms of double cosets of the symmetric group, and we investigate their automorphisms. Understanding tanglegrams better will isolate the distinct problems on leaf-labeled pairs of trees and reveal natural symmetries of spaces associated with such problems.