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Sample records for understanding mathematics featuring

  1. 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.

  2. Understanding engineering mathematics

    CERN Document Server

    Cox, Bill

    2001-01-01

    * Unique interactive style enables students to diagnose their strengths and weaknesses and focus their efforts where needed* Ideal for self-study and tutorial work, building from an initially supportive approach to the development of independent learning skills * Free website includes solutions to all exercises, additional topics and applications, guide to learning mathematics, and practice materialStudents today enter engineering courses with a wide range of mathematical skills, due to the many different pre-university qualifications studied. Bill Cox''s aim is for students to gain a thorough understanding of the maths they are studying, by first strengthening their background in the essentials of each topic. His approach allows a unique self-paced study style, in which students Review their strengths and weaknesses through self-administered diagnostic tests, then focus on Revision where they need it, to finally Reinforce the skills required.The book is structured around a highly successful ''transition'' ma...

  3. Understanding Legacy Features with Featureous

    DEFF Research Database (Denmark)

    Olszak, Andrzej; Jørgensen, Bo Nørregaard

    2011-01-01

    Feature-centric comprehension of source code is essential during software evolution. However, such comprehension is oftentimes difficult to achieve due the discrepancies between structural and functional units of object-oriented programs. We present a tool for feature-centric analysis of legacy...

  4. Understanding Mathematics: Some Key Factors

    Science.gov (United States)

    Ali, Asma Amanat; Reid, Norman

    2012-01-01

    Mathematics is well known as a subject area where there can be problems in terms of understanding as well as retaining positive attitudes. In a large study involving 813 school students (ages approximately 10-12) drawn from two different school systems in Pakistan, the effect of limited working memory capacity on performance in mathematics was…

  5. 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…

  6. Understanding Understanding Mathematics. Artificial Intelligence Memo No. 488.

    Science.gov (United States)

    Michener, Edwina Rissland

    This document is concerned with the important extra-logical knowledge that is often outside of traditional discussions in mathematics, and looks at some of the ingredients and processes involved in the understanding of mathematics. The goal is to develop a conceptual framework in which to talk about mathematical knowledge and to understand the…

  7. Mathematics understanding and anxiety in collaborative teaching

    Science.gov (United States)

    Ansari, B. I.; Wahyu, N.

    2017-12-01

    This study aims to examine students’ mathematical understanding and anxiety using collaborative teaching. The sample consists of 51 students in the 7th-grade of MTs N Jeureula, one of the Islamic public junior high schools in Jeureula, Aceh, Indonesia. A test of mathematics understanding was administered to the students twice during the period of two months. The result suggests that there is a significant increase in mathematical understanding in the pre-test and post-test. We categorized the students into the high, intermediate, and low level of prior mathematics knowledge. In the high-level prior knowledge, there is no difference of mathematical understanding between the experiment and control group. Meanwhile, in the intermediate and low level of prior knowledge, there is a significant difference of mathematical understanding between the experiment and control group. The mathematics anxiety is at an intermediate level in the experiment class and at a high level in the control group. There is no interaction between the learning model and the students’ prior knowledge towards the mathematical understanding, but there are interactions towards the mathematics anxiety. It indicates that the collaborative teaching model and the students’ prior knowledge do not simultaneously impacts on the mathematics understanding but the mathematics anxiety.

  8. Understanding Mathematics Classroom Teaching: Hermeneutics Inquiry

    Science.gov (United States)

    Wang, Xiong

    2015-01-01

    In order to understand meaning of mathematics classroom teaching, this paper uses narrative to present the meaning through hermeneutics inquiry from the author's research experiences. There are two threads in the research experience: research on classroom teaching and students' understanding in classroom teaching. The narrative provides not only a…

  9. Understanding connections in the school mathematics curriculum

    Directory of Open Access Journals (Sweden)

    Willy Mwakapenda

    2008-05-01

    Full Text Available I identify and discuss ways in which different types of connections are described in the South African mathematics National Curriculum Statement and its related documents, particularly at the Further Education and Training (FET level. I argue that connections are central to the way the discipline of mathematics, its learning outcomes, and assessment standards are conceptualised. The notions of representation and integration are found to be key aspects in understanding connections in mathematics. Using these two notions, I then analyse connections in the National Curriculum Statement and its related documents. Finally, theoretical and practical implications of connections in the curriculum are identified.

  10. A Check List for Evaluating Persuasive Features of Mathematics Courseware

    Science.gov (United States)

    Aris, Baharuddin; Gharbaghi, Alireza; Ahmad, Maizah Hura; Rosli, Mohd Shafie

    2013-01-01

    The main purpose of this study is to introduce a check list for evaluating persuasive features of mathematics courseware. Since mathematics is a source of anxiety among students (Zeidner & Matthews, 2010), this research is an attempt to employ persuasive features that can be used in mathematics courseware. Specifically, we sought to determine…

  11. Understanding Number Sequences Leads to Understanding Mathematics Concepts

    Science.gov (United States)

    Pasnak, Robert; Schmerold, Katrina Lea; Robinson, Melissa Fetterer; Gadzichowski, K. Marinka; Bock, Allison M.; O'Brien, Sarah Eva; Kidd, Julie K.; Gallington, Deb A.

    2016-01-01

    Ninety-six first grade students in an urban school system were tested in October and May on reading, mathematics, and their understanding of sequences of letters and numbers. A time lag analysis was subsequently conducted. In such analyses, cross-correlations between the first measurement of one variable and the second measurement of another are…

  12. 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…

  13. Characterizing Students' Understandings of Mathematical Proof.

    Science.gov (United States)

    Knuth, Eric J.; Elliott, Rebekah L.

    1998-01-01

    Discusses the characteristics of students' responses in terms of mathematical sophistication demonstrated that might be expected as they engage in a rich mathematical task that requires them to justify their solutions. (ASK)

  14. 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…

  15. The influence of Missouri mathematics project on seventh grade students’ mathematical understanding ability

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    Rezeki, S.; Setyawan, A. A.; Amelia, S.

    2018-01-01

    Mathematical understanding ability is a primary goal of Indonesian national education goals. However, various sources has shown that Indonesian students’ mathematical understanding ability is still relatively low. This study used quasi-experimental research design to examine the effectiveness of the application of Missouri Mathematics Project (MMP) on students’ mathematical understanding ability. The participants of the study were seventh grade students in Pekanbaru, Riau Province, Indonesia. They were selected purposively and represented as high, medium, and low-quality schools. The result of this study indicated that there was a significant effect of MMP on the overall students’ mathematical understanding ability and in all categories, except for low school level.

  16. Drawing as a tool for an insight into mathematical understanding

    Directory of Open Access Journals (Sweden)

    Alenka Lipovec

    2016-10-01

    Full Text Available Visual representations allow us to interpret the meanings of mathematical concepts, relationships and processes, therefore they play an important role in mathematics education. In the present study, we analysed participants’ understanding of basic mathematical concepts through drawings. Symbolic representation of mathematical concept was provided (e.g., 17 – 9 to participants and they were asked to represent the given concept through a picture. We were interested if high school students and future teachers (N = 345 adequately (in accordance with mathematical definition depicted given mathematical concept. The data were analysed using a combination of qualitative and quantitative analyses. The results show that participants quite adequately depicted basic mathematical concepts. Less abstract concepts were depicted more accurately. It was also noted, that 4th year students, studying to teach at primary level, have performed better than others. In qualitative content analysis two themes emerged. Those themes illustrate two ways of mathematical understanding (instrumental and relational and two types of mathematical knowledge (procedural and conceptual. The research results can serve researchers in the creation of new research instruments for measuring mathematical understanding and help teachers to find new approaches that will offer them an insight into students’ mathematical understanding.

  17. Examining Preservice Elementary Mathematics Teachers' Understandings about Irrational Numbers

    Science.gov (United States)

    Guven, Bulent; Cekmez, Erdem; Karatas, Ilhan

    2011-01-01

    The purpose of this study is to provide an account of preservice elementary mathematics teachers' understandings about irrational numbers. Three dimensions of preservice mathematics teachers' understandings are examined: defining rational and irrational numbers, placing rational and irrational numbers on the number line, and operations with…

  18. Mathematical Understanding of the Underprivileged Students through GeoGebra

    Science.gov (United States)

    Amam, A.; Fatimah, A. T.; Hartono, W.; Effendi, A.

    2017-09-01

    A student’s mathematical understanding in high school from poor families in the district of Ciamis is still low. After reviews the various literature and earlier research, consequently, researchers convince that learning mathematics with GeoGebra can help students improve for the better understanding. Our long-term goal of this research is to support the implementation of new curriculum, namely ICT-based learning mathematics. Another goal is to give a basic mastery skill regarding mathematics software to students from underprivileged families. Moreover, the specific objective of this study is to examine the students’ mathematical understanding from underprivileged families after the implementation of learning with GeoGebra. We use a quantitative comparative research method to determine differences in the mathematical understanding of students’ from underprivileged families before and after mathematics learning with GeoGebra. Accordingly, the students of senior high school from underprivileged family in Baregbeg, Ciamis district, are the population of this study. This research is using purposive sampling. The instrument is in the form of a test question, which is the test of mathematical understanding. Research results show that the mathematical understanding students’ from underprivileged families after the mathematics learning with GeoGebra becomes better than before. The novelty of this research is that students understand the material of trigonometry through the use of modules, aided by GeoGebra in learning activities. Thus, the understanding has an impact on improving students’ mathematical understanding. Students also master the use of GeoGebra Software. Implementing these two things will be very useful for the next lesson.

  19. Profile of Metacognition of Mathematics and Mathematics Education Students in Understanding the Concept of Integral Calculus

    Science.gov (United States)

    Misu, La; Ketut Budayasa, I.; Lukito, Agung

    2018-03-01

    This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.

  20. Turning Points: Using Teachers' Mathematics Life Stories to Understand the Implementation of Mathematics Education Reform

    Science.gov (United States)

    Drake, Corey

    2006-01-01

    In this study, teachers' narrative descriptions of themselves as learners and teachers of mathematics were used to understand teachers' interpretations and implementations of a reform-oriented mathematics curriculum. Twenty elementary school teachers' mathematics life stories were categorized into six types, based on teachers' descriptions of both…

  1. Promoting the Understanding of Mathematics in Physics at Secondary Level

    Science.gov (United States)

    Thompson, Alaric

    2016-01-01

    This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…

  2. 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…

  3. GeoGebra Tool for Building Conceptual Understanding in Mathematics

    Directory of Open Access Journals (Sweden)

    Daniela Velichová

    2010-05-01

    Full Text Available At the beginning of the 3rd millennium we are facing dramatic changes in the basic nature of teaching and learning strategies caused by massive use of new ICT. We can benefit from this development in general, and in mathematics especially, as currently available dynamic and visual learning environments as software GeoGebra could affect our perspective in terms of the content and comprehension of mathematics education. Few ideas are presented on how GeoGebra can be used as tool for creating cognitive connections between different representations of mathematical concepts, which form the necessary background for better conceptual understanding, steady knowledge and mathematical literacy.

  4. Literature Review of Applying Visual Method to Understand Mathematics

    Directory of Open Access Journals (Sweden)

    Yu Xiaojuan

    2015-01-01

    Full Text Available As a new method to understand mathematics, visualization offers a new way of understanding mathematical principles and phenomena via image thinking and geometric explanation. It aims to deepen the understanding of the nature of concepts or phenomena and enhance the cognitive ability of learners. This paper collates and summarizes the application of this visual method in the understanding of mathematics. It also makes a literature review of the existing research, especially with a visual demonstration of Euler’s formula, introduces the application of this method in solving relevant mathematical problems, and points out the differences and similarities between the visualization method and the numerical-graphic combination method, as well as matters needing attention for its application.

  5. Understanding Immunology via Engineering Design: The Role of Mathematical Prototyping

    Directory of Open Access Journals (Sweden)

    David J. Klinke

    2012-01-01

    type 1 diabetes and the dynamics of dendritic cells in the lung. This paper is intended to illustrate some of the nuances associated with applying mathematical modeling to improve understanding of the dynamics of disease progression in humans.

  6. Improving students’ understanding of mathematical concept using maple

    Science.gov (United States)

    Ningsih, Y. L.; Paradesa, R.

    2018-01-01

    This study aimed to improve students’ understanding of mathematical concept ability through implementation of using Maple in learning and expository learning. This study used a quasi-experimental research with pretest-posttest control group design. The sample on this study was 61 students in the second semester of Mathematics Education of Universitas PGRI Palembang, South Sumatera in academic year 2016/2017. The sample was divided into two classes, one class as the experiment class who using Maple in learning and the other class as a control class who received expository learning. Data were collective through the test of mathematical initial ability and mathematical concept understanding ability. Data were analyzed by t-test and two ways ANOVA. The results of this study showed (1) the improvement of students’ mathematical concept understanding ability who using Maple in learning is better than those who using expository learning; (2) there is no interaction between learning model and students’ mathematical initial ability toward the improvement of students’ understanding of mathematical concept ability.

  7. Fostering Mathematical Understanding through Physical and Virtual Manipulatives

    Science.gov (United States)

    Loong, Esther Yook Kin

    2014-01-01

    When solving mathematical problems, many students know the procedure to get to the answer but cannot explain why they are doing it in that way. According to Skemp (1976) these students have instrumental understanding but not relational understanding of the problem. They have accepted the rules to arriving at the answer without questioning or…

  8. Understanding post-operative temperature drop in cardiac surgery: a mathematical model

    NARCIS (Netherlands)

    Tindall, M. J.; Peletier, M. A.; Severens, N. M. W.; Veldman, D. J.; de Mol, B. A. J. M.

    2008-01-01

    A mathematical model is presented to understand heat transfer processes during the cooling and re-warming of patients during cardiac surgery. Our compartmental model is able to account for many of the qualitative features observed in the cooling of various regions of the body including the central

  9. What Financial Dilemmas Reveal about Students' Social and Mathematical Understanding

    Science.gov (United States)

    Sawatzki, Carly

    2013-01-01

    Everyday financial dilemmas require us to draw on social, interdisciplinary, and mathematical understandings simultaneously and in synergy if we are to make informed financial decisions. Financial literacy is enjoying an elevated status across the "Australian Curriculum." This paper reviews some of the literature on financial literacy,…

  10. Characterizing Student Mathematics Teachers' Levels of Understanding in Spherical Geometry

    Science.gov (United States)

    Guven, Bulent; Baki, Adnan

    2010-01-01

    This article presents an exploratory study aimed at the identification of students' levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, "task-based interviews" were held with eight student…

  11. Mathematics and science teachers' understanding and practices of ...

    African Journals Online (AJOL)

    The aim of the study reported in this paper was to reveal how Rwandan school teachers of Mathematics and science at the secondary school level understand and implement learner-centered pedagogy. The study was qualitative in nature. It employed qualitative methods of data collection including in-depth interviews and ...

  12. Mathematical vs. conceptual understanding: Where do we draw the line?

    Science.gov (United States)

    Sadaghiani, Homeyra; Aguilera, Nicholas

    2013-01-01

    This research involved high school physics students and how they learn to understand Newton's laws as they relate to falling bodies and projectile motion. Students in introductory, algebra-based, high school physics classes were evaluated based on their prior knowledge through a pretest, designed to assess their initial comprehension of the motion of falling bodies and projectiles. Groups were divided and taught separately with an emphasis on either mathematical derivation of equations, followed by brief conceptual discussions, or on thorough conceptual analysis, followed by a brief mathematical verification. After a posttest was given, an evaluation of the responses and explanations of each group of students was used to determine which method of instruction was more effective. Results indicate that after the conceptual group and math groups achieved similar scores on the pretest, the conceptual group obtained a slightly higher normalized gain of 25% on the posttest, compared to the mathematical group's normalized gain of 16% (unpaired two-tailed t-test P value for posttest results was 0.1037) and, while within standard deviations, also achieved higher overall scores on all posttest questions and higher normalized gains on all but one posttest question. Further, most students, even thoes in the mathematically-instructed group, were more inclined to give conceptually-based responses on postest questions than mathematically-based ones. In the context of this topic, the dominating difficulty for both groups was in analyzing two-dimensional projectile motion and, more specifically, the behavior of each onedimensional component of such motion.

  13. The role of mathematics for physics teaching and understanding

    Science.gov (United States)

    Pospiech, Gesche; Eylon, BatSheva; Bagno, Esther; Lehavi, Yaron; Geyer, Marie-Annette

    2016-05-01

    -1That mathematics is the "language of physics" implies that both areas are deeply interconnected, such that often no separation between "pure" mathematics and "pure" physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers' background and experiences. The results fit well into the derived model of PCK.

  14. The role of mathematics for physics teaching and understanding

    International Nuclear Information System (INIS)

    Pospiech, G; Geyer, M.A.; Eylon, B.; Bagno, E.; Lehavi, Y.

    2015-01-01

    That mathematics is the “language of physics” implies that both areas are deeply interconnected, such that often no separation between “pure” mathematics and “pure” physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers’ background and experiences. The results fit well into the derived model of PCK.

  15. DESIGN OF LEARNING MATERIALS ON LIMIT FUNCTION BASED MATHEMATICAL UNDERSTANDING

    Directory of Open Access Journals (Sweden)

    Muchamad Subali Noto

    2018-02-01

    Full Text Available In learning process, students are currently cannot be separated from learning difficulties, including the study material algebra limit function. It because the level of students' mathematical understanding regarding the material is still quite low. This study aimed to analyze the barriers to student learning, designing learning materials based on the material mathematics understanding algebra limit function is valid, determine teacher intervention during the implementation of learning materials and to analyze barriers to student learning after the implementation of learning materials. This research is a qualitative research study design using the form Didactical Design Research. Stages of research conducted: 1 analysis of the situation didactic before learning, 2 analysis of metapedadidatik and 3 the retrospective analysis. Data collection techniques used were tests, interviews, questionnaires, and documentation. The instrument used was a matter TKPM (Comprehension Mathematical Ability Test, interview, validation sheet materials, and documentation guidelines. Research results obtained are students experiencing obstacle to learning the material limit algebra functions. These obstacles are 1 students' difficulties in relating the material prerequisites to limit problems. 2 students can not write properly limit symbol, 3 students can not apply a limit theorem, 4 students are not able to determine the limit value at one point, and 5 students cannot determine the value of the limit at infinity. Learning materials that have been made have validation level of  with very valid criteria. The response was given when the student intervention, generally in accordance with response prediction so that interventions carried out in accordance with the design that has been made. After learning materials student learning obstacles implemented reduced/minimized.

  16. The Influence of Symbols and Equations on Understanding Mathematical Equivalence

    Science.gov (United States)

    Powell, Sarah R.

    2015-01-01

    Students with mathematics difficulty demonstrate lower mathematics performance than typical-performing peers. One contributing factor to lower mathematics performance may be misunderstanding of mathematics symbols. In several studies related to the equal sign (=), students who received explicit instruction on the relational definition (i.e.,…

  17. Examining What Teachers Do When They Display Their Best Practice: Teaching Mathematics for Understanding

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    Silver, Edward

    2010-01-01

    Despite several decades of research in psychology and mathematics education pointing to the importance of learning mathematics with understanding, other research on teachers' instructional practice in mathematics classrooms has found a remarkably consistent characterization of mathematics teaching in the United States as generally doing little to…

  18. Mathematical Representation by Students in Building Relational Understanding on Concepts of Area and Perimeter of Rectangle

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    Anwar, Rahmad Bustanul; Yuwono, Ipung; As'ari, Abdur Rahman; Sisworo; Dwi, Rahmawati

    2016-01-01

    Representation is an important aspect of learners in building a relational understanding of mathematical concepts. But the ability of a mathematical representation of students in building relational understanding is still very limited. The purpose of this research is to description of mathematical representation of students who appear in building…

  19. Examining Students' Mathematical Understanding of Geometric Transformations Using the Pirie-Kieren Model

    Science.gov (United States)

    Gülkilika, Hilal; Ugurlu, Hasan Hüseyin; Yürük, Nejla

    2015-01-01

    Students should learn mathematics with understanding. This is one of the ideas in the literature on mathematics education that everyone supports, from educational politicians to curriculum developers, from researchers to teachers, and from parents to students. In order to decide whether or not students understand mathematics we should first…

  20. Understanding the Chinese Approach to Creative Teaching in Mathematics Classrooms

    Science.gov (United States)

    Niu, Weihua; Zhou, Zheng; Zhou, Xinlin

    2017-01-01

    Using Amabile's componential theory of creativity as a framework, this paper analyzes how Chinese mathematics teachers achieve creative teaching through acquiring in-depth domain-specific knowledge in mathematics, developing creativity-related skills, as well as stimulating student interest in learning mathematics, through well-crafted,…

  1. Towards Understanding the Origins of Children's Difficulties in Mathematics Learning

    Science.gov (United States)

    Mulligan, Joanne

    2011-01-01

    Contemporary research from a psychology of mathematics education perspective has turned increasing attention to the structural development of mathematics as an explanation for the wide differences in mathematical competence shown upon school entry and in the early school years. Patterning, multiplicative reasoning and spatial structuring are three…

  2. Building Bridges of Mathematical Understanding for All Children.

    Science.gov (United States)

    Price, Jack

    1996-01-01

    These remarks are adapted from the Presidential Address at the National Council of Teachers of Mathematics in April 1996. The common goal of improving mathematics education for all is stated, and the importance of connecting mathematics to real-life situations is discussed. (AIM)

  3. Beyond Motivation: Exploring Mathematical Modeling as a Context for Deepening Students' Understandings of Curricular Mathematics

    Science.gov (United States)

    Zbiek, Rose Mary; Conner, Annamarie

    2006-01-01

    Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

  4. ANIE: A Mathematical Algorithm for Automated Indexing of Planar Deformation Features in Shocked Quartz

    Science.gov (United States)

    Huber, M. S.; Ferrière, L.; Losiak, A.; Koeberl, C.

    2011-03-01

    A mathematical method of indexing planar deformation features in quartz and a Microsoft Excel macro for automated indexing is presented, allowing for more rapid and accurate results than the previously used manual method.

  5. The idiopathic interstitial pneumonias: understanding key radiological features

    Energy Technology Data Exchange (ETDEWEB)

    Dixon, S. [Department of Radiology, Churchill Hospital, Old Road, Oxford OX3 7LJ (United Kingdom); Benamore, R., E-mail: Rachel.Benamore@orh.nhs.u [Department of Radiology, Churchill Hospital, Old Road, Oxford OX3 7LJ (United Kingdom)

    2010-10-15

    Many radiologists find it challenging to distinguish between the different interstitial idiopathic pneumonias (IIPs). The British Thoracic Society guidelines on interstitial lung disease (2008) recommend the formation of multidisciplinary meetings, with diagnoses made by combined radiological, pathological, and clinical findings. This review focuses on understanding typical and atypical radiological features on high-resolution computed tomography between the different IIPs, to help the radiologist determine when a confident diagnosis can be made and how to deal with uncertainty.

  6. President's Report: Building Bridges of Mathematical Understanding for All Children.

    Science.gov (United States)

    Price, Jack

    1996-01-01

    Remarks adapted from the Presidential Address at the 74th Annual Meeting of the National Council of Teachers of Mathematics in April 1996 charge educators with believing that every student can learn mathematics, every teacher must have adequate support and professional development opportunities, and every parent must have a vested interest in…

  7. Understanding Mathematics and Culture in Rural Contexts. ERIC Digest.

    Science.gov (United States)

    Bush, William S.

    This ERIC Digest provides an overview of concepts, writers, and tenets associated with the study of mathematics and culture and offers researchers a framework for the field, particularly with regard to rural contexts. (Author)

  8. A structural equation modeling analysis of students' understanding in basic mathematics

    Science.gov (United States)

    Oktavia, Rini; Arif, Salmawaty; Ferdhiana, Ridha; Yuni, Syarifah Meurah; Ihsan, Mahyus

    2017-11-01

    This research, in general, aims to identify incoming students' understanding and misconceptions of several basic concepts in mathematics. The participants of this study are the 2015 incoming students of Faculty of Mathematics and Natural Science of Syiah Kuala University, Indonesia. Using an instrument that were developed based on some anecdotal and empirical evidences on students' misconceptions, a survey involving 325 participants was administered and several quantitative and qualitative analysis of the survey data were conducted. In this article, we discuss the confirmatory factor analysis using Structural Equation Modeling (SEM) on factors that determine the new students' overall understanding of basic mathematics. The results showed that students' understanding on algebra, arithmetic, and geometry were significant predictors for their overall understanding of basic mathematics. This result supported that arithmetic and algebra are not the only predictors of students' understanding of basic mathematics.

  9. Mathematical Model of the Public Understanding of Space Science

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    Prisniakov, V.; Prisniakova, L.

    The success in deployment of the space programs now in many respects depends on comprehension by the citizens of necessity of programs, from "space" erudition of country. Purposefulness and efficiency of the "space" teaching and educational activity depend on knowledge of relationships between separate variables of such process. The empirical methods of ``space'' well-information of the taxpayers should be supplemented by theoretical models permitting to demonstrate a ways of control by these processes. Authors on the basis of their experience of educational activity during 50- years of among the students of space-rocket profession obtain an equation of ``space" state of the society determining a degree of its knowledge about Space, about achievements in its development, about indispensable lines of investigations, rates of informatization of the population. It is supposed, that the change of the space information consists of two parts: (1) - from going of the information about practical achievements, about development special knowledge requiring of independent financing, and (2) from intensity of dissemination of the ``free" information of a general educational line going to the population through mass-media, book, in family, in educational institutions, as a part of obligatory knowledge of any man, etc. In proposed model the level space well-information of the population depends on intensity of dissemination in the society of the space information, and also from a volume of financing of space-rocket technology, from a part of population of the employment in the space-rocket programs, from a factor of education of the population in adherence to space problems, from welfare and mentality of the people, from a rate of unemployment and material inequality. Obtained in the report on these principles the equation of a space state of the society corresponds to catastrophe such as cusp, the analysis has shown which one ways of control of the public understanding of space

  10. Investigating Alignment between Elementary Mathematics Teacher Education and Graduates' Teaching of Mathematics for Conceptual Understanding

    Science.gov (United States)

    Jansen, Amanda; Berk, Dawn; Meikle, Erin

    2017-01-01

    In this article, Amanda Jansen, Dawn Berk, and Erin Meikle investigate the impact of mathematics teacher education on teaching practices. In their study they interviewed six first-year teachers who graduated from the same elementary teacher education program and who were oriented toward teaching mathematics conceptually. They observed each teacher…

  11. Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

    Science.gov (United States)

    Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

    2017-01-01

    This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

  12. How we understand mathematics conceptual integration in the language of mathematical description

    CERN Document Server

    Woźny, Jacek

    2018-01-01

    This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested...

  13. Understanding Practices in Mathematics Education: Structure and Text

    Science.gov (United States)

    Morgan, Candia

    2014-01-01

    The practices of mathematics education can be investigated at a wide variety of levels: from the actions of individual students or teachers through classroom interactions, school structures, curriculum specifications and materials, teacher development programmes and local, national or international systems of instruction and assessment. These…

  14. Prospective Mathematics Teachers' Understanding of the Base Concept

    Science.gov (United States)

    Horzum, Tugba; Ertekin, Erhan

    2018-01-01

    The purpose of this study is to analyze what kind of conceptions prospective mathematics teachers (PMTs) have about the base concept (BC). One-hundred and thirty-nine PMTs participated in the study. In this qualitative research, data were obtained through open-ended questions, the semi-structured interviews and pictures of geometric figures drawn…

  15. Reflective Learning and Prospective Teachers' Conceptual Understanding, Critical Thinking, Problem Solving, and Mathematical Communication Skills

    Science.gov (United States)

    Junsay, Merle L.

    2016-01-01

    This is a quasi-experimental study that explored the effects of reflective learning on prospective teachers' conceptual understanding, critical thinking, problem solving, and mathematical communication skills and the relationship of these variables. It involved 60 prospective teachers from two basic mathematics classes of an institution of higher…

  16. Using Cooperative Teams-Game-Tournament in 11 Religious School to Improve Mathematics Understanding and Communication

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    Veloo, Arsaythamby; Md-Ali, Ruzlan; Chairany, Sitie

    2016-01-01

    Purpose: This paper was part of a larger study which looked into the effect of implementing Cooperative Teams-Games-Tournament (TGT) on understanding of and communication in mathematics. The study had identified the main and interaction effect of using Cooperative TGT for learning mathematics in religious secondary school classrooms. A…

  17. Exploring Positioning as an Analytical Tool for Understanding Becoming Mathematics Teachers' Identities

    Science.gov (United States)

    Skog, Kicki; Andersson, Annica

    2015-01-01

    The aim of this article is to explore how a sociopolitical analysis can contribute to a deeper understanding of critical aspects for becoming primary mathematics teachers' identities during teacher education. The question we ask is the following: How may power relations in university settings affect becoming mathematics teachers' subject…

  18. Comparison of Student Understanding of Line Graph Slope in Physics and Mathematics

    Science.gov (United States)

    Planinic, Maja; Milin-Sipus, Zeljka; Katic, Helena; Susac, Ana; Ivanjek, Lana

    2012-01-01

    This study gives an insight into the differences between student understanding of line graph slope in the context of physics (kinematics) and mathematics. Two pairs of parallel physics and mathematics questions that involved estimation and interpretation of line graph slope were constructed and administered to 114 Croatian second year high school…

  19. Teaching with Procedural Variation: A Chinese Way of Promoting Deep Understanding of Mathematics

    Science.gov (United States)

    Lai, Mun Yee; Murray, Sara

    2012-01-01

    In mathematics education, there has been tension between deep learning and repetitive learning. Western educators often emphasize the need for students to construct a conceptual understanding of mathematical symbols and rules before they practise the rules (Li, 2006). On the other hand, Chinese learners tend to be oriented towards rote learning…

  20. Mathematics Professional Development: Critical Features for Developing Leadership Skills and Building Teachers' Capacity

    Science.gov (United States)

    Koellner, Karen; Jacobs, Jennifer; Borko, Hilda

    2011-01-01

    This article focuses on three features of professional development (PD) programs that play an important role in developing leadership skills and building teachers' capacity: (1) fostering a professional learning community, (2) developing teachers' mathematical knowledge for teaching, and (3) adapting PD to support local needs and interests. We…

  1. A cognitive framework for analyzing and describing introductory students' use and understanding of mathematics in physics

    Science.gov (United States)

    Tuminaro, Jonathan

    Many introductory, algebra-based physics students perform poorly on mathematical problem solving tasks in physics. There are at least two possible, distinct reasons for this poor performance: (1) students simply lack the mathematical skills needed to solve problems in physics, or (2) students do not know how to apply the mathematical skills they have to particular problem situations in physics. While many students do lack the requisite mathematical skills, a major finding from this work is that the majority of students possess the requisite mathematical skills, yet fail to use or interpret them in the context of physics. In this thesis I propose a theoretical framework to analyze and describe students' mathematical thinking in physics. In particular, I attempt to answer two questions. What are the cognitive tools involved in formal mathematical thinking in physics? And, why do students make the kinds of mistakes they do when using mathematics in physics? According to the proposed theoretical framework there are three major theoretical constructs: mathematical resources, which are the knowledge elements that are activated in mathematical thinking and problem solving; epistemic games, which are patterns of activities that use particular kinds of knowledge to create new knowledge or solve a problem; and frames, which are structures of expectations that determine how individuals interpret situations or events. The empirical basis for this study comes from videotaped sessions of college students solving homework problems. The students are enrolled in an algebra-based introductory physics course. The videotapes were transcribed and analyzed using the aforementioned theoretical framework. Two important results from this work are: (1) the construction of a theoretical framework that offers researchers a vocabulary (ontological classification of cognitive structures) and grammar (relationship between the cognitive structures) for understanding the nature and origin of

  2. Middle School Mathematics Teachers' Knowledge of Students' Understanding of Core Algebraic Concepts: Equal Sign and Variable

    Science.gov (United States)

    Asquith, Pamela; Stephens, Ana C.; Knuth, Eric J.; Alibali, Martha W.

    2007-01-01

    This article reports results from a study focused on teachers' knowledge of students' understanding of core algebraic concepts. In particular, the study examined middle school mathematics teachers' knowledge of students' understanding of the equal sign and variable, and students' success applying their understanding of these concepts. Interview…

  3. Life on the Number Line: Routes to Understanding Fraction Magnitude for Students with Difficulties Learning Mathematics

    Science.gov (United States)

    Gersten, Russell; Schumacher, Robin F.; Jordan, Nancy C.

    2017-01-01

    Magnitude understanding is critical for students to develop a deep understanding of fractions and more advanced mathematics curriculum. The research reports in this special issue underscore magnitude understanding for fractions and emphasize number lines as both an assessment and an instructional tool. In this commentary, we discuss how number…

  4. Student’s mathematical understanding ability based on self-efficacy

    Science.gov (United States)

    Ramdhani, M. R.; Usodo, B.; Subanti, S.

    2017-11-01

    Materials in mathematics are provided not only as an ability to memorize, but also to train the ability of mathematical understanding. Students’ mathematical understanding ability is influenced by the students’ belief in solving the given problems. This research aim to determine the mathematical understanding ability of junior high school students. This research is descriptive qualitative research. Data collection was done through a test, questionnaire, and interview. The result showed that students with high self-efficacy category could master the three indicators of students’ mathematical understanding ability well, namely translation, interpretation, and exploration. Students with moderate self-efficacy category can master translation indicator and able to achieve interpretation indicator but they unable to reach exploration indicator. Students with low self-efficacy category only master the translation, but they cannot achieve the interpretation and exploration indicators. So, the students who have high, moderate or low self-efficacy master the indicator of mathematical understanding based on the level of understanding capabilities on each student.

  5. Mathematical Understanding and Proving Abilities: Experiment With Undergraduate Student By Using Modified Moore Learning Approach

    Directory of Open Access Journals (Sweden)

    Rippi Maya

    2011-07-01

    Full Text Available This paper reports findings of  a  post test experimental control group design conducted to investigate the role of modified Moore learning approach  on improving students’ mathematical understanding and proving abilities. Subject of study were 56 undergradute students of one state university in Bandung, who took advanced abstract algebra course. Instrument of study were a set test of mathematical understanding ability, a set test of mathematical proving ability, and a set of students’ opinion scale on modified Moore learning approach. Data were analyzed by using two path ANOVA. The study found that proof construction process was more difficult than mathematical understanding  task  for all students, and students still posed some difficulties on constructing mathematical proof task.  The study also found there were not differences  between students’  abilities on mathematical understanding and on proving abilities of  the both classes, and both abilities were classified as mediocre. However, in modified Moore learning approach class there were more students who got above average grades on mathematical understanding than those of conventional class. Moreover, students performed positive  opinion toward  modified Moore learning approach. They  were  active in questioning and solving problems, and in explaining their works in front of class as well, while students of conventional teaching prefered to listen to lecturer’s explanation. The study also found that there was no interaction between learning approach and students’ prior mathematics ability on mathematical understanding and proving abilities,  but  there were  quite strong  association between students’ mathematical understanding and proving abilities.Keywords:  modified Moore learning approach, mathematical understanding ability, mathematical proving ability. DOI: http://dx.doi.org/10.22342/jme.2.2.751.231-250

  6. An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving

    Science.gov (United States)

    Yuli Eko Siswono, Tatag; Wachidul Kohar, Ahmad; Kurniasari, Ika; Puji Astuti, Yuliani

    2016-02-01

    Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers‘ responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers’ work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.

  7. Understanding Protein-Protein Interactions Using Local Structural Features

    DEFF Research Database (Denmark)

    Planas-Iglesias, Joan; Bonet, Jaume; García-García, Javier

    2013-01-01

    of this classification suggests that the balance between favoring and disfavoring structural features determines if a pair of proteins interacts or not. Our results are in agreement with previous works and support the funnel-like intermolecular energy landscape theory that explains PPIs. We have used these features...

  8. Developing a Deeper Understanding of "Mathematics Teaching Expertise": An Examination of Three Chinese Mathematics Teachers' Resource Systems as Windows into Their Work and Expertise

    Science.gov (United States)

    Pepin, Birgit; Xu, Binyan; Trouche, Luc; Wang, Chongyang

    2017-01-01

    In order to develop a deeper understanding of mathematics teaching expertise, in this study we use the Documentational Approach to Didactics to explore the resource systems of three Chinese mathematics "expert" teachers. Exploiting the Western and Eastern literature we examine the notion of "mathematics teaching expertise", as…

  9. 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.

  10. Localization of neural efficiency of the mathematically gifted brain through a feature subset selection method.

    Science.gov (United States)

    Zhang, Li; Gan, John Q; Wang, Haixian

    2015-10-01

    Based on the neural efficiency hypothesis and task-induced EEG gamma-band response (GBR), this study investigated the brain regions where neural resource could be most efficiently recruited by the math-gifted adolescents in response to varying cognitive demands. In this experiment, various GBR-based mental states were generated with three factors (level of mathematical ability, task complexity, and short-term learning) modulating the level of neural activation. A feature subset selection method based on the sequential forward floating search algorithm was used to identify an "optimal" combination of EEG channel locations, where the corresponding GBR feature subset could obtain the highest accuracy in discriminating pairwise mental states influenced by each experiment factor. The integrative results from multi-factor selections suggest that the right-lateral fronto-parietal system is highly involved in neural efficiency of the math-gifted brain, primarily including the bilateral superior frontal, right inferior frontal, right-lateral central and right temporal regions. By means of the localization method based on single-trial classification of mental states, new GBR features and EEG channel-based brain regions related to mathematical giftedness were identified, which could be useful for the brain function improvement of children/adolescents in mathematical learning through brain-computer interface systems.

  11. 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.

  12. Semantic feature extraction for interior environment understanding and retrieval

    Science.gov (United States)

    Lei, Zhibin; Liang, Yufeng

    1998-12-01

    In this paper, we propose a novel system of semantic feature extraction and retrieval for interior design and decoration application. The system, V2ID(Virtual Visual Interior Design), uses colored texture and spatial edge layout to obtain simple information about global room environment. We address the domain-specific segmentation problem in our application and present techniques for obtaining semantic features from a room environment. We also discuss heuristics for making use of these features (color, texture, edge layout, and shape), to retrieve objects from an existing database. The final resynthesized room environment, with the original scene and objects from the database, is created for the purpose of animation and virtual walk-through.

  13. Motion sensors in mathematics teaching: learning tools for understanding general math concepts?

    Science.gov (United States)

    Urban-Woldron, Hildegard

    2015-05-01

    Incorporating technology tools into the mathematics classroom adds a new dimension to the teaching of mathematics concepts and establishes a whole new approach to mathematics learning. In particular, gathering data in a hands-on and real-time method helps classrooms coming alive. The focus of this paper is on bringing forward important mathematics concepts such as functions and rate of change with the motion detector. Findings from the author's studies suggest that the motion detector can be introduced from a very early age and used to enliven classes at any level. Using real-world data to present the main functions invites an experimental approach to mathematics and encourages students to engage actively in their learning. By emphasizing learning experiences with computer-based motion detectors and aiming to involve students in mathematical representations of real-world phenomena, six learning activities, which were developed in previous research studies, will be presented. Students use motion sensors to collect physical data that are graphed in real time and then manipulate and analyse them. Because data are presented in an immediately understandable graphical form, students are allowed to take an active role in their learning by constructing mathematical knowledge from observation of the physical world. By utilizing a predict-observe-explain format, students learn about slope, determining slope and distance vs. time graphs through motion-filled activities. Furthermore, exploring the meaning of slope, viewed as the rate of change, students acquire competencies for reading, understanding and interpreting kinematics graphs involving a multitude of mathematical representations. Consequently, the students are empowered to efficiently move among tabular, graphical and symbolic representation to analyse patterns and discover the relationships between different representations of motion. In fact, there is a need for further research to explore how mathematics teachers

  14. Sensitivity to general and specific numerical features in typical achievers and children with mathematics learning disability.

    Science.gov (United States)

    Rotem, Avital; Henik, Avishai

    2015-01-01

    We examined the development of sensitivity to general and specific numerical features in typical achievers and in 6th and 8th graders with mathematics learning disability (MLD), using two effects in mental multiplication: operand-relatedness (i.e., difficulty in avoiding errors that are related to the operands via a shared multiplication row) and decade-consistency (i.e., difficulty in avoiding errors that are operand related and also share a decade with the true result). Responses to decade-consistent products were quick but erroneous. In line with the processing sequence in adults, children first became sensitive to the general numerical feature of operand-relatedness (typical achievers--from 3rd grade; children with MLD in 8th grade) and only later to the specific feature of decade-consistency (typical achievers--from 4th grade, but only from 6th grade in a mature pattern). Implications of the numerical sensitivity in children with MLD are discussed.

  15. Understanding Structural Features of Microbial Lipases–-An Overview

    Directory of Open Access Journals (Sweden)

    John Geraldine Sandana Mala

    2008-01-01

    Full Text Available The structural elucidations of microbial lipases have been of prime interest since the 1980s. Knowledge of structural features plays an important role in designing and engineering lipases for specific purposes. Significant structural data have been presented for few microbial lipases, while, there is still a structure-deficit, that is, most lipase structures are yet to be resolved. A search for ‘lipase structure’ in the RCSB Protein Data Bank ( http://www.rcsb.org/pdb/ returns only 93 hits (as of September 2007 and, the NCBI database ( http://www.ncbi.nlm.nih.gov reports 89 lipase structures as compared to 14719 core nucleotide records. It is therefore worthwhile to consider investigations on the structural analysis of microbial lipases. This review is intended to provide a collection of resources on the instrumental, chemical and bioinformatics approaches for structure analyses. X-ray crystallography is a versatile tool for the structural biochemists and is been exploited till today. The chemical methods of recent interests include molecular modeling and combinatorial designs. Bioinformatics has surged striking interests in protein structural analysis with the advent of innumerable tools. Furthermore, a literature platform of the structural elucidations so far investigated has been presented with detailed descriptions as applicable to microbial lipases. A case study of Candida rugosa lipase (CRL has also been discussed which highlights important structural features also common to most lipases. A general profile of lipase has been vividly described with an overview of lipase research reviewed in the past.

  16. INTERCULTURAL FEATURES AND THE THEME OF TRAVELLING IN BILINGUAL MATHEMATICS LESSONS

    Directory of Open Access Journals (Sweden)

    Zuzana Naštická

    2016-08-01

    Full Text Available The present qualitative research is focused on bilingual mathematics education. The research presents findings of a case study of one bilingual Slovak and English mathematics 40-minute lesson within an after school elective bilingual mathematics course running weekly since October, 2015. The lesson took place in March, 2016, and was attended by nine learners aged 12-13, eight boys and one girl. The learners are cases of successive school additive bilingual education. The elective course as a whole is a case of immerse bilingual educational programme. In terms of sociolinguistic settings, the course lessons are cases of bilingual education with external second language. The researcher designed and realized the course lessons in terms of CLIL approach, i.e. Content and Language Integrated Learning. The main aim of the case study was to examine if bilingual mathematics instruction does or does not prevent learners from solving math word problems. Secondly, the analysis of transcription of the lesson audio-record served for identification of intercultural features which might hinder the learning process. The analysis of the transcribed audio-record indicates that the bilingual context did not prevent students from solving math word problems, although each of the students worked at their individual rate. On the other hand, some students were confused by the comma as a thousands-separator in multi-digit numbers, and this actually hindered their learning and problem solving process. This fact has been identified as an intercultural difference which had to be explicitly explained to the students. In order to lessen the possible negative influences of bilingual context on mathematics education, teachers need to predict students’ responses to various intercultural differences which students are unfamiliar with.

  17. Growing understanding of undergraduate mathematics: a good frame produces better tomatoes

    Science.gov (United States)

    Barton, Bill

    2011-10-01

    I lay a new theoretical framework across my own lecturing in order to understand what is happening. On the one hand, this is a test of the framework. On the other, I gain insights into both better practices and better course design. The framework constructs undergraduate teaching as the interaction between the discipline and the university pedagogical context. Overlaying this are three levels of teaching intent: pragmatic, epistemic, and heuristic. The resulting framework supports my growing understanding of lecturing practice. It also proves useful in analysing three characteristics of university mathematics: student responsibility for learning; enculturation of the discipline of mathematics; and the tyranny of examples. The framework is a tool for redesigning courses and developing delivery formats that are likely to enhance student learning and behaviour objectives of undergraduate mathematics. However, the analysis shows a deficiency of the framework in its paucity of attention to student learning in a university context. Extending the framework in this way is the next task.

  18. Understanding the Gender Gap in Mathematics Achievement: The Role of Self-Efficacy and Stereotype Threat

    Science.gov (United States)

    Schwery, Denise; Hulac, David; Schweinle, Amy

    2016-01-01

    This literature review provides school psychologists with an understanding of the important issues related to the gender gap in mathematics achievement. The extant literature suggests that girls tend to receive lower scores than boys on standardized math tests, but in general these differences tend to be small. However, girls have better classroom…

  19. On the Axiomatization of Mathematical Understanding: Continuous Functions in the Transition to Topology

    Science.gov (United States)

    Cheshire, Daniel C.

    2017-01-01

    The introduction to general topology represents a challenging transition for students of advanced mathematics. It requires the generalization of their previous understanding of ideas from fields like geometry, linear algebra, and real or complex analysis to fit within a more abstract conceptual system. Students must adopt a new lexicon of…

  20. Mathematical Understanding and Proving Abilities: Experiment with Undergraduate Student by Using Modified Moore Learning Approach

    Science.gov (United States)

    Maya, Rippi; Sumarmo, Utari

    2011-01-01

    This paper reports findings of a post test experimental control group design conducted to investigate the role of modified Moore learning approach on improving students' mathematical understanding and proving abilities. Subjects of study were 56 undergraduate students of one state university in Bandung, who took advanced abstract algebra course.…

  1. Shifting Preservice Teachers' Beliefs and Understandings to Support Pedagogical Change in Mathematics

    Science.gov (United States)

    Letwinsky, Karim Medico; Cavender, Monica

    2018-01-01

    Many preservice teacher (PST) programs throughout the world are preparing students to implement the Core Standards, which require deeper conceptual understandings of mathematics and an informed approach for teaching. In this qualitative multi-case study, researchers explored the teaching methods for two university instructors and changes in PSTs…

  2. Introduction to insurance mathematics technical and financial features of risk transfers

    CERN Document Server

    Olivieri, Annamaria

    2015-01-01

    This second edition expands the first chapters, which focus on the approach to risk management issues discussed in the first edition, to offer readers a better understanding of the risk management process and the relevant quantitative phases. In the following chapters the book examines life insurance, non-life insurance and pension plans, presenting the technical and financial aspects of risk transfers and insurance without the use of complex mathematical tools.   The book is written in a comprehensible style making it easily accessible to advanced undergraduate and graduate students in Economics, Business and Finance, as well as undergraduate students in Mathematics who intend starting on an actuarial qualification path. With the systematic inclusion of practical topics, professionals will find this text useful when working in insurance and pension related areas, where investments, risk analysis and financial reporting play a major role.

  3. Mathematical modeling applied to understand the host-pathogen interaction of HIV infection in Bangladesh

    Directory of Open Access Journals (Sweden)

    S. K. Sahani

    2017-10-01

    Full Text Available The most urgent public health problem today is to devise effective strategies to minimize the destruction caused by the AIDS epidemic. The understanding of HIV infection through mathematical modeling have made a significant contribution. The interaction of host to pathogen have been determined by fitting mathematical models to experimental data. In Bangladesh, the increasing rate of HIV infection comparing to the other countries of the world is not so high. Among the most at risk population of Bangladesh the HIV prevalent is still considered to be low with prevalence 1 then HIV infection persists.

  4. "Bigger Number Means You Plus!"--Teachers Learning to Use Clinical Interviews to Understand Students' Mathematical Thinking

    Science.gov (United States)

    Heng, Mary Anne; Sudarshan, Akhila

    2013-01-01

    This paper examines the perceptions and understandings of ten grades 1 and 2 Singapore mathematics teachers as they learned to use clinical interviews (Ginsburg, "Human Development" 52:109-128, 2009) to understand students' mathematical thinking. This study challenged teachers' pedagogical assumptions about what it means to teach for…

  5. Mathematical understanding of nature essays on amazing physical phenomena and their understanding by mathematicians

    CERN Document Server

    Arnold, V I

    2014-01-01

    This collection of 39 short stories gives the reader a unique opportunity to take a look at the scientific philosophy of Vladimir Arnold, one of the most original contemporary researchers. Topics of the stories included range from astronomy, to mirages, to motion of glaciers, to geometry of mirrors and beyond. In each case Arnold's explanation is both deep and simple, which makes the book interesting and accessible to an extremely broad readership. Original illustrations hand drawn by the author help the reader to further understand and appreciate Arnold's view on the relationship between math

  6. An introduction to mathematical finance with applications understanding and building financial intuition

    CERN Document Server

    Petters, Arlie O

    2016-01-01

    This textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamental understanding of key financial ideas and tools that form the basis for building realistic models, including those that may become proprietary. Numerous carefully chosen examples and exercises reinforce the student’s conceptual understanding and facility with applications. The exercises are divided into conceptual, application-based, and theoretical problems, which probe the material deeper. The book is aimed toward advanced undergraduates and first-year graduate students who are new to finance or want a more rigorous treatment of the mathematical models used within. While no background in finance is assumed, prerequisite math courses include multivariable calculus, probability, and linear algebra. The authors introduce additional mathematical tools as needed. The entire...

  7. Computer-based image studies on tumor nests mathematical features of breast cancer and their clinical prognostic value.

    Science.gov (United States)

    Wang, Lin-Wei; Qu, Ai-Ping; Yuan, Jing-Ping; Chen, Chuang; Sun, Sheng-Rong; Hu, Ming-Bai; Liu, Juan; Li, Yan

    2013-01-01

    The expending and invasive features of tumor nests could reflect the malignant biological behaviors of breast invasive ductal carcinoma. Useful information on cancer invasiveness hidden within tumor nests could be extracted and analyzed by computer image processing and big data analysis. Tissue microarrays from invasive ductal carcinoma (n = 202) were first stained with cytokeratin by immunohistochemical method to clearly demarcate the tumor nests. Then an expert-aided computer analysis system was developed to study the mathematical and geometrical features of the tumor nests. Computer recognition system and imaging analysis software extracted tumor nests information, and mathematical features of tumor nests were calculated. The relationship between tumor nests mathematical parameters and patients' 5-year disease free survival was studied. There were 8 mathematical parameters extracted by expert-aided computer analysis system. Three mathematical parameters (number, circularity and total perimeter) with area under curve >0.5 and 4 mathematical parameters (average area, average perimeter, total area/total perimeter, average (area/perimeter)) with area under curve nests could be a useful parameter to predict the prognosis of early stage breast invasive ductal carcinoma.

  8. The effect of problem posing and problem solving with realistic mathematics education approach to the conceptual understanding and adaptive reasoning

    Science.gov (United States)

    Mahendra, Rengga; Slamet, Isnandar; Budiyono

    2017-12-01

    One of the difficulties of students in learning mathematics is on the subject of geometry that requires students to understand abstract things. The aim of this research is to determine the effect of learning model Problem Posing and Problem Solving with Realistic Mathematics Education Approach to conceptual understanding and students' adaptive reasoning in learning mathematics. This research uses a kind of quasi experimental research. The population of this research is all seventh grade students of Junior High School 1 Jaten, Indonesia. The sample was taken using stratified cluster random sampling technique. The test of the research hypothesis was analyzed by using t-test. The results of this study indicate that the model of Problem Posing learning with Realistic Mathematics Education Approach can improve students' conceptual understanding significantly in mathematics learning. In addition tu, the results also showed that the model of Problem Solving learning with Realistic Mathematics Education Approach can improve students' adaptive reasoning significantly in learning mathematics. Therefore, the model of Problem Posing and Problem Solving learning with Realistic Mathematics Education Approach is appropriately applied in mathematics learning especially on the subject of geometry so as to improve conceptual understanding and students' adaptive reasoning. Furthermore, the impact can improve student achievement.

  9. ASSESSING CONCEPTUAL UNDERSTANDING IN MATHEMATICS: Using Derivative Function to Solve Connected Problems

    Directory of Open Access Journals (Sweden)

    Nevin ORHUN

    2013-07-01

    Full Text Available Open and distance education plays an important role in the actualization of cultural goals as well as in societal developments. This is an independent teaching and learning method for mathematics which forms the dynamic of scientific thinking. Distance education is an important alternative to traditional teaching applications. These contributions brought by technology enable students to participate actively in having access to information and questioning it. Such an application increases students’ motivation and teaches how mathematics can be used in daily life. Derivative is a mathematical concept which can be used in many areas of daily life. The aim of this study is to enable the concept of derivatives to be understood well by using the derivative function in the solution of various problems. It also aims at interpreting difficulties theoretically in the solution of problems and determining mistakes in terms of teaching methods. In this study, how various aspects of derivatives are understood is emphasized. These aspects concern the explanation of concepts and process, and also their application to certain concepts in physics. Students’ depth of understanding of derivatives was analyzed based on two aspects of understanding; theoretical analysis and contextual application. Follow-up interviews were conducted with five students. The results show that the students preferred to apply an algebraic symbolic aspect instead of using logical meanings of function and its derivative. In addition, in relation to how the graph of the derivative function affects the aspect of function, it was determined that the students displayed low performance.

  10. Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics.

    Science.gov (United States)

    DeCaro, Marci S

    2016-10-01

    An important goal in mathematics is to flexibly use and apply multiple, efficient procedures to solve problems and to understand why these procedures work. One factor that may limit individuals' ability to notice and flexibly apply strategies is the mental set induced by the problem context. Undergraduate (N = 41, Experiment 1) and fifth- and sixth-grade students (N = 87, Experiment 2) solved mathematical equivalence problems in one of two set-inducing conditions. Participants in the complex-first condition solved problems without a repeated addend on both sides of the equal sign (e.g., 7 + 5 + 9 = 3 + _), which required multistep strategies. Then these students solved problems with a repeated addend (e.g., 7 + 5 + 9 = 7 + _), for which a shortcut strategy could be readily used (i.e., adding 5 + 9). Participants in the shortcut-first condition solved the same problem set but began with the shortcut problems. Consistent with laboratory studies of mental set, participants in the complex-first condition were less likely to use the more efficient shortcut strategy when possible. In addition, these participants were less likely to demonstrate procedural flexibility and conceptual understanding on a subsequent assessment of mathematical equivalence knowledge. These findings suggest that certain problem-solving contexts can help or hinder both flexibility in strategy use and deeper conceptual thinking about the problems.

  11. 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

  12. The unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement.

    Science.gov (United States)

    Wong, Terry Tin-Yau

    2017-12-01

    The current study examined the unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement. A sample of 124 fourth graders was tested on their arithmetic operation understanding (as reflected by their understanding of arithmetic principles and the knowledge about the application of arithmetic operations) and their precision of rational number magnitude representation. They were also tested on their mathematics achievement and arithmetic computation performance as well as the potential confounding factors. The findings suggested that both arithmetic operation understanding and numerical magnitude representation uniquely predicted children's mathematics achievement. The findings highlight the significance of arithmetic operation understanding in mathematics learning. Copyright © 2017 Elsevier Inc. All rights reserved.

  13. Using Mathematical Software to Introduce Fourier Transforms in Physical Chemistry to Develop Improved Understanding of Their Applications in Analytical Chemistry

    Science.gov (United States)

    Miller, Tierney C.; Richardson, John N.; Kegerreis, Jeb S.

    2016-01-01

    This manuscript presents an exercise that utilizes mathematical software to explore Fourier transforms in the context of model quantum mechanical systems, thus providing a deeper mathematical understanding of relevant information often introduced and treated as a "black-box" in analytical chemistry courses. The exercise is given to…

  14. Understanding the Technological, Pedagogical, and Mathematical Issues That Emerge as Secondary Mathematics Teachers Design Lessons That Integrate Technology

    Science.gov (United States)

    Gonzalez, Marggie Denise

    2016-01-01

    This multiple case study examines four groups of secondary mathematics teachers engaged in a Lesson Study approach to professional development where they planned and taught lessons that integrate technology. Informed by current literature, a framework was developed to focus on the dimensions of teacher's knowledge to teach mathematics with…

  15. Understanding Experimental LCMV Infection of Mice: The Role of Mathematical Models

    Directory of Open Access Journals (Sweden)

    Gennady Bocharov

    2015-01-01

    Full Text Available Virus infections represent complex biological systems governed by multiple-level regulatory processes of virus replication and host immune responses. Understanding of the infection means an ability to predict the systems behaviour under various conditions. Such predictions can only rely upon quantitative mathematical models. The model formulations should be tightly linked to a fundamental step called “coordinatization” (Hermann Weyl, that is, the definition of observables, parameters, and structures that enable the link with a biological phenotype. In this review, we analyse the mathematical modelling approaches to LCMV infection in mice that resulted in quantification of some fundamental parameters of the CTL-mediated virus control including the rates of T cell turnover, infected target cell elimination, and precursor frequencies. We show how the modelling approaches can be implemented to address diverse aspects of immune system functioning under normal conditions and in response to LCMV and, importantly, make quantitative predictions of the outcomes of immune system perturbations. This may highlight the notion that data-driven applications of meaningful mathematical models in infection biology remain a challenge.

  16. A Mathematical Model for the Hippocampus: Towards the Understanding of Episodic Memory and Imagination

    Science.gov (United States)

    Tsuda, I.; Yamaguti, Y.; Kuroda, S.; Fukushima, Y.; Tsukada, M.

    How does the brain encode episode? Based on the fact that the hippocampus is responsible for the formation of episodic memory, we have proposed a mathematical model for the hippocampus. Because episodic memory includes a time series of events, an underlying dynamics for the formation of episodic memory is considered to employ an association of memories. David Marr correctly pointed out in his theory of archecortex for a simple memory that the hippocampal CA3 is responsible for the formation of associative memories. However, a conventional mathematical model of associative memory simply guarantees a single association of memory unless a rule for an order of successive association of memories is given. The recent clinical studies in Maguire's group for the patients with the hippocampal lesion show that the patients cannot make a new story, because of the lack of ability of imagining new things. Both episodic memory and imagining things include various common characteristics: imagery, the sense of now, retrieval of semantic information, and narrative structures. Taking into account these findings, we propose a mathematical model of the hippocampus in order to understand the common mechanism of episodic memory and imagination.

  17. A Picture is Worth a Thousand Words: Examining learners’ illustrations to understand Attitudes towards Mathematics

    Directory of Open Access Journals (Sweden)

    Farhat Syyeda

    2015-04-01

    Full Text Available This article presents my experience of using pictures/images drawn by children as a form of data in research and discusses the merits and implications of employing this method. It comes from research of a mixed method exploratory case study to investigate the attitudes of 11 and 15 year old secondary school students (in the East Midlands towards Mathematics. The aim of this research was to gain an insight into the emotions, cognition, beliefs and behaviour of learners regarding Maths and the factors which influence their attitude. Besides using the tried and tested data collection tools such as focus groups and questionnaires, the children were asked to draw pictures illustrating their vision of Maths and its impact on their lives. The idea was to offer them an alternative medium of communication to exhibit their feelings and thoughts. Students used emoticons, numerals, figures, characters and mathematical symbols to show their favourable/unfavourable attitudes towards Maths and their understanding of the importance of Maths in future life. The results of visual data in this study conform to the findings of the other forms of data collected and show that boys and higher ability students have a more positive attitude towards Mathematics as compared to girls and low ability students.

  18. 100 commonly asked questions in math class answers that promote mathematical understanding, grades 6-12

    CERN Document Server

    Posamentier, Alfred S (Steven); Germain-Williams, Terri L (Lynn); Paris, Elaine S; Lehmann, Ingmar H (Horst)

    2013-01-01

    100 ways to get students hooked on math! That one question got you stumped? Or maybe you have the answer, but it's not all that compelling. Al Posamentier and his coauthors to the rescue with this handy reference containing fun answers to students'100 most frequently asked math questions. Even if you already have the answers, Al's explanations are certain to keep kids hooked. The big benefits? You'll discover high-interest ways to Teach to the Common Core's math content standards Promote inquiry and process in mathematical thinking Build procedural skills and conceptual understanding Encourage

  19. [Bone Cell Biology Assessed by Microscopic Approach. A mathematical approach to understand bone remodeling].

    Science.gov (United States)

    Kameo, Yoshitaka; Adachi, Taiji

    2015-10-01

    It is well known that bone tissue can change its outer shape and internal structure by remodeling according to a changing mechanical environment. However, the mechanism of bone functional adaptation induced by the collaborative metabolic activities of bone cells in response to mechanical stimuli remains elusive. In this article, we focus on the hierarchy of bone structure and function from the microscopic cellular level to the macroscopic tissue level. We provide an overview of a mathematical approach to understand the adaptive changes in trabecular morphology under the application of mechanical stress.

  20. Description of Student’s Metacognitive Ability in Understanding and Solving Mathematics Problem

    Science.gov (United States)

    Ahmad, Herlina; Febryanti, Fatimah; Febryanti, Fatimah; Muthmainnah

    2018-01-01

    This research was conducted qualitative which was aim to describe metacognitive ability to understand and solve the problems of mathematics. The subject of the research was the first year students at computer and networking department of SMK Mega Link Majene. The sample was taken by purposive sampling technique. The data obtained used the research instrument based on the form of students achievements were collected by using test of student’s achievement and interview guidance. The technique of collecting data researcher had observation to ascertain the model that used by teacher was teaching model of developing metacognitive. The technique of data analysis in this research was reduction data, presentation and conclusion. Based on the whole findings in this study it was shown that student’s metacognitive ability generally not develops optimally. It was because of limited scope of the materials, and cognitive teaching strategy handled by verbal presentation and trained continuously in facing cognitive tasks, such as understanding and solving problem.

  1. Analysis of Undergraduate Students’ Mathematical Understanding Ability of the Limit of Function Based on APOS Theory Perspective

    Science.gov (United States)

    Afgani, M. W.; Suryadi, D.; Dahlan, J. A.

    2017-09-01

    The aim of this study was to know the level of undergraduate students’ mathematical understanding ability based on APOS theory perspective. The APOS theory provides an evaluation framework to describe the level of students’ understanding and mental structure about their conception to a mathematics concept. The levels of understanding in APOS theory are action, process, object, and schema conception. The subjects were 59 students of mathematics education whom had attended a class of the limit of function at a university in Palembang. The method was qualitative descriptive with 4 test items. The result showed that most of students were still at the level of action conception. They could calculate and use procedure precisely to the mathematics objects that was given, but could not reach the higher conception yet.

  2. Mathematics

    CERN Document Server

    Stein, Sherman K

    2010-01-01

    Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi

  3. Understanding and quantifying cognitive complexity level in mathematical problem solving items

    Directory of Open Access Journals (Sweden)

    SUSAN E. EMBRETSON

    2008-09-01

    Full Text Available The linear logistic test model (LLTM; Fischer, 1973 has been applied to a wide variety of new tests. When the LLTM application involves item complexity variables that are both theoretically interesting and empirically supported, several advantages can result. These advantages include elaborating construct validity at the item level, defining variables for test design, predicting parameters of new items, item banking by sources of complexity and providing a basis for item design and item generation. However, despite the many advantages of applying LLTM to test items, it has been applied less often to understand the sources of complexity for large-scale operational test items. Instead, previously calibrated item parameters are modeled using regression techniques because raw item response data often cannot be made available. In the current study, both LLTM and regression modeling are applied to mathematical problem solving items from a widely used test. The findings from the two methods are compared and contrasted for their implications for continued development of ability and achievement tests based on mathematical problem solving items.

  4. Mathematics

    International Nuclear Information System (INIS)

    Demazure, M.

    1988-01-01

    The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr

  5. Developing mathematics edutainment media for Android based on students’ understanding and interest: a teachers’ review

    Science.gov (United States)

    Setyaningrum, W.; Waryanto, N. H.

    2018-03-01

    This paper aimed to describe the development of interactive edutainment mathematics media using Construct 2 software for grade 7 Junior High School, and to determine the quality of the interactive edutainment media developed in regards to improve students’ understanding and interest. This research employs Research and Development design, which media was developed using ADDIE model consisting of analysing, designing, developing, implementing and evaluating. This paper focuses on the steps of development and validity of the interactive media from teachers’ point of view. The teachers review focuses on three aspects – instructional, audio-visual and operational design. The review suggested that the media was very good in regard to the three aspects, with the average score was 144.55 from the maximum score of 175. Several contexts used in the game, however, need to be adjusted to students age.

  6. Effects of Understanding the Problem Statement on Students' Mathematical Performance of Senior Secondary Schools in Borno State, Nigeria

    Science.gov (United States)

    Banus, Abdullahi Audu; Dauda, Bala

    2015-01-01

    The study assessed the relative effectiveness of understanding the problem statement on students' mathematical behaviours in Borno State Secondary Schools. The study was guided by an objective: to determine the Understanding the problem statement on student's performance in senior secondary school and a null hypothesis: there was no effect of…

  7. The Effect of Brain Based Learning on Second Grade Junior Students’ Mathematics Conceptual Understanding on Polyhedron

    Directory of Open Access Journals (Sweden)

    I Made Suarsana

    2017-06-01

    Full Text Available The aim of this study is to examine the effect of Brain Based Learning on second grade junior high school students’ conceptual understanding on polyhedron. This study was conducted by using post-test only control group quasi-experimental design. The subjects of this study were 148 students that divided into three classes. Two classes were taken as sample by using cluster random sampling technique. One of the classes was randomly selected as an experimental group and the other as control group. There were 48 students in experimental group and 51 students in control group. The data were collected with post-test which contained mathematical conceptual understanding on fractions. The post-test consisted of 8 essay question types.  The normality and variance homogeny test result showed that the scores are normally distributed and have no difference in variance. The data were analyzed by using one tailed t-test with significance level of 5%. The result of data analysis revealed that the value of t-test = 6,7096 greater than t-table = 1,987, therefore; the null hypothesis is rejected. There is positive effect of of Brain Based Learning on second grade junior students’ conceptual understanding in polyhedron.

  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. How Syntactic Reasoners Can Develop Understanding, Evaluate Conjectures, and Generate Counterexamples in Advanced Mathematics

    Science.gov (United States)

    Weber, Keith

    2009-01-01

    This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…

  10. Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process

    Science.gov (United States)

    Bal, Aytgen Pinar; Doganay, Ahmet

    2014-01-01

    The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

  11. Mathematics Teachers' Support and Retention: Using Maslow's Hierarchy to Understand Teachers' Needs

    Science.gov (United States)

    Fisher, Molly H.; Royster, David

    2016-01-01

    As part of a larger study, four mathematics teachers from diverse backgrounds and teaching situations report their ideas on teacher stress, mathematics teacher retention, and their feelings about the needs of mathematics teachers, as well as other information crucial to retaining quality teachers. The responses from the participants were used to…

  12. Stance and Engagement in Pure Mathematics Research Articles: Linking Discourse Features to Disciplinary Practices

    Science.gov (United States)

    McGrath, Lisa; Kuteeva, Maria

    2012-01-01

    Recent ESP research into academic writing has shown how writers convey their stance and interact with readers across different disciplines. However, little research has been carried out into the disciplinary writing practices of the pure mathematics academic community from an ESP genre analysis perspective. This study begins to address this gap by…

  13. Assessment of Genetics Understanding. Under What Conditions Do Situational Features Have an Impact on Measures?

    Science.gov (United States)

    Schmiemann, Philipp; Nehm, Ross H.; Tornabene, Robyn E.

    2017-12-01

    Understanding how situational features of assessment tasks impact reasoning is important for many educational pursuits, notably the selection of curricular examples to illustrate phenomena, the design of formative and summative assessment items, and determination of whether instruction has fostered the development of abstract schemas divorced from particular instances. The goal of our study was to employ an experimental research design to quantify the degree to which situational features impact inferences about participants' understanding of Mendelian genetics. Two participant samples from different educational levels and cultural backgrounds (high school, n = 480; university, n = 444; Germany and USA) were used to test for context effects. A multi-matrix test design was employed, and item packets differing in situational features (e.g., plant, animal, human, fictitious) were randomly distributed to participants in the two samples. Rasch analyses of participant scores from both samples produced good item fit, person reliability, and item reliability and indicated that the university sample displayed stronger performance on the items compared to the high school sample. We found, surprisingly, that in both samples, no significant differences in performance occurred among the animal, plant, and human item contexts, or between the fictitious and "real" item contexts. In the university sample, we were also able to test for differences in performance between genders, among ethnic groups, and by prior biology coursework. None of these factors had a meaningful impact upon performance or context effects. Thus some, but not all, types of genetics problem solving or item formats are impacted by situational features.

  14. Understanding Visceral Leishmaniasis Disease Transmission and its Control—A Study Based on Mathematical Modeling

    Directory of Open Access Journals (Sweden)

    Abhishek Subramanian

    2015-09-01

    Full Text Available Understanding the transmission and control of visceral leishmaniasis, a neglected tropical disease that manifests in human and animals, still remains a challenging problem globally. To study the nature of disease spread, we have developed a compartment-based mathematical model of zoonotic visceral leishmaniasis transmission among three different populations—human, animal and sandfly; dividing the human class into asymptomatic, symptomatic, post-kala-azar dermal leishmaniasis and transiently infected. We analyzed this large model for positivity, boundedness and stability around steady states in different diseased and disease-free scenarios and derived the analytical expression for basic reproduction number (R0. Sensitive parameters for each infected population were identified and varied to observe their effects on the steady state. Epidemic threshold R0 was calculated for every parameter variation. Animal population was identified to play a protective role in absorbing infection, thereby controlling the disease spread in human. To test the predictive ability of the model, seasonal fluctuation was incorporated in the birth rate of the sandflies to compare the model predictions with real data. Control scenarios on this real population data were created to predict the degree of control that can be exerted on the sensitive parameters so as to effectively reduce the infected populations.

  15. Dienes AEM as an alternative mathematics teaching aid to enhance Indonesian students’ understanding of algebra concept

    Science.gov (United States)

    Soro, S.; Maarif, S.; Kurniawan, Y.; Raditya, A.

    2018-01-01

    The aim of this study is to find out the effect of Dienes AEM (Algebra Experience Materials) on the ability of understanding concept of algebra on the senior high school student in Indonesia. This research is an experimental research with subject of all high school students in Indonesia. The samples taken were high school students in three provinces namely DKI Jakarta Province, West Java Province and Banten Province. From each province was taken senior high school namely SMA N 9 Bekasi West Java, SMA N 94 Jakarta and SMA N 5 Tangerang, Banten. The number of samples in this study was 114 high school students of tenth grade as experimental class and 115 high school students of tenth grade as control class. Learning algebra concept is needed in learning mathematics, besides it is needed especially to educate students to be able to think logically, systematically, critically, analytically, creatively, and cooperation. Therefore in this research will be developed an effective algebra learning by using Dienes AEM. The result of this research is that there is a significant influence on the students’ concept comprehension ability taught by using Dienes AEM learning as an alternative to instill the concept of algebra compared to the students taught by conventional learning. Besides, the students’ learning motivation increases because students can construct the concept of algebra with props.

  16. Investigating a Link between Pre-Calculus Students' Uses of Graphing Calculators and Their Understanding of Mathematical Symbols

    Science.gov (United States)

    Kenney, Rachael H.

    2014-01-01

    This study examined ways in which students make use of a graphing calculator and how use relates to comfort and understanding with mathematical symbols. Analysis involved examining students' words and actions in problem solving to identify evidence of algebraic insight. Findings suggest that some symbols and symbolic structures had strong…

  17. The Impact of Mathematics Teachers' Effectiveness on Students' Learning in the Two Realms of: Knowledge and Understanding

    Directory of Open Access Journals (Sweden)

    Nafiseh Ramezani-Monfared

    2015-12-01

    Full Text Available Effective teachers focus on the students' appropriate academic achievement and have positive impact on their performance. The need to evaluate the effectiveness of teachers on students' performance and learning areas seems necessary. This study was conducted with the aim to investigate the effectiveness of mathematics teachers on the learning of high school second-grade female students. Considering this purpose, survey research method was used. The population of this study included female mathematics teachers of girl high schools as well as female high school students of the zone 1 of Qom city during the school year 2013-2014. In the present study, quasi-cluster sampling method was used and the second grade was selected from among all the grades of the high schools in zone 1 of Qom city, and the study was conducted on 15 female mathematics teachers in this grade and 359 female students of these teachers. Using a questionnaire and a mathematics test, Mann-Whitney statistical results showed that mathematics scores of students who had effective teachers, were lower in the realm of knowledge compared to the students who did not have effective teachers, and mathematics scores of students who had effective teachers, in the realm of understanding were higher, compared to the students who did not have effective teachers.

  18. Helping Early Childhood Educators to Understand and Assess Young Children's Mathematical Minds

    Science.gov (United States)

    Ginsburg, Herbert P.

    2016-01-01

    This issue of "ZDM Mathematics Education" focuses on the formative assessment of young children's mathematical thinking, with an emphasis on computer-based approaches drawing upon on cognitive and educational research. The authors discuss several different assessment methods, including clinical interviewing, observation, and testing,…

  19. Using the Construct of the Didactic Contract to Understand Student Transition into University Mathematics Education

    Science.gov (United States)

    Pepin, Birgit

    2014-01-01

    In this article the concept of the Didactic Contract is used to investigate student "transition" from upper secondary into university mathematics education. The findings are anchored in data from the TransMaths project, more particularly the case of an ethnic minority student's journey from his school to a university mathematics course…

  20. Research on Mathematics and Science Education: From Beliefs to Cognition, from Problem Solving to Understanding.

    Science.gov (United States)

    Ahtee, Maija, Ed.; Bjorkqvist, Ole, Ed.; Pehkonen, Erkki, Ed.; Vatanen, Virpi, Ed.

    This book contains selected research papers presented at seminars held throughout the year 2000 in Finland by members of the Finnish Association for Research in Mathematics and Science Education (FARMSE) and students at the Finnish Graduate School of Mathematics, Physics, and Chemistry Education. This volume also contains papers professor Laurence…

  1. 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…

  2. Understanding Mathematics Achievement: An Analysis of the Effects of Student and Family Factors

    Science.gov (United States)

    Goforth, Kate; Noltemeyer, Amity; Patton, Jon; Bush, Kevin R.; Bergen, Doris

    2014-01-01

    Educators are increasingly recognising the importance of improving students' mathematics achievement. Much of the current research focuses on the impact of instructional variables on mathematics achievement. The goal of this study was to examine the influence of less researched variables--family and student factors. Participants were 747…

  3. Profound Understanding of Emergent Mathematics: Broadening the Construct of Teachers' Disciplinary Knowledge

    Science.gov (United States)

    Davis, Brent; Renert, Moshe

    2013-01-01

    We discuss the teachers' disciplinary knowledge of mathematics in this article, arguing two main points as we report on a 2-year study involving 22 practicing teachers. First we argue that teachers' knowledge of mathematics might be productively construed as a complex evolving form, a significant dimension of which is tacit knowledge. Second,…

  4. A Special Assignment from NASA: Understanding Earth's Atmosphere through the Integration of Science and Mathematics

    Science.gov (United States)

    Fox, Justine E.; Glen, Nicole J.

    2012-01-01

    Have your students ever wondered what NASA scientists do? Have they asked you what their science and mathematics lessons have to do with the real world? This unit about Earth's atmosphere can help to answer both of those questions. The unit described here showcases "content specific integration" of science and mathematics in that the lessons meet…

  5. Exploring ESL Students' Understanding of Mathematics in the Early Years: Factors That Make a Difference

    Science.gov (United States)

    Miller, Jodie; Warren, Elizabeth

    2014-01-01

    Students living in disadvantaged contexts and whose second language is English (ESL) are at risk of not succeeding in school mathematics. It has been internationally recognised that students' socioeconomic background and their achievements in mathematics is more pronounced for Australian students (Thomson et al. 2011). This gap is even more…

  6. Some aspects of executive functions as predictors of understanding textual mathematical tasks in students with mild intellectual disability

    Directory of Open Access Journals (Sweden)

    Japundža-Milisavljević Mirjana

    2016-01-01

    Full Text Available The most significant segment during the process of solving mathematical tasks is translation from mathematical to native language, in the basis o which, among others, are the following factors: resistance to distraction and forming adequate verbal strategies. The goal of this research is to evaluate the contribution of some aspects of executive functions in explaining the variance of solving illustrative mathematical tasks in students with mild intellectual disability. The sample consists of 90 students with mild intellectual disability aged from 12 to 16 (M=14.7; SD=1.6, of both sexes (44.4% boys and 55.6% girls. The Twenty questions test and the Stroop test were used to estimate the executive functions. Verbal problem tasks were used for the purpose of understanding mathematical language The obtained results show that the estimated aspects of executive functions are significant predictors of understanding mathematical language in students with intellectual disabilities. The strongest predictor is distraction resistance (p=0.01.

  7. Using confirmatory factor analysis to understand executive control in preschool children: sources of variation in emergent mathematic achievement.

    Science.gov (United States)

    Bull, Rebecca; Espy, Kimberly Andrews; Wiebe, Sandra A; Sheffield, Tiffany D; Nelson, Jennifer Mize

    2011-07-01

    Latent variable modeling methods have demonstrated utility for understanding the structure of executive control (EC) across development. These methods are utilized to better characterize the relation between EC and mathematics achievement in the preschool period, and to understand contributing sources of individual variation. Using the sample and battery of laboratory tasks described in Wiebe, Espy and Charak (2008), latent EC was related strongly to emergent mathematics achievement in preschool, and was robust after controlling for crystallized intellectual skills. The relation between crystallized skills and emergent mathematics differed between girls and boys, although the predictive association between EC and mathematics did not. Two dimensions of the child 's social environment contributed to mathematics achievement: social network support through its relation to EC and environmental stressors through its relation with crystallized skills. These findings underscore the need to examine the dimensions, mechanisms, and individual pathways that influence the development of early competence in basic cognitive processes that underpin early academic achievement. © 2010 Blackwell Publishing Ltd.

  8. Metaphors We Do Math By: A Comparative Case Study of Public and Catholic School Teachers’ Understanding of the Common Core State Standards in Mathematics

    OpenAIRE

    Branch, Jennifer Danielle

    2016-01-01

    The United States has undergone multiple mathematics reforms since the 1980s with each reform setting out to increase national test scores and improve mathematics education in the nation’s schools. The current reform, the Common Core State Standards for Mathematics (CCSSM), seeks to create mathematically proficient students through a more active and rigorous curriculum. The goal of this yearlong study was to examine the understanding that intermediate and middle school math teachers make of t...

  9. The social competence of Latino kindergartners and growth in mathematical understanding.

    Science.gov (United States)

    Galindo, Claudia; Fuller, Bruce

    2010-05-01

    We know that social competence contributes to young children's adaptation to, and cognitive learning within, classroom settings. Yet initial evidence is mixed on the social competencies that Latino children bring to kindergarten and the extent to which these skills advance cognitive growth. Building from ecocultural and developmental-risk theory, this paper shows children's social competence to be adaptive to the normative expectations and cognitive requirements of culturally bounded settings in both the home and classroom. Latino socialization in the home may yield social competencies that teachers value rather than reflect "risk factors" that constrain children's school readiness. We draw on the Early Childhood Longitudinal Study, kindergarten cohort (N = 19,590) to detail 5 social competencies at entry to school--self-control, interpersonal skills, approaches to learning, internalizing and externalizing problem behaviors--and to examine variability among Latino subgroups. We then test the extent to which baseline variation in social competence accounts for children's cognitive growth during the kindergarten year. We find that Latino children from poor, but not middle-class, families display weaker social competencies vis-à-vis White children (all relationships p cognitive growth, which is shaped most strongly by positive approaches to learning. The disparities in competencies observed for Latino children from poor families, relative to White children, are significant yet much smaller than gaps in baseline levels of mathematical understanding. We discuss how the consonance or mismatch between competencies acquired at home and those valued by teachers must consider cultural differences, social-class position, and variation among diverse Latino subgroups. 2010 APA, all rights reserved

  10. Using CNN Features to Better Understand What Makes Visual Artworks Special

    Science.gov (United States)

    Brachmann, Anselm; Barth, Erhardt; Redies, Christoph

    2017-01-01

    One of the goal of computational aesthetics is to understand what is special about visual artworks. By analyzing image statistics, contemporary methods in computer vision enable researchers to identify properties that distinguish artworks from other (non-art) types of images. Such knowledge will eventually allow inferences with regard to the possible neural mechanisms that underlie aesthetic perception in the human visual system. In the present study, we define measures that capture variances of features of a well-established Convolutional Neural Network (CNN), which was trained on millions of images to recognize objects. Using an image dataset that represents traditional Western, Islamic and Chinese art, as well as various types of non-art images, we show that we need only two variance measures to distinguish between the artworks and non-art images with a high classification accuracy of 93.0%. Results for the first variance measure imply that, in the artworks, the subregions of an image tend to be filled with pictorial elements, to which many diverse CNN features respond (richness of feature responses). Results for the second measure imply that this diversity is tied to a relatively large variability of the responses of individual CNN feature across the subregions of an image. We hypothesize that this combination of richness and variability of CNN feature responses is one of properties that makes traditional visual artworks special. We discuss the possible neural underpinnings of this perceptual quality of artworks and propose to study the same quality also in other types of aesthetic stimuli, such as music and literature. PMID:28588537

  11. Using CNN Features to Better Understand What Makes Visual Artworks Special

    Directory of Open Access Journals (Sweden)

    Anselm Brachmann

    2017-05-01

    Full Text Available One of the goal of computational aesthetics is to understand what is special about visual artworks. By analyzing image statistics, contemporary methods in computer vision enable researchers to identify properties that distinguish artworks from other (non-art types of images. Such knowledge will eventually allow inferences with regard to the possible neural mechanisms that underlie aesthetic perception in the human visual system. In the present study, we define measures that capture variances of features of a well-established Convolutional Neural Network (CNN, which was trained on millions of images to recognize objects. Using an image dataset that represents traditional Western, Islamic and Chinese art, as well as various types of non-art images, we show that we need only two variance measures to distinguish between the artworks and non-art images with a high classification accuracy of 93.0%. Results for the first variance measure imply that, in the artworks, the subregions of an image tend to be filled with pictorial elements, to which many diverse CNN features respond (richness of feature responses. Results for the second measure imply that this diversity is tied to a relatively large variability of the responses of individual CNN feature across the subregions of an image. We hypothesize that this combination of richness and variability of CNN feature responses is one of properties that makes traditional visual artworks special. We discuss the possible neural underpinnings of this perceptual quality of artworks and propose to study the same quality also in other types of aesthetic stimuli, such as music and literature.

  12. Using CNN Features to Better Understand What Makes Visual Artworks Special.

    Science.gov (United States)

    Brachmann, Anselm; Barth, Erhardt; Redies, Christoph

    2017-01-01

    One of the goal of computational aesthetics is to understand what is special about visual artworks. By analyzing image statistics, contemporary methods in computer vision enable researchers to identify properties that distinguish artworks from other (non-art) types of images. Such knowledge will eventually allow inferences with regard to the possible neural mechanisms that underlie aesthetic perception in the human visual system. In the present study, we define measures that capture variances of features of a well-established Convolutional Neural Network (CNN), which was trained on millions of images to recognize objects. Using an image dataset that represents traditional Western, Islamic and Chinese art, as well as various types of non-art images, we show that we need only two variance measures to distinguish between the artworks and non-art images with a high classification accuracy of 93.0%. Results for the first variance measure imply that, in the artworks, the subregions of an image tend to be filled with pictorial elements, to which many diverse CNN features respond ( richness of feature responses). Results for the second measure imply that this diversity is tied to a relatively large variability of the responses of individual CNN feature across the subregions of an image. We hypothesize that this combination of richness and variability of CNN feature responses is one of properties that makes traditional visual artworks special. We discuss the possible neural underpinnings of this perceptual quality of artworks and propose to study the same quality also in other types of aesthetic stimuli, such as music and literature.

  13. From everyday problem to a mathematical solution - understanding student reasoning by identifying their chain of reference

    DEFF Research Database (Denmark)

    Dreyøe, Jonas; Larsen, Dorte Moeskær; Misfeldt, Morten

    2018-01-01

    students. In this analysis, we apply the idea of the chain of reference from the studies of Bruno Latour (1999) to the exploration, generation, and formalization of scientific knowledge. This framework allows us to combine knowledge from mathematics education about language and representations......This paper investigates a group of students’ reasoning in an inquiry-oriented and open mathematical investigation developed as a part of a large-scale intervention. We focus on the role of manipulatives, articulations, and representations in collaborative mathematical reasoning among grade 5......, manipulatives, and reasoning in a way that allows us to follow the material traces of students’ mathematical reasoning and hence discuss the possibilities, limitations, and pedagogical consequences of the application of Latour’s (1999) framework....

  14. Mathematics teachers' support and retention: using Maslow's hierarchy to understand teachers' needs

    Science.gov (United States)

    Fisher, Molly H.; Royster, David

    2016-10-01

    As part of a larger study, four mathematics teachers from diverse backgrounds and teaching situations report their ideas on teacher stress, mathematics teacher retention, and their feelings about the needs of mathematics teachers, as well as other information crucial to retaining quality teachers. The responses from the participants were used to develop a hierarchy of teachers' needs that resembles Maslow's hierarchy, which can be used to better support teachers in various stages of their careers. The interviews revealed both non content-specific and content-specific needs within the hierarchy. The responses show that teachers found different schools foster different stress levels and that as teachers they used a number of resources for reducing stress. Other mathematics-specific ideas are also discussed such as the amount of content and pedagogy courses required for certification.

  15. Understanding technology use and constructivist strategies when addressing Saudi primary students' mathematics difficulties.

    OpenAIRE

    Alabdulaziz, M.; Higgins, S.

    2017-01-01

    This paper will investigate the relationship between technology use and the use of constructivist strategies when addressing Saudi primary students' mathematics difficulties. Semi-structured interviews and observations were used for the purpose of this research, which were undertaken with three mathematics teachers from school A which used technology, and the other three from school B, which did not use technology. We found that technology can support constructivist approach when teaching and...

  16. Exploring the Cognitive Demand and Features of Problem Solving Tasks in Primary Mathematics Classrooms

    Science.gov (United States)

    McCormick, Melody

    2016-01-01

    Student learning is greatest in classrooms where students engage in problem solving tasks that are cognitively demanding. However, there are growing concerns that many Australian students are given limited opportunities to engage in these types of tasks. 108 upper primary school teachers were surveyed to examine task features and cognitive demand…

  17. Do Word-Problem Features Differentially Affect Problem Difficulty as a Function of Students' Mathematics Difficulty with and without Reading Difficulty?

    Science.gov (United States)

    Powell, Sarah R.; Fuchs, Lynn S.; Fuchs, Douglas; Cirino, Paul T.; Fletcher, Jack M.

    2009-01-01

    This study examined whether and, if so, how word-problem features differentially affect problem difficulty as a function of mathematics difficulty (MD) status: no MD (n = 109), MD only (n = 109), or MD in combination with reading difficulties (MDRD; n = 109). The problem features were problem type (total, difference, or change) and position of…

  18. Teachers' Understanding of the Role of Executive Functions in Mathematics Learning

    Science.gov (United States)

    Gilmore, Camilla; Cragg, Lucy

    2014-01-01

    Cognitive psychology research has suggested an important role for executive functions, the set of skills that monitor and control thought and action, in learning mathematics. However, there is currently little evidence about whether teachers are aware of the importance of these skills and, if so, how they come by this information. We conducted an online survey of teachers' views on the importance of a range of skills for mathematics learning. Teachers rated executive function skills, and in particular inhibition and shifting, to be important for mathematics. The value placed on executive function skills increased with increasing teaching experience. Most teachers reported that they were aware of these skills, although few knew the term “executive functions.” This awareness had come about through their teaching experience rather than from formal instruction. Researchers and teacher educators could do more to highlight the importance of these skills to trainee or new teachers. PMID:25674156

  19. 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 ...

  20. Observation of surface features on an active landslide, and implications for understanding its history of movement

    Directory of Open Access Journals (Sweden)

    M. Parise

    2003-01-01

    which determines frequent variations in the presence and distribution of surface features, as evidenced by the multi-year observations there performed. In addition, monitoring of the inactive material just ahead of the active toe showed that this sector is experiencing deformation caused by the advancing toe. Mapping and interpretation of the different generations of flank ridges at the narrowest and central part of the active Slumgullion landslide evidenced, on the other hand, the gradual narrowing of the mass movement, which was accompanied by a reduction in the thickness of the material involved in landsliding. Multi-time observation of the surface features at the Slumgullion earthflow allowed to reconstruct the evolution of specific sectors of the mass movement. This low-cost approach, whose only requirements are the availability of a detailed topographic map, and repeated surveying, is therefore particularly useful to better understand the kinematics of active mass movements, also in order to design the more appropriate stabilization works.

  1. Understanding Participation Rates in Post-16 Mathematics and Physics: Conceptualising and Operationalising the UPMAP Project

    Science.gov (United States)

    Reiss, Michael; Hoyles, Celia; Mujtaba, Tamjid; Riazi-Farzad, Bijan; Rodd, Melissa; Simon, Shirley; Stylianidou, Fani

    2011-01-01

    We report on a project currently in progress that aims to identify through research the range of factors (individual, school and out-of-school, including home) and their interactions that influence post-16 (i.e. post-compulsory) participation in mathematics and physics in the UK and to assess their relative importance among different student…

  2. Effects of Consistency and Adequacy of Language Information on Understanding Elementary Mathematics Word Problems.

    Science.gov (United States)

    Leong, Che Kan; Jerred, Wendy D.

    2001-01-01

    A study involving 91 children (ages 3-5) divided into more able and less able sub-groups found mathematical word problems containing inconsistent information were more difficult than those with consistent information. Word problems containing inadequate and redundant information were more difficult to explain than those items with just enough…

  3. Developing Conceptual Understanding and Definitional Clarity in Linear Algebra through the Three Worlds of Mathematical Thinking

    Science.gov (United States)

    Hannah, John; Stewart, Sepideh; Thomas, Michael

    2016-01-01

    Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall's three worlds (embodied, symbolic and…

  4. Understanding Women's Underrepresentation in Science, Technology, Engineering, and Mathematics: The Role of Social Coping

    Science.gov (United States)

    Morganson, Valerie J.; Jones, Meghan P.; Major, Debra A.

    2010-01-01

    Enrollment of women in science, technology, engineering, and mathematics (STEM) majors is disproportionately small and declining. This study examines social coping to explain the gender gap. Women undergraduates reported using significantly more social coping than did men. Multiple regression analyses revealed that social coping was a stronger…

  5. Facilitating Student Understanding of Buffering by an Integration of Mathematics and Chemical Concepts

    Science.gov (United States)

    Curtright, Robert; Emry, Randall; Heaton, Ruth M.; Markwell, John

    2004-01-01

    We describe a simple undergraduate exercise involving the titration of a weak acid by a strong base using a pH meter and a micropipette. Students then use their data and carry out graphical analyses with a spreadsheet. The analyses involve using mathematical concepts such as first-derivative and semi-log plots and provide an opportunity for…

  6. Self-Determination Theory and Middle School Mathematics Teachers: Understanding the Motivation to Attain Professional Development

    Science.gov (United States)

    Crawford, Amy K.

    2017-01-01

    The purpose of this phenomenological research study was to use Self-Determination Theory as a framework to analyze middle school mathematics teachers' motivation to attain effective professional development concerning Ohio's Learning Standards as well as other instructional aspects that affect the classroom. Teachers are exceptionally busy meeting…

  7. Exploring ESL students' understanding of mathematics in the early years: factors that make a difference

    Science.gov (United States)

    Miller, Jodie; Warren, Elizabeth

    2014-12-01

    Students living in disadvantaged contexts and whose second language is English (ESL) are at risk of not succeeding in school mathematics. It has been internationally recognised that students' socioeconomic background and their achievements in mathematics is more pronounced for Australian students (Thomson et al. 2011). This gap is even more prominent for students who also have English as their second language (ESL). This paper explores the impact of the representations, oral language and engagement in mathematics (RoleM) learning experiences on ESL students' performance in mathematics in the early years (foundation-year 2). All students participating in the study are from disadvantaged contexts ( n = 461). The sample comprised 328 students who identified themselves as having English as a second language (ESL) and 133 mainstream students. Pre- and post-tests were conducted at the commencement and completion of each school year. All students demonstrated a significant improvement on their post-test scores, with ESL students displaying greater gains than the mainstream students. Additionally, students' results were meeting norm-referenced expectations for students of the same age. A hypothesised taxonomy was developed to further investigate which types of test items foundation ESL students displayed greatest gains. ESL students again outperformed the mainstream cohort on all levels of test categorisation, including questions that were linguistically and conceptually challenging for foundation students.

  8. Teachers' Understanding of the Role of Executive Functions in Mathematics Learning

    Science.gov (United States)

    Gilmore, Camilla; Cragg, Lucy

    2014-01-01

    Cognitive psychology research has suggested an important role for executive functions, the set of skills that monitor and control thought and action, in learning mathematics. However, there is currently little evidence about whether teachers are aware of the importance of these skills and, if so, how they come by this information. We conducted an…

  9. Mathematics Teaching Practices with Technology that Support Conceptual Understanding for Latino/a Students

    Science.gov (United States)

    Zahner, William; Velazquez, Griselda; Moschkovich, Judit; Vahey, Phil; Lara-Meloy, Teresa

    2012-01-01

    We analyze how three seventh grade mathematics teachers from a majority Latino/a, linguistically diverse region of Texas taught the same lesson on interpreting graphs of motion as part of the Scaling Up SimCalc study (Roschelle et al., 2010). The students of two of the teachers made strong learning gains as measured by a curriculum-aligned…

  10. Can Executive Functions Help to Understand Children with Mathematical Learning Disorders and to Improve Instruction?

    Science.gov (United States)

    Desoete, Annemie; De Weerdt, Frauke

    2013-01-01

    Working memory, inhibition and naming speed was assessed in 22 children with mathematical learning disorders (MD), 17 children with a reading learning disorder (RD), and 45 children without any learning problems between 8 and 12 years old. All subjects with learning disorders performed poorly on working memory tasks, providing evidence that they…

  11. Learning Fractions by Splitting: Using Learning Analytics to Illuminate the Development of Mathematical Understanding

    Science.gov (United States)

    Martin, Taylor; Petrick Smith, Carmen; Forsgren, Nicole; Aghababyan, Ani; Janisiewicz, Philip; Baker, Stephanie

    2015-01-01

    The struggle with fraction learning in kindergarten through Grade 12 in the United States is a persistent problem and one of the major stumbling blocks to succeeding in higher mathematics. Research into this problem has identified several areas where students commonly struggle with fractions. While there are many theories of fraction learning,…

  12. Subtypes and comorbidity in mathematical learning disabilities: Multidimensional study of verbal and visual memory processes is key to understanding.

    Science.gov (United States)

    Szűcs, D

    2016-01-01

    A large body of research suggests that mathematical learning disability (MLD) is related to working memory impairment. Here, I organize part of this literature through a meta-analysis of 36 studies with 665 MLD and 1049 control participants. I demonstrate that one subtype of MLD is associated with reading problems and weak verbal short-term and working memory. Another subtype of MLD does not have associated reading problems and is linked to weak visuospatial short-term and working memory. In order to better understand MLD we need to precisely define potentially modality-specific memory subprocesses and supporting executive functions, relevant for mathematical learning. This can be achieved by taking a multidimensional parametric approach systematically probing an extended network of cognitive functions. Rather than creating arbitrary subgroups and/or focus on a single factor, highly powered studies need to position individuals in a multidimensional parametric space. This will allow us to understand the multidimensional structure of cognitive functions and their relationship to mathematical performance. © 2016 Elsevier B.V. All rights reserved.

  13. Mathematical models are a powerful method to understand and control the spread of Huanglongbing

    Directory of Open Access Journals (Sweden)

    Rachel A. Taylor

    2016-11-01

    Full Text Available Huanglongbing (HLB, or citrus greening, is a global citrus disease occurring in almost all citrus growing regions. It causes substantial economic burdens to individual growers, citrus industries and governments. Successful management strategies to reduce disease burden are desperately needed but with so many possible interventions and combinations thereof it is difficult to know which are worthwhile or cost-effective. We review how mathematical models have yielded useful insights into controlling disease spread for other vector-borne plant diseases, and the small number of mathematical models of HLB. We adapt a malaria model to HLB, by including temperature-dependent psyllid traits, “flushing” of trees, and economic costs, to show how models can be used to highlight the parameters that require more data collection or that should be targeted for intervention. We analyze the most common intervention strategy, insecticide spraying, to determine the most cost-effective spraying strategy. We find that fecundity and feeding rate of the vector require more experimental data collection, for wider temperatures ranges. Also, the best strategy for insecticide intervention is to spray for more days rather than pay extra for a more efficient spray. We conclude that mathematical models are able to provide useful recommendations for managing HLB spread.

  14. Mathematical models are a powerful method to understand and control the spread of Huanglongbing.

    Science.gov (United States)

    Taylor, Rachel A; Mordecai, Erin A; Gilligan, Christopher A; Rohr, Jason R; Johnson, Leah R

    2016-01-01

    Huanglongbing (HLB), or citrus greening, is a global citrus disease occurring in almost all citrus growing regions. It causes substantial economic burdens to individual growers, citrus industries and governments. Successful management strategies to reduce disease burden are desperately needed but with so many possible interventions and combinations thereof it is difficult to know which are worthwhile or cost-effective. We review how mathematical models have yielded useful insights into controlling disease spread for other vector-borne plant diseases, and the small number of mathematical models of HLB. We adapt a malaria model to HLB, by including temperature-dependent psyllid traits, "flushing" of trees, and economic costs, to show how models can be used to highlight the parameters that require more data collection or that should be targeted for intervention. We analyze the most common intervention strategy, insecticide spraying, to determine the most cost-effective spraying strategy. We find that fecundity and feeding rate of the vector require more experimental data collection, for wider temperatures ranges. Also, the best strategy for insecticide intervention is to spray for more days rather than pay extra for a more efficient spray. We conclude that mathematical models are able to provide useful recommendations for managing HLB spread.

  15. 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

  16. A mathematical model towards understanding the mechanism of neuronal regulation of wake-NREMS-REMS states.

    Directory of Open Access Journals (Sweden)

    Rupesh Kumar

    Full Text Available In this study we have constructed a mathematical model of a recently proposed functional model known to be responsible for inducing waking, NREMS and REMS. Simulation studies using this model reproduced sleep-wake patterns as reported in normal animals. The model helps to explain neural mechanism(s that underlie the transitions between wake, NREMS and REMS as well as how both the homeostatic sleep-drive and the circadian rhythm shape the duration of each of these episodes. In particular, this mathematical model demonstrates and confirms that an underlying mechanism for REMS generation is pre-synaptic inhibition from substantia nigra onto the REM-off terminals that project on REM-on neurons, as has been recently proposed. The importance of orexinergic neurons in stabilizing the wake-sleep cycle is demonstrated by showing how even small changes in inputs to or from those neurons can have a large impact on the ensuing dynamics. The results from this model allow us to make predictions of the neural mechanisms of regulation and patho-physiology of REMS.

  17. Understanding electricity generation in osmotic microbial fuel cells through integrated experimental investigation and mathematical modeling.

    Science.gov (United States)

    Qin, Mohan; Ping, Qingyun; Lu, Yaobin; Abu-Reesh, Ibrahim M; He, Zhen

    2015-11-01

    Osmotic microbial fuel cells (OsMFCs) are a new type of MFCs with integrating forward osmosis (FO). However, it is not well understood why electricity generation is improved in OsMFCs compared to regular MFCs. Herein, an approach integrating experimental investigation and mathematical model was adopted to address the question. Both an OsMFC and an MFC achieved similar organic removal efficiency, but the OsMFC generated higher current than the MFC with or without water flux, resulting from the lower resistance of FO membrane. Combining NaCl and glucose as a catholyte demonstrated that the catholyte conductivity affected the electricity generation in the OsMFC. A mathematical model of OsMFCs was developed and validated with the experimental data. The model predicated the variation of internal resistance with increasing water flux, and confirmed the importance of membrane resistance. Increasing water flux with higher catholyte conductivity could decrease the membrane resistance. Copyright © 2015 Elsevier Ltd. All rights reserved.

  18. Relational Understanding of the Derivative Concept through Mathematical Modeling: A Case Study

    Science.gov (United States)

    Sahin, Zulal; Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat

    2015-01-01

    The purpose of this study was to investigate three second-year graduate students' awareness and understanding of the relationships among the "big ideas" that underlie the concept of derivative through modeling tasks and Skemp's distinction between relational and instrumental understanding. The modeling tasks consisting of warm-up,…

  19. SU-D-BRA-05: Toward Understanding the Robustness of Radiomics Features in CT

    International Nuclear Information System (INIS)

    Mackin, D; Zhang, L; Yang, J; Jones, A; Court, L; Fave, X; Fried, D; Taylor, B; Rodriguez-Rivera, E; Dodge, C

    2015-01-01

    Purpose: To gauge the impact of inter-scanner variability on radiomics features in computed tomography (CT). Methods: We compared the radiomics features calculated for 17 scans of the specially designed Credence Cartridge Radiomics (CCR) phantom with those calculated for 20 scans of non–small cell lung cancer (NSCLC) tumors. The scans were acquired at four medical centers using General Electric, Philips, Siemens, and Toshiba CT scanners. Each center used its own routine thoracic imaging protocol. To produce a large dynamic range of radiomics feature values, the CCR phantom has 10 cartridges comprising different materials. The features studied were derived from the neighborhood gray-tone difference matrix or image intensity histogram. To quantify the significance of the inter-scanner variability, we introduced the metric “feature noise”, which compares the ratio of inter-scanner variability and inter-patient variability in decibels, positive values indicating substantial noise. We performed hierarchical clustering based to look for dependence of the features on the scan acquisition parameters. Results: For 5 of the 10 features studied, the inter-scanner variability was larger than the inter-patient variability. Of the 10 materials in the phantom, shredded rubber seemed to produce feature values most similar to those of the NSCLC tumors. The feature busyness had the greatest feature noise (14.3 dB), whereas texture strength had the least (−14.6 dB). Hierarchical clustering indicated that the features depended in part on the scanner manufacturer, image slice thickness, and pixel size. Conclusion: The variability in the values of radiomics features calculated for CT images of a radiomics phantom can be substantial relative to the variability in the values of these features calculated for CT images of NSCLC tumors. These inter-scanner differences and their effects should be carefully considered in future radiomics studies

  20. Understanding the Uncanny: Both Atypical Features and Category Ambiguity Provoke Aversion toward Humanlike Robots

    Directory of Open Access Journals (Sweden)

    Megan K. Strait

    2017-08-01

    Full Text Available Robots intended for social contexts are often designed with explicit humanlike attributes in order to facilitate their reception by (and communication with people. However, observation of an “uncanny valley”—a phenomenon in which highly humanlike entities provoke aversion in human observers—has lead some to caution against this practice. Both of these contrasting perspectives on the anthropomorphic design of social robots find some support in empirical investigations to date. Yet, owing to outstanding empirical limitations and theoretical disputes, the uncanny valley and its implications for human-robot interaction remains poorly understood. We thus explored the relationship between human similarity and people's aversion toward humanlike robots via manipulation of the agents' appearances. To that end, we employed a picture-viewing task (Nagents = 60 to conduct an experimental test (Nparticipants = 72 of the uncanny valley's existence and the visual features that cause certain humanlike robots to be unnerving. Across the levels of human similarity, we further manipulated agent appearance on two dimensions, typicality (prototypic, atypical, and ambiguous and agent identity (robot, person, and measured participants' aversion using both subjective and behavioral indices. Our findings were as follows: (1 Further substantiating its existence, the data show a clear and consistent uncanny valley in the current design space of humanoid robots. (2 Both category ambiguity, and more so, atypicalities provoke aversive responding, thus shedding light on the visual factors that drive people's discomfort. (3 Use of the Negative Attitudes toward Robots Scale did not reveal any significant relationships between people's pre-existing attitudes toward humanlike robots and their aversive responding—suggesting positive exposure and/or additional experience with robots is unlikely to affect the occurrence of an uncanny valley effect in humanoid robotics

  1. Understanding the Uncanny: Both Atypical Features and Category Ambiguity Provoke Aversion toward Humanlike Robots.

    Science.gov (United States)

    Strait, Megan K; Floerke, Victoria A; Ju, Wendy; Maddox, Keith; Remedios, Jessica D; Jung, Malte F; Urry, Heather L

    2017-01-01

    Robots intended for social contexts are often designed with explicit humanlike attributes in order to facilitate their reception by (and communication with) people. However, observation of an "uncanny valley"-a phenomenon in which highly humanlike entities provoke aversion in human observers-has lead some to caution against this practice. Both of these contrasting perspectives on the anthropomorphic design of social robots find some support in empirical investigations to date. Yet, owing to outstanding empirical limitations and theoretical disputes, the uncanny valley and its implications for human-robot interaction remains poorly understood. We thus explored the relationship between human similarity and people's aversion toward humanlike robots via manipulation of the agents' appearances. To that end, we employed a picture-viewing task ( N agents = 60) to conduct an experimental test ( N participants = 72) of the uncanny valley's existence and the visual features that cause certain humanlike robots to be unnerving. Across the levels of human similarity, we further manipulated agent appearance on two dimensions, typicality (prototypic, atypical, and ambiguous) and agent identity (robot, person), and measured participants' aversion using both subjective and behavioral indices. Our findings were as follows: (1) Further substantiating its existence, the data show a clear and consistent uncanny valley in the current design space of humanoid robots. (2) Both category ambiguity, and more so, atypicalities provoke aversive responding, thus shedding light on the visual factors that drive people's discomfort. (3) Use of the Negative Attitudes toward Robots Scale did not reveal any significant relationships between people's pre-existing attitudes toward humanlike robots and their aversive responding-suggesting positive exposure and/or additional experience with robots is unlikely to affect the occurrence of an uncanny valley effect in humanoid robotics. This work furthers

  2. Understanding the Growth of ESL Paragraph Writing Skills and Its Relationships with Linguistic Features

    Science.gov (United States)

    Aryadoust, Vahid

    2016-01-01

    This study sought to examine the development of paragraph writing skills of 116 English as a second language university students over the course of 12 weeks and the relationship between the linguistic features of students' written texts as measured by Coh-Metrix--a computational system for estimating textual features such as cohesion and…

  3. Assessing the Impact of Computer Programming in Understanding Limits and Derivatives in a Secondary Mathematics Classroom

    Science.gov (United States)

    de Castro, Christopher H.

    2011-01-01

    This study explored the development of student's conceptual understandings of limit and derivative when utilizing specifically designed computational tools. Fourteen students from a secondary Advanced Placement Calculus AB course learned and explored the limit and derivative concepts from differential calculus using visualization tools in the…

  4. Bridging the Gap: Fraction Understanding Is Central to Mathematics Achievement in Students from Three Different Continents

    Science.gov (United States)

    Torbeyns, Joke; Schneider, Michael; Xin, Ziqiang; Siegler, Robert S.

    2015-01-01

    Numerical understanding and arithmetic skills are easier to acquire for whole numbers than fractions. The "integrated theory of numerical development" posits that, in addition to these differences, whole numbers and fractions also have important commonalities. In both, students need to learn how to interpret number symbols in terms of…

  5. Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3-5

    Science.gov (United States)

    Otto, Albert; Caldwell, Janet; Hancock, Sarah Wallus; Zbiek, Rose Mary

    2011-01-01

    This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3-5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modeled by multiplication have an element that represents the scalar and an element that…

  6. Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9-12

    Science.gov (United States)

    Lloyd, Gwendolyn; Beckmann, Sybilla; Zbiek, Rose Mary; Cooney, Thomas

    2010-01-01

    Are sequences functions? What can't the popular "vertical line test" be applied in some cases to determine if a relation is a function? How does the idea of rate of change connect with simpler ideas about proportionality as well as more advanced topics in calculus? Helping high school students develop a robust understanding of functions requires…

  7. The role of visual representations in college students' understanding of mathematical notation.

    Science.gov (United States)

    Atagi, Natsuki; DeWolf, Melissa; Stigler, James W; Johnson, Scott P

    2016-09-01

    Developing understanding of fractions involves connections between nonsymbolic visual representations and symbolic representations. Initially, teachers introduce fraction concepts with visual representations before moving to symbolic representations. Once the focus is shifted to symbolic representations, the connections between visual representations and symbolic notation are considered to be less useful, and students are rarely asked to connect symbolic notation back to visual representations. In 2 experiments, we ask whether visual representations affect understanding of symbolic notation for adults who understand symbolic notation. In a conceptual fraction comparison task (e.g., Which is larger, 5 / a or 8 / a? ), participants were given comparisons paired with accurate, helpful visual representations, misleading visual representations, or no visual representations. The results show that even college students perform significantly better when accurate visuals are provided over misleading or no visuals. Further, eye-tracking data suggest that these visual representations may affect performance even when only briefly looked at. Implications for theories of fraction understanding and education are discussed. PsycINFO Database Record (c) 2016 APA, all rights reserved

  8. Understanding circadian regulation of carbohydrate metabolism in Arabidopsis using mathematical models.

    Science.gov (United States)

    Webb, Alex A R; Satake, Akiko

    2015-04-01

    C3 plants assimilate carbon by photosynthesis only during the day, but carbon resources are also required for growth and maintenance at night. To avoid carbon starvation, many plants store a part of photosynthetic carbon in starch during the day, and degrade it to supply sugars for growth at night. In Arabidopsis, starch accumulation in the day and degradation at night occur almost linearly, with the shape of this diel starch profile adaptively changing to allow continuous supply of sugar even in long-night conditions. The anticipation of dawn required to ensure linear consumption of starch to almost zero at dawn presumably requires the circadian clock. We review the links between carbon metabolism and the circadian clock, and mathematical models aimed at explaining the diel starch profile. These models can be considered in two classes, those that assume the level of available starch is sensed and the system ensures linearity of starch availability, and those in which sugar sensing is assumed, yielding linearity of starch availability as an emergent property of sucrose homeostasis. In the second class of model the feedback from starch metabolism to the circadian clock is considered to be essential for adaptive response to diverse photoperiods, consistent with recent empirical data demonstrating entrainment of the circadian clock by photosynthesis. Knowledge concerning the mechanisms regulating the dynamics of starch metabolism and sugar homeostasis in plants is required to develop new theories about the limitations of growth and biomass accumulation. © The Author 2015. Published by Oxford University Press on behalf of Japanese Society of Plant Physiologists. All rights reserved. For permissions, please email: journals.permissions@oup.com.

  9. UNDERSTANDING STUDENTS' OPINION ON CO-OPERATIVE LEARNING IMPLEMENTATION IN MATHEMATICS

    OpenAIRE

    Shefali Pandya

    2017-01-01

    The study seeks to understand students’ opinion about implementation of co-operative learning approach. An experiment on co-operative learning approach was conducted on 78 students of standard IX studying in schools affiliated to the SSC Board and with English as the medium of instruction. It has used one tool, namely, Co-operative Learning Implementation Opinionnaire. It was found that on the whole, students are substantially satisfied with the implementation of co-operative learning approac...

  10. Assessing Key Epistemic Features of Didactic-Mathematical Knowledge of Prospective Teachers: The Case of The Derivative

    Science.gov (United States)

    Pino-Fan, Luis R.; Godino, Juan D.; Font, Vicenç

    2018-01-01

    In recent years, there has been a growing interest in studying the knowledge that mathematics teachers require in order for their teaching to be effective. However, only a few studies have focused on the design and application of instruments that are capable of exploring different aspects of teachers' didactic-mathematical knowledge about specific…

  11. 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...

  12. The utility of simple mathematical models in understanding gene regulatory dynamics

    Science.gov (United States)

    Mackey, Michael C.; Santillán, Moisés; Tyran-Kamińska, Marta; Zeron, Eduardo S.

    2015-01-01

    Abstract In this review, we survey work that has been carried out in the attempts of biomathematicians to understand the dynamic behaviour of simple bacterial operons starting with the initial work of the 1960’s. We concentrate on the simplest of situations, discussing both repressible and inducible systems and then turning to concrete examples related to the biology of the lactose and tryptophan operons. We conclude with a brief discussion of the role of both extrinsic noise and so-called intrinsic noise in the form of translational and/or transcriptional bursting. PMID:25402755

  13. THE APPLICATION OF RECIPROCAL TEACHING METHOD FOR IMPROVING THE UNDERSTANDING OF MATHEMATICS CONCEPT OF 7TH GRADE STUDENTS SMP NEGERI 2 DEPOK.

    Directory of Open Access Journals (Sweden)

    Tatag Bagus Argikas

    2016-10-01

    Full Text Available This research aims to: (1 describe the implementation of learning mathematics with Reciprocal Teaching methods that is for improving the concept of learning understanding mathematic in class VIIA SMP Negeri 2 Depok. (2 Knowing the increased understanding of student learning in class VIIA SMP Negeri 2 Depok use Reciprocal Teaching methods. This research constitutes an action in class that is according along the teacher. The data of research was collated by sheet observations and each evaluation of cycles. That is done in two cycles. The first was retrieved the average value of student learning achievement of 70.96%. The second was retrieved achievement of 90.32%. Thus this learning model can increase student learning understanding.   Key word: The understanding of Mathematical Concept, Reciprocal Teaching Method.

  14. Using mathematical models to understand the effect of nanoscale roughness on protein adsorption for improving medical devices

    Directory of Open Access Journals (Sweden)

    Ercan B

    2013-09-01

    Full Text Available Batur Ercan,1 Dongwoo Khang,2 Joseph Carpenter,3 Thomas J Webster1 1Department of Chemical Engineering, Northeastern University, Boston, MA, USA; 2School of Materials Science and Engineering and Center for PRC and RIGET, Gyeongsang National University, Jinju, South Korea; 3School of Medicine, Stanford University, Stanford, CA, USA Abstract: Surface roughness and energy significantly influence protein adsorption on to biomaterials, which, in turn, controls select cellular adhesion to determine the success and longevity of an implant. To understand these relationships at a fundamental level, a model was originally proposed by Khang et al to correlate nanoscale surface properties (specifically, nanoscale roughness and energy to protein adsorption, which explained the greater cellular responses on nanostructured surfaces commonly reported in the literature today. To test this model for different surfaces from what was previously used to develop that model, in this study we synthesized highly ordered poly(lactic-co-glycolic acid surfaces of identical chemistry but altered nanoscale surface roughness and energy using poly(dimethylsiloxane molds of polystyrene beads. Fibronectin and collagen type IV adsorption studies showed a linear adsorption behavior as the surface nanoroughness increased. This supported the general trends observed by Khang et al. However, when fitting such data to the mathematical model established by Khang et al, a strong correlation did not result. Thus, this study demonstrated that the equation proposed by Khang et al to predict protein adsorption should be modified to accommodate for additional nanoscale surface property contributions (ie, surface charge to make the model more accurate. In summary, results from this study provided an important step in developing future mathematical models that can correlate surface properties (such as nanoscale roughness and surface energy to initial protein adsorption events important to

  15. Understanding XPO1 target networks using systems biology and mathematical modeling.

    Science.gov (United States)

    Muqbil, Irfana; Kauffman, Michael; Shacham, Sharon; Mohammad, Ramzi M; Azmi, Asfar S

    2014-01-01

    The nuclear transport protein Exportin 1 (XPO1), also called chromosome region maintenance 1 (CRM1), is over-expressed 2- 4 fold in cancer. XPO1 is one of seven nuclear exporter proteins, and is solely responsible for the transport of the major tumor suppressor proteins (TSPs) from the nucleus to the cytoplasm. XPO1 exports any protein that carries a leucine-rich, hydrophobic nuclear export sequence (NES). A number of inhibitors have been discovered that block XPO1 function and thereby restore TSPs to the nucleus of both malignant and normal cells. However, natural product, irreversible XPO1 antagonists such as leptomycin B (LMB) have proven toxic in both preclinical models and in the clinic. Recently, orally bioavailable, drug-like small molecule, potent and selective inhibitors of XPO1 mediated nuclear export ("SINE") have been designed and are undergoing clinical evaluations in both humans and canines with cancer. The breadth of clinical applicability and long-term viability of an XPO1 inhibition strategy requires a deeper evaluation of the consequence of global re-organization of proteins in cancer and normal cells. Unfortunately, most of the studies on XPO1 inhibitors have focused on evaluating a limited number of TSPs or other proteins. Because XPO1 carries ~220 mammalian proteins out of the nucleus, such reductionism has not permitted a global understanding of cellular behavior upon drug-induced disruption of XPO1 function. The consequence of XPO1 inhibition requires holistic investigations that consider the entire set of XPO1 targets and their respective pathways modulated without losing key details. Systems biology is one such holistic approach that can be applied to understand XPO1 regulated proteins along with the downstream players involved. This review provides comprehensive evaluations of the different computational tools that can be utilized in the better understanding of XPO1 and its target. We anticipate that such holistic approaches can allow for

  16. FEATURES OF INVESTMENT PROCESS UNDERSTANDING BY A. SMITH AS THE FOUNDER OF CLASSICAL THEORY

    Directory of Open Access Journals (Sweden)

    T. Ovcharenko

    2013-03-01

    Full Text Available The paper examines the essence and the nature of the concept of “investment”. The main conceptual elements of a scientific theory of Adam Smith are defined. The features of the investment process by Adam Smith as the driving mechanism for social and economic development of a society are revealed.

  17. Gestures and Insight in Advanced Mathematical Thinking

    Science.gov (United States)

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

    2011-01-01

    What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding--in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities.…

  18. Do word-problem features differentially affect problem difficulty as a function of students' mathematics difficulty with and without reading difficulty?

    Science.gov (United States)

    Powell, Sarah R; Fuchs, Lynn S; Fuchs, Douglas; Cirino, Paul T; Fletcher, Jack M

    2009-01-01

    This study examined whether and, if so, how word-problem features differentially affect problem difficulty as a function of mathematics difficulty (MD) status: no MD (n = 109), MD only (n = 109), or MD in combination with reading difficulties (MDRD; n = 109). The problem features were problem type (total, difference, or change) and position of missing information in the number sentence representing the word problem (first, second, or third position). Students were assessed on 14 word problems near the beginning of third grade. Consistent with the hypothesis that mathematical cognition differs as a function of MD subtype, problem type affected problem difficulty differentially for MDRD versus MD-only students; however, the position of missing information in word problems did not. Implications for MD subtyping and for instruction are discussed.

  19. Understanding the Program Effectiveness of Early Mathematics Interventions for Prekindergarten and Kindergarten Environments: A Meta-Analytic Review

    Science.gov (United States)

    Wang, Aubrey H.; Firmender, Janine M.; Power, Joshua R.; Byrnes, James P.

    2016-01-01

    Research Findings: The early childhood years are critical in developing early mathematics skills, but the opportunities one has to learn mathematics tend to be limited, preventing the development of significant mathematics learning. By conducting a meta-analysis of 29 experimental and quasi-experimental studies that have been published since 2000,…

  20. Elementary Mathematics Teachers' Beliefs and Practices: Understanding the Influence of Teaching in a STEAM Setting

    Science.gov (United States)

    Negreiros, Melissa

    2017-01-01

    Many elementary mathematics teachers hold beliefs about the teaching and learning of mathematics and enact practices that are not aligned with the recommendations of reform efforts in the field of mathematics education (Stigler & Hiebert, 2009). For standards-based reform to gain any significant success, many teachers will have to alter the…

  1. 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.

  2. Implementation of cooperative learning model type STAD with RME approach to understanding of mathematical concept student state junior high school in Pekanbaru

    Science.gov (United States)

    Nurhayati, Dian Mita; Hartono

    2017-05-01

    This study aims to determine whether there is a difference in the ability of understanding the concept of mathematics between students who use cooperative learning model Student Teams Achievement Division type with Realistic Mathematic Education approach and students who use regular learning in seventh grade SMPN 35 Pekanbaru. This study was quasi experiments with Posttest-only Control Design. The populations in this research were all the seventh grade students in one of state junior high school in Pekanbaru. The samples were a class that is used as the experimental class and one other as the control class. The process of sampling is using purposive sampling technique. Retrieval of data in this study using the documentation, observation sheets, and test. The test use t-test formula to determine whether there is a difference in student's understanding of mathematical concepts. Before the t-test, should be used to test the homogeneity and normality. Based in the analysis of these data with t0 = 2.9 there is a difference in student's understanding of mathematical concepts between experimental and control class. Percentage of students experimental class with score more than 65 was 76.9% and 56.4% of students control class. Thus be concluded, the ability of understanding mathematical concepts students who use the cooperative learning model type STAD with RME approach better than students using the regular learning. So that cooperative learning model type STAD with RME approach is well used in learning process.

  3. Research in collegiate mathematics education V

    CERN Document Server

    Selden, Annie; Harel, Guershon; Hitt, Fernando

    2003-01-01

    This fifth volume of Research in Collegiate Mathematics Education presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. The articles in RCME are peer-reviewed for two major features: (1) advancing our understanding of collegiate mathematics education, and (2) readability by a wide audience of practicing mathematicians interested in issues affecting their own students. This is not a collection of scholarly arcana, but a compilation of useful and informative research regarding the ways our students think about and learn mathematics.

  4. Children's Understanding of Indebtedness as a Feature of Reciprocal Help Exchanges between Peers.

    Science.gov (United States)

    De Cooke, Peggy A.

    1992-01-01

    Studied 120 children's understanding of indebtedness. Fifth graders reported a diminished obligation to reciprocate help that was given at a low cost to the helper; the obligation remained high for first and third graders. All children reported more obligation to reciprocate help from acquaintances than help from friends. (LB)

  5. Early Childhood Spirituality in Education: Towards an Understanding of the Distinctive Features of Young Children's Spirituality

    Science.gov (United States)

    Adams, Kate; Bull, Rebecca; Maynes, Mary-Louise

    2016-01-01

    Early years education is a holistic endeavour, with some education policies including spiritual development as part of that approach. However, studies exploring the spirituality of young children are scarce, which limits understanding of the phenomenon and its full application in educational settings. Furthermore, nurturing children's spiritual…

  6. Design and Development Computer-Based E-Learning Teaching Material for Improving Mathematical Understanding Ability and Spatial Sense of Junior High School Students

    Science.gov (United States)

    Nurjanah; Dahlan, J. A.; Wibisono, Y.

    2017-02-01

    This paper aims to make a design and development computer-based e-learning teaching material for improving mathematical understanding ability and spatial sense of junior high school students. Furthermore, the particular aims are (1) getting teaching material design, evaluation model, and intrument to measure mathematical understanding ability and spatial sense of junior high school students; (2) conducting trials computer-based e-learning teaching material model, asessment, and instrument to develop mathematical understanding ability and spatial sense of junior high school students; (3) completing teaching material models of computer-based e-learning, assessment, and develop mathematical understanding ability and spatial sense of junior high school students; (4) resulting research product is teaching materials of computer-based e-learning. Furthermore, the product is an interactive learning disc. The research method is used of this study is developmental research which is conducted by thought experiment and instruction experiment. The result showed that teaching materials could be used very well. This is based on the validation of computer-based e-learning teaching materials, which is validated by 5 multimedia experts. The judgement result of face and content validity of 5 validator shows that the same judgement result to the face and content validity of each item test of mathematical understanding ability and spatial sense. The reliability test of mathematical understanding ability and spatial sense are 0,929 and 0,939. This reliability test is very high. While the validity of both tests have a high and very high criteria.

  7. Understanding the effects of pre-processing on extracted signal features from gait accelerometry signals.

    Science.gov (United States)

    Millecamps, Alexandre; Lowry, Kristin A; Brach, Jennifer S; Perera, Subashan; Redfern, Mark S; Sejdić, Ervin

    2015-07-01

    Gait accelerometry is an important approach for gait assessment. Previous contributions have adopted various pre-processing approaches for gait accelerometry signals, but none have thoroughly investigated the effects of such pre-processing operations on the obtained results. Therefore, this paper investigated the influence of pre-processing operations on signal features extracted from gait accelerometry signals. These signals were collected from 35 participants aged over 65years: 14 of them were healthy controls (HC), 10 had Parkinson׳s disease (PD) and 11 had peripheral neuropathy (PN). The participants walked on a treadmill at preferred speed. Signal features in time, frequency and time-frequency domains were computed for both raw and pre-processed signals. The pre-processing stage consisted of applying tilt correction and denoising operations to acquired signals. We first examined the effects of these operations separately, followed by the investigation of their joint effects. Several important observations were made based on the obtained results. First, the denoising operation alone had almost no effects in comparison to the trends observed in the raw data. Second, the tilt correction affected the reported results to a certain degree, which could lead to a better discrimination between groups. Third, the combination of the two pre-processing operations yielded similar trends as the tilt correction alone. These results indicated that while gait accelerometry is a valuable approach for the gait assessment, one has to carefully adopt any pre-processing steps as they alter the observed findings. Copyright © 2015 Elsevier Ltd. All rights reserved.

  8. Recognition and understanding of goals and roles: The key internal features of mental health court teams.

    Science.gov (United States)

    Gallagher, Mary; Skubby, David; Bonfine, Natalie; Munetz, Mark R; Teller, Jennifer L S

    2011-01-01

    The increasing involvement of people with mental illness in the criminal justice system has led to the formation of specialty programs such as mental health courts (hereafter MHCs). We discuss MHCs and the teams serving these courts. Specifically, we examine team members' perceptions of MHC goals and their own and others' roles on the MHC team. Using a semi-structured interview instrument, we conducted 59 face-to-face interviews with criminal justice and mental health treatment personnel representing 11 Ohio MHCs. Findings from our qualitative data analyses reveal that MHC personnel understand individuals' roles within the teams, recognize and appreciate the importance of different roles, and share common goals. MHCs could foster this level of understanding and agreement by working to recruit and retain individuals with experience in or willingness to learn about both the criminal justice and mental health systems. Future research should explore the impact of MHC team functioning on client outcomes. Copyright © 2011 Elsevier Ltd. All rights reserved.

  9. Mathematics as verbal behavior.

    Science.gov (United States)

    Marr, M Jackson

    2015-04-01

    "Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. Copyright © 2015 Elsevier B.V. All rights reserved.

  10. Understanding the selection of core head design features to match precisely challenging well applications

    Energy Technology Data Exchange (ETDEWEB)

    Zambrana, Roberto; Sousa, J. Tadeu V. de; Antunes, Ricardo [Halliburton Servicos Ltda., Rio de Janeiro, RJ (Brazil)

    2008-07-01

    Reliable rock mechanical information is very important for optimum reservoir development. This information can help specialists to accurately estimate reserves, reservoir compaction, sand production, stress field orientation, etc. In all cases, the solutions to problems involving rock mechanics lead to significant cost savings. Consequently, it is important that the decisions be based on the most accurate information possible. For the describing rock mechanics, cores represent the major source of data and therefore should be of good quality. However, there are several well conditions that cause coring and core recovery to be difficult, for example: unconsolidated formations; laminated and fractured rocks; critical mud losses, etc. The problem becomes even worse in high-inclination wells with long horizontal sections. In such situations, the optimum selections of core heads become critical. This paper will discuss the most important design features that enable core heads to be matched precisely to various challenging applications. Cases histories will be used to illustrate the superior performance of selected core heads. They include coring in horizontal wells and in harsh well conditions with critical mud losses. (author)

  11. Pelvic angles: a mathematically rigorous definition which is consistent with a conventional clinical understanding of the terms.

    Science.gov (United States)

    Baker, R

    2001-02-01

    The most common definition of pelvic angles in conventional gait analysis uses the sequence tilt, obliquity, rotation. This is used in most commercially available gait analysis software. This definition of angles, however, is not in agreement with the conventional clinical understanding of the terms when both tilt and rotation are large. This paper shows that by using the sequence rotation, obliquity, tilt it is possible to make a mathematically rigorous definition of pelvic angles which it is consistent with that conventional clinical usage. A model of the pelvis in which the hips are maintained level is developed. It is shown that as tilt and rotation are varied, in a clinically relevant range, that obliquity measured using the conventional sequence can be as much as 10 degrees. By definition it is 0 degrees for the new sequence. A case study shows that measures of obliquity correlate better with the relative height of the hips using the new sequence than the conventional one. It is proposed that use of the new sequence would lead to data which is easier to interpret clinically.

  12. Mathematical modelling

    DEFF Research Database (Denmark)

    Blomhøj, Morten

    2004-01-01

    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......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...

  13. Predicting Scientific Understanding of Prospective Elementary Teachers: Role of Gender, Education Level, Courses in Science, and Attitudes toward Science and Mathematics

    Science.gov (United States)

    Kumar, David D.; Morris, John D.

    2005-01-01

    A multiple regression analysis of the relationship between prospective teachers' scientific understanding and Gender, Education Level (High School, College), Courses in Science (Biology, Chemistry, Physics, Earth Science, Astronomy, and Agriculture), Attitude Towards Science, and Attitude Towards Mathematics is reported. Undergraduate elementary…

  14. Features of Knowledge Building in Biology: Understanding Undergraduate Students’ Ideas about Molecular Mechanisms

    Science.gov (United States)

    Southard, Katelyn; Wince, Tyler; Meddleton, Shanice; Bolger, Molly S.

    2016-01-01

    Research has suggested that teaching and learning in molecular and cellular biology (MCB) is difficult. We used a new lens to understand undergraduate reasoning about molecular mechanisms: the knowledge-integration approach to conceptual change. Knowledge integration is the dynamic process by which learners acquire new ideas, develop connections between ideas, and reorganize and restructure prior knowledge. Semistructured, clinical think-aloud interviews were conducted with introductory and upper-division MCB students. Interviews included a written conceptual assessment, a concept-mapping activity, and an opportunity to explain the biomechanisms of DNA replication, transcription, and translation. Student reasoning patterns were explored through mixed-method analyses. Results suggested that students must sort mechanistic entities into appropriate mental categories that reflect the nature of MCB mechanisms and that conflation between these categories is common. We also showed how connections between molecular mechanisms and their biological roles are part of building an integrated knowledge network as students develop expertise. We observed differences in the nature of connections between ideas related to different forms of reasoning. Finally, we provide a tentative model for MCB knowledge integration and suggest its implications for undergraduate learning. PMID:26931398

  15. Why Is the Learning of Elementary Arithmetic Concepts Difficult? Semiotic Tools for Understanding the Nature of Mathematical Objects

    Science.gov (United States)

    Godino, Juan D.; Font, Vicenc; Wilhelmi, Miguel R.; Lurduy, Orlando

    2011-01-01

    The semiotic approach to mathematics education introduces the notion of "semiotic system" as a tool to describe mathematical activity. The semiotic system is formed by the set of signs, the production rules of signs and the underlying meaning structures. In this paper, we present the notions of system of practices and configuration of objects and…

  16. 21st-Century Urban Renewal: Mathematical Understanding of Real-World Graphical Data Using Geospatial Technologies

    Science.gov (United States)

    DeBay, Dennis J.

    2017-01-01

    The introduction of real-world, meaningful tasks in mathematics classrooms promises to create opportunities for enhancing students' learning through active engagement with mathematical ideas; however, researchers have given little consideration to the contexts in which urban high-school students live. The case study of three students reported in…

  17. Features of Knowledge Building in Biology: Understanding Undergraduate Students' Ideas about Molecular Mechanisms.

    Science.gov (United States)

    Southard, Katelyn; Wince, Tyler; Meddleton, Shanice; Bolger, Molly S

    2016-01-01

    Research has suggested that teaching and learning in molecular and cellular biology (MCB) is difficult. We used a new lens to understand undergraduate reasoning about molecular mechanisms: the knowledge-integration approach to conceptual change. Knowledge integration is the dynamic process by which learners acquire new ideas, develop connections between ideas, and reorganize and restructure prior knowledge. Semistructured, clinical think-aloud interviews were conducted with introductory and upper-division MCB students. Interviews included a written conceptual assessment, a concept-mapping activity, and an opportunity to explain the biomechanisms of DNA replication, transcription, and translation. Student reasoning patterns were explored through mixed-method analyses. Results suggested that students must sort mechanistic entities into appropriate mental categories that reflect the nature of MCB mechanisms and that conflation between these categories is common. We also showed how connections between molecular mechanisms and their biological roles are part of building an integrated knowledge network as students develop expertise. We observed differences in the nature of connections between ideas related to different forms of reasoning. Finally, we provide a tentative model for MCB knowledge integration and suggest its implications for undergraduate learning. © 2016 K. Southard 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).

  18. An image-processing method to detect sub-optical features based on understanding noise in intensity measurements.

    Science.gov (United States)

    Bhatia, Tripta

    2018-02-01

    Accurate quantitative analysis of image data requires that we distinguish between fluorescence intensity (true signal) and the noise inherent to its measurements to the extent possible. We image multilamellar membrane tubes and beads that grow from defects in the fluid lamellar phase of the lipid 1,2-dioleoyl-sn-glycero-3-phosphocholine dissolved in water and water-glycerol mixtures by using fluorescence confocal polarizing microscope. We quantify image noise and determine the noise statistics. Understanding the nature of image noise also helps in optimizing image processing to detect sub-optical features, which would otherwise remain hidden. We use an image-processing technique "optimum smoothening" to improve the signal-to-noise ratio of features of interest without smearing their structural details. A high SNR renders desired positional accuracy with which it is possible to resolve features of interest with width below optical resolution. Using optimum smoothening, the smallest and the largest core diameter detected is of width [Formula: see text] and [Formula: see text] nm, respectively, discussed in this paper. The image-processing and analysis techniques and the noise modeling discussed in this paper can be used for detailed morphological analysis of features down to sub-optical length scales that are obtained by any kind of fluorescence intensity imaging in the raster mode.

  19. Adult and juvenile dermatomyositis: are the distinct clinical features explained by our current understanding of serological subgroups and pathogenic mechanisms?

    Science.gov (United States)

    2013-01-01

    Adult and juvenile dermatomyositis share the hallmark features of pathognomic skin rash and muscle inflammation, but are heterogeneous disorders with a range of additional disease features and complications. The frequency of important clinical features such as calcinosis, interstitial lung disease and malignancy varies markedly between adult and juvenile disease. These differences may reflect different disease triggers between children and adults, but whilst various viral and other environmental triggers have been implicated, results are so far conflicting. Myositis-specific autoantibodies can be detected in both adults and children with idiopathic inflammatory myopathies. They are associated with specific disease phenotypes and complications, and divide patients into clinically homogenous subgroups. Interestingly, whilst the same autoantibodies are found in both adults and children, the disease features remain different within autoantibody subgroups, particularly with regard to life-threatening disease associations, such as malignancy and rapidly progressive interstitial lung disease. Our understanding of the mechanisms that underlie these differences is limited by a lack of studies directly comparing adults and children. Dermatomyositis is an autoimmune disease, which is believed to develop as a result of an environmental trigger in a genetically predisposed individual. Age-specific host immune responses and muscle physiology may be additional complicating factors that have significant impact on disease presentation. Further study into this area may produce new insights into disease pathogenesis. PMID:23566358

  20. THE FEATURES OF TRAINING OF TEACHERS AND STUDENTS TO THE USE OF INFORMATION TECHNOLOGIES TRAINING OF MATHEMATICS IN HIGHER EDUCATIONAL ESTABLISHMENTS

    Directory of Open Access Journals (Sweden)

    Y. I. Sinko

    2012-10-01

    Full Text Available The article deals with the current issues to improve the educational process at higher school on the basis of introduction of information and communication technologies training. The main attention was paid to the problem of determining the conditions, psychological and pedagogical features of application of existing pedagogical software systems for teaching mathematics in higher educational establishments. Teachers’ and students’ appropriate training to the use of information technologies training should be considered one of the conditions for increasing of efficiency of the process of informatization of education.

  1. the role of mathematical modelling in understanding the epidemiology and control of sheep transmissible spongiform encephalopathies: a review

    NARCIS (Netherlands)

    Gubbins, S.; Touzeau, S.; Hagenaars, T.H.J.

    2010-01-01

    To deal with the incompleteness of observations and disentangle the complexities of transmission much use has been made of mathematical modelling when investigating the epidemiology of sheep transmissible spongiform encephalopathies (TSE) and, in particular, scrapie. Importantly, these modelling

  2. Comparison of the Effects of Computer-Based Practice and Conceptual Understanding Interventions on Mathematics Fact Retention and Generalization

    Science.gov (United States)

    Kanive, Rebecca; Nelson, Peter M.; Burns, Matthew K.; Ysseldyke, James

    2014-01-01

    The authors' purpose was to determine the effects of computer-based practice and conceptual interventions on computational fluency and word-problem solving of fourth- and fifth-grade students with mathematics difficulties. A randomized pretest-posttest control group design found that students assigned to the computer-based practice intervention…

  3. Instructional Experiences That Align with Conceptual Understanding in the Transition from High School Mathematics to College Calculus

    Science.gov (United States)

    Wade, Carol H.; Sonnert, Gerhard; Sadler, Philip M.; Hazari, Zahra

    2017-01-01

    Using data from the first National study on high school preparation for college calculus success, the Factors Influencing College Success in Mathematics (FICSMath) project, this article connects student high school instructional experiences to college calculus performance. The findings reported here reveal that students were better prepared for…

  4. Developing an Understanding of What Constitutes Mathematics Teacher Educator PCK: A Case Study of a Collaboration between Two Teacher Educators

    Science.gov (United States)

    Muir, Tracey; Wells, Jill; Chick, Helen

    2017-01-01

    Previous research into the knowledge required for teaching has focused primarily on pre-service and in-service teachers' knowledge. What is less researched, however, is the role of the teacher educator in helping pre-service teachers (PSTs) develop the knowledge needed in order to teach mathematics to students. The focus thus shifts from examining…

  5. Mathematics and art a cultural history

    CERN Document Server

    Gamwell, Lynn

    2016-01-01

    This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell’s comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians’ search for the foundations of their science, such as David Hilbert’s conception of mathematics as an arrangement of meaning-free signs, as well as artists’ search for the essence of their craft, such as Aleksandr Rodchenko’s monochrome paintings. She shows t...

  6. Mathematical foundation of computer science

    CERN Document Server

    Singh, YN

    2005-01-01

    The interesting feature of this book is its organization and structure. That consists of systematizing of the definitions, methods, and results that something resembling a theory. Simplicity, clarity, and precision of mathematical language makes theoretical topics more appealing to the readers who are of mathematical or non-mathematical background. For quick references and immediate attentions¾concepts and definitions, methods and theorems, and key notes are presented through highlighted points from beginning to end. Whenever, necessary and probable a visual approach of presentation is used. The amalgamation of text and figures make mathematical rigors easier to understand. Each chapter begins with the detailed contents, which are discussed inside the chapter and conclude with a summary of the material covered in the chapter. Summary provides a brief overview of all the topics covered in the chapter. To demonstrate the principles better, the applicability of the concepts discussed in each topic are illustrat...

  7. The concept of resources and documents as means to understand mathematics teachers use of digital platforms in the classroom

    DEFF Research Database (Denmark)

    Tamborg, Andreas Lindenskov

    2018-01-01

    Currently, digital learning platforms are being implemented in Danish elementary schools. These platforms are developed with a dual aim of both supporting teachers’ planning and classroom teaching. This paper investigates and discusses the opportunities of using the documentational approach...... to study Danish mathematics teachers’ use of these platforms for classroom teaching and preliminary findings here of in the context of an ongoing PhD project....

  8. Effect of Inquiry-Based Computer Simulation Modeling on Pre-Service Teachers' Understanding of Homeostasis and Their Perceptions of Design Features

    Science.gov (United States)

    Chabalengula, Vivien; Fateen, Rasheta; Mumba, Frackson; Ochs, Laura Kathryn

    2016-01-01

    This study investigated the effect of an inquiry-based computer simulation modeling (ICoSM) instructional approach on pre-service science teachers' understanding of homeostasis and its related concepts, and their perceived design features of the ICoSM and simulation that enhanced their conceptual understanding of these concepts. Fifty pre-service…

  9. 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.

  10. A history of Japanese mathematics

    CERN Document Server

    Smith, David E

    2004-01-01

    One of the first books to show Westerners the nature of Japanese mathematics, this survey highlights the leading features in the development of the wasan, the Japanese system of mathematics. Topics include the use of the soroban, or abacus; the application of sangi, or counting rods, to algebra; the discoveries of the 17th-century sage Seki Kowa; the yenri, or circle principle; the work of 18th-century geometer Ajima Chokuyen; and Wada Nei's contributions to the understanding of hypotrochoids. Unabridged republication of the classic 1914 edition. 74 figures. Index.

  11. Mathematical Modeling Using MATLAB

    National Research Council Canada - National Science Library

    Phillips, Donovan

    1998-01-01

    .... Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process...

  12. Students' Mathematical Noticing

    Science.gov (United States)

    Lobato, Joanne; Hohensee, Charles; Rhodehamel, Bohdan

    2013-01-01

    Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats…

  13. 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,…

  14. Finite mathematics models and applications

    CERN Document Server

    Morris, Carla C

    2015-01-01

    Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.

  15. 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…

  16. Mathematical writing

    CERN Document Server

    Vivaldi, Franco

    2014-01-01

    This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student.   The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition.   Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150...

  17. Mathematical biophysics

    CERN Document Server

    Rubin, Andrew

    2014-01-01

    This book presents concise descriptions and analysis of the classical and modern models used in mathematical biophysics. The authors ask the question "what new information can be provided by the models that cannot be obtained directly from experimental data?" Actively developing fields such as regulatory mechanisms in cells and subcellular systems and electron transport and energy transport in membranes are addressed together with more classical topics such as metabolic processes, nerve conduction and heart activity, chemical kinetics, population dynamics, and photosynthesis. The main approach is to describe biological processes using different mathematical approaches necessary to reveal characteristic features and properties of simulated systems. With the emergence of powerful mathematics software packages such as MAPLE, Mathematica, Mathcad, and MatLab, these methodologies are now accessible to a wide audience. Provides succinct but authoritative coverage of a broad array of biophysical topics and models Wr...

  18. Profile of Metacognition of Mathematics Pre-Service Teachers in Understanding the Concept of Integral Calculus with Regard Gender Differences

    Science.gov (United States)

    Misu, L.; Budayasa, I. K.; Lukito, A.

    2018-01-01

    This research is to describe metacognition profile of female and male mathematics’ pre-service teachers in understanding the concept of integral calculus. The subjects of this study are one female and 1 male mathematics’ pre-service teachers who have studied integral calculus. This research type is an explorative study with the qualitative approach. The main data collection of this research was obtained by using Interview technique. In addition, there are supporting data which is the result of the written work of research subjects (SP) in understanding the question of integral calculus. The results of this study are as follows: There is a difference in metacognition profiles between male and female mathematics’ pre-service teachers in the understanding concept of integral calculus in the interpreting category, especially the definite integral concept. While in the category of exemplifying, there is no difference in metacognition profile between male and female mathematics’ pre-service teachers either the definite integral concept and the indefinite integral concept.

  19. 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...

  20. Understanding early serum hepatitis D virus and HBsAg kinetics during pegylated interferon-alfa therapy via mathematical modeling

    Science.gov (United States)

    Guedj, Jeremie; Rotman, Yaron; Cotler, Scott J.; Koh, Christopher; Schmid, Peter; Albrecht, Jeff; Haynes-Williams, Vanessa; Liang, Jake T.; Hoofnagle, Jay H.; Heller, Theo; Dahari, Harel

    2014-01-01

    There is little information on the early kinetics of hepatitis delta virus (HDV) and hepatitis B surface antigen (HBsAg) during interferon-α therapy. Here a mathematical model was developed and fitted to frequent HDV and HBsAg kinetic data from 10 patients during the first 28 weeks of pegylated-interferon-α2a (peg-IFN) therapy. Three patients achieved a complete virological response (CVR), defined as undetectable HDV 6 months after treatment stopped with loss of HBsAg and anti-HBsAg seroconversion. After initiation of therapy a median delay of 9 days (interquartile range IQR:[5;15]) was observed with no significant changes in HDV level. Thereafter, HDV declined in a biphasic manner, where a rapid first-phase lasting for 25 days (IQR:[23;58]) was followed by a slower or plateau second-phase. The model predicts that the main effect of peg-IFN is to reduce HDV production/release with a median effectiveness of 96% (IQR:[93;99.8]). Median serum HDV half-life (t1/2) was estimated to 2.9 days (IQR:[1.5;5.3]) with pretreatment production and clearance of about 1010 (IQR:[109.8-1010.8]) virions/day. None of the patients with flat 2nd phase in HDV achieved CVR. HBsAg kinetics of decline paralleled the second-phase of HDV decline consistent with HBsAg-productive-infected cells being the main source of production of HDV, with a median t1/2 of 135 days (IQR:[20-460]. The interferon lambda-3 polymorphism (rs12979860) was not associated with kinetic parameters. Conclusions Modeling results provide insights into HDV-host dynamics, the relationship between serum HBsAg levels and HBsAg-infected cells, IFN's mode of action and its effectiveness. The observation that a flat second phase in HDV and HBsAg kinetics was associated with failure to achieve CVR provides the basis to develop early stopping rules during peg-IFN treatment in HDV-infected patients. PMID:25098971

  1. Utah's New Mathematics Core

    Science.gov (United States)

    Utah State Office of Education, 2011

    2011-01-01

    Utah has adopted more rigorous mathematics standards known as the Utah Mathematics Core Standards. They are the foundation of the mathematics curriculum for the State of Utah. The standards include the skills and understanding students need to succeed in college and careers. They include rigorous content and application of knowledge and reflect…

  2. Learning Environments in Mathematics

    Science.gov (United States)

    Turner, Vanshelle E.

    2017-01-01

    Learning mathematics is problematic for most primary school age children because mathematics is rote and the memorization of steps rather than an approach to seeing relationships that builds inquiry and understanding. Therefore, the traditional "algorithmic" way of teaching mathematics has not fully prepared students to be critical…

  3. Segmentation of photospheric magnetic elements corresponding to coronal features to understand the EUV and UV irradiance variability

    Science.gov (United States)

    Zender, J. J.; Kariyappa, R.; Giono, G.; Bergmann, M.; Delouille, V.; Damé, L.; Hochedez, J.-F.; Kumara, S. T.

    2017-09-01

    Context. The magnetic field plays a dominant role in the solar irradiance variability. Determining the contribution of various magnetic features to this variability is important in the context of heliospheric studies and Sun-Earth connection. Aims: We studied the solar irradiance variability and its association with the underlying magnetic field for a period of five years (January 2011-January 2016). We used observations from the Large Yield Radiometer (LYRA), the Sun Watcher with Active Pixel System detector and Image Processing (SWAP) on board PROBA2, the Atmospheric Imaging Assembly (AIA), and the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). Methods: The Spatial Possibilistic Clustering Algorithm (SPoCA) is applied to the extreme ultraviolet (EUV) observations obtained from the AIA to segregate coronal features by creating segmentation maps of active regions (ARs), coronal holes (CHs) and the quiet sun (QS). Further, these maps are applied to the full-disk SWAP intensity images and the full-disk (FD) HMI line-of-sight (LOS) magnetograms to isolate the SWAP coronal features and photospheric magnetic counterparts, respectively. We then computed full-disk and feature-wise averages of EUV intensity and line of sight (LOS) magnetic flux density over ARs/CHs/QS/FD. The variability in these quantities is compared with that of LYRA irradiance values. Results: Variations in the quantities resulting from the segmentation, namely the integrated intensity and the total magnetic flux density of ARs/CHs/QS/FD regions, are compared with the LYRA irradiance variations. We find that the EUV intensity over ARs/CHs/QS/FD is well correlated with the underlying magnetic field. In addition, variations in the full-disk integrated intensity and magnetic flux density values are correlated with the LYRA irradiance variations. Conclusions: Using the segmented coronal features observed in the EUV wavelengths as proxies to isolate the underlying

  4. Analysis of syntactic and semantic features for fine-grained event-spatial understanding in outbreak news reports

    Directory of Open Access Journals (Sweden)

    Chanlekha Hutchatai

    2010-03-01

    Full Text Available Abstract Background Previous studies have suggested that epidemiological reasoning needs a fine-grained modelling of events, especially their spatial and temporal attributes. While the temporal analysis of events has been intensively studied, far less attention has been paid to their spatial analysis. This article aims at filling the gap concerning automatic event-spatial attribute analysis in order to support health surveillance and epidemiological reasoning. Results In this work, we propose a methodology that provides a detailed analysis on each event reported in news articles to recover the most specific locations where it occurs. Various features for recognizing spatial attributes of the events were studied and incorporated into the models which were trained by several machine learning techniques. The best performance for spatial attribute recognition is very promising; 85.9% F-score (86.75% precision/85.1% recall. Conclusions We extended our work on event-spatial attribute recognition by focusing on machine learning techniques, which are CRF, SVM, and Decision tree. Our approach avoided the costly development of an external knowledge base by employing the feature sources that can be acquired locally from the analyzed document. The results showed that the CRF model performed the best. Our study indicated that the nearest location and previous event location are the most important features for the CRF and SVM model, while the location extracted from the verb's subject is the most important to the Decision tree model.

  5. Feature Selection by Reordering

    Czech Academy of Sciences Publication Activity Database

    Jiřina, Marcel; Jiřina jr., M.

    2005-01-01

    Roč. 2, č. 1 (2005), s. 155-161 ISSN 1738-6438 Institutional research plan: CEZ:AV0Z10300504 Keywords : feature selection * data reduction * ordering of features Subject RIV: BA - General Mathematics

  6. 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

  7. Mathematics Education and Language Diversity

    DEFF Research Database (Denmark)

    Moschkovich, Judit; Planas, Nuria

    This book examines multiple facets of language diversity and mathematics education. It features renowned authors from around the world and explores the learning and teaching of mathematics in contexts that include multilingual classrooms, indigenous education, teacher education, blind and deaf...

  8. Find your future in mathematics

    CERN Document Server

    Gunzehauser, Kelly

    2016-01-01

    "Find Your Future in Mathematics introduces 8 high-interest mathematical careers via reader-friendly profiles and sidebar features that inspire extended learning, online research, and critical thinking skills. Back matter includes additional learning activities"-- Provided by publisher.

  9. Visual Soccer Analytics: Understanding the Characteristics of Collective Team Movement Based on Feature-Driven Analysis and Abstraction

    Directory of Open Access Journals (Sweden)

    Manuel Stein

    2015-10-01

    Full Text Available With recent advances in sensor technologies, large amounts of movement data have become available in many application areas. A novel, promising application is the data-driven analysis of team sport. Specifically, soccer matches comprise rich, multivariate movement data at high temporal and geospatial resolution. Capturing and analyzing complex movement patterns and interdependencies between the players with respect to various characteristics is challenging. So far, soccer experts manually post-analyze game situations and depict certain patterns with respect to their experience. We propose a visual analysis system for interactive identification of soccer patterns and situations being of interest to the analyst. Our approach builds on a preliminary system, which is enhanced by semantic features defined together with a soccer domain expert. The system includes a range of useful visualizations to show the ranking of features over time and plots the change of game play situations, both helping the analyst to interpret complex game situations. A novel workflow includes improving the analysis process by a learning stage, taking into account user feedback. We evaluate our approach by analyzing real-world soccer matches, illustrate several use cases and collect additional expert feedback. The resulting findings are discussed with subject matter experts.

  10. 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 ...

  11. An introduction to mathematical modeling a course in mechanics

    CERN Document Server

    Oden, Tinsley J

    2011-01-01

    A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equation...

  12. Qualitative and quantitative approach towards the molecular understanding of structural, vibrational and optical features of urea ninhydrin monohydrate

    Energy Technology Data Exchange (ETDEWEB)

    Sasikala, V. [Department of Physics, Bishop Moore College, Mavelikara, Alappuzha, Kerala 690110 (India); Sajan, D., E-mail: drsajanbmc@gmail.com [Department of Physics, Bishop Moore College, Mavelikara, Alappuzha, Kerala 690110 (India); Chaitanya, K. [Department of Chemistry, Nanjing University of Science and Technology, Xialingwei 200, Nanjing (China); Sundius, Tom [Department of Physics, University of Helsinki (Finland); Devi, T. Uma [Department of Physics, Government Arts College for Women (Autonomous), Pudukottai (India)

    2017-04-15

    In this study, single crystals of urea ninhydrin monohydrate (UNMH) have been grown by slow evaporation method. The grown crystals were characterized by FT-IR, FT-Raman and UV-Vis-NIR spectroscopies. The Kurtz and Perry powder method was employed to confirm the near-zero SHG efficiency of the as-grown centrosymmetric UNMH crystal. The third order nonlinearity of the crystal has been studied by the open aperture Z-scan method. The nonlinear absorption coefficient is calculated and the potentiality of UNMH in optical limiting applications is identified. The molecular geometry and the origin of optical non-linearity at the molecular level have been investigated by the density functional theory. The normal coordinate analysis was carried out to assign the molecular vibrational modes. Vibrational spectral studies confirms the presence of weak O-H⋯O and moderate O-H⋯O type hydrogen bonds in the molecule as well as O-H⋯O, N-H⋯O and blue-shifted C-H⋯O type H-bonds in the crystal. The intramolecular charge transfer interactions and the electronic absorption mechanisms have been discussed. The static and the dynamic values of hyperpolarizabilities for UNMH were estimated theoretically by DFT methods. - Highlights: • Molecular geometric and NBO interaction features of UNMH were analyzed. • Vibrational spectral features and types of H-bonding in isolated gaseous phase molecule were discussed. • Electronic absorption maxima of different phases of UNMH were found out. • The non-linear absorption behaviour of UNMH is investigated using z-scan. • First- and second- order hyperpolarizability values were estimated theoretically.

  13. To What Extent Is Mathematical Ability Predictive of Performance in a Methodology and Statistics Course? Can an Action Research Approach Be Used to Understand the Relevance of Mathematical Ability in Psychology Undergraduates?

    Science.gov (United States)

    Bourne, Victoria J.

    2014-01-01

    Research methods and statistical analysis is typically the least liked and most anxiety provoking aspect of a psychology undergraduate degree, in large part due to the mathematical component of the content. In this first cycle of a piece of action research, students' mathematical ability is examined in relation to their performance across…

  14. Assessment and realistic mathematics education

    NARCIS (Netherlands)

    Heuvel-Panhuizen, M.H.A.M. van den

    1996-01-01

    This book describes the consequences of Realistic Mathematics Education (RME) for assessing students’ understanding of mathematics in primary school. RME is the Dutch answer to the worldwide need to reform mathematics education. Changed ideas about mathematics as a school subject, its goals,

  15. Finding Meaning in Mathematical Mnemonics

    Science.gov (United States)

    Miller, Geoffrey; Obara, Samuel

    2017-01-01

    A mathematical mnemonic is a visual cue or verbal strategy that is used to aid initial memorisation and recall of a mathematical concept or procedure. Used wisely, mathematical mnemonics can benefit students' performance and understanding. Explorations into how mathematical mnemonics work can also offer students opportunities to engage in proof…

  16. Mathematical Competences

    DEFF Research Database (Denmark)

    Westphael, Henning; Mogensen, Arne

    2013-01-01

    In this article we present the notion of Mathematical competences as a tool to describe the mathematically gifted students.......In this article we present the notion of Mathematical competences as a tool to describe the mathematically gifted students....

  17. 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...

  18. Understanding Mathematics-A Review

    Indian Academy of Sciences (India)

    Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 3 · Current Issue Volume 23 | Issue 3. March 2018. Home · Volumes & Issues · Categories · Special Issues · Search · Editorial Board · Information for Authors · Subscription ...

  19. 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

  20. Understanding non-enzymatic aminophospholipid glycation and its inhibition. Polar head features affect the kinetics of Schiff base formation.

    Science.gov (United States)

    Caldés, Catalina; Vilanova, Bartolomé; Adrover, Miquel; Muñoz, Francisco; Donoso, Josefa

    2011-08-01

    Non-enzymatic aminophospholipid glycation is an especially important process because it alters the stability of lipid bilayers and interferes with cell function and integrity as a result. However, the kinetic mechanism behind this process has scarcely been studied. As in protein glycation, the process has been suggested to involve the formation of a Schiff base as the initial, rate-determining step. In this work, we conducted a comparative kinetic study of Schiff base formation under physiological conditions in three low-molecular weight analogues of polar heads in the naturally occurring aminophospholipids O-phosphorylethanolamine (PEA), O-phospho-DL-serine (PSer) and 2-aminoethylphenethylphosphate (APP) with various glycating carbonyl compounds (glucose, arabinose and acetol) and the lipid glycation inhibitor pyridoxal 5'-phosphate (PLP). Based on the results, the presence of a phosphate group and a carboxyl group in α position respect to the amino group decrease the formation constant for the Schiff base relative to amino acids. On the other hand, esterifying the phosphate group with a non-polar substituent in APP increases the stability of its Schiff base. The observed kinetic formation constants of aminophosphates with carbonyl groups were smaller than those for PLP. Our results constitute an important contribution to understanding the competitive inhibition effect of PLP on aminophospholipid glycation. Copyright © 2011 Elsevier Ltd. All rights reserved.

  1. Mathematics in Ancient India

    Indian Academy of Sciences (India)

    In this series of articles, we intend to have a glimpse of some of the landmarks in ancient In- dian mathematics with special emphasis on num- ber theory. This issue features a brief overview of some of the high peaks of mathematics in an- cient India. In the next part we shall describe. Aryabhata's general solution in integers ...

  2. Dyslexia, Dyspraxia and Mathematics.

    Science.gov (United States)

    Yeo, Dorian

    This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…

  3. EFFECT OF MATHEMATICS LEARNING ON THE DEVELOPMENT OF MATHEMATICS CREATIVITY

    OpenAIRE

    Dr. Jyoti Sharma

    2017-01-01

    The paper presents an empirical study done in Indian classrooms to understand the effect of mathematics learning experiences on the development of mathematics creativity. The study was designed in two stages, at stage I, it was planned to find out scope, practice and promotion of creative thinking in mathematics classroom; teachers’ own engagements with creative mathematical task and teachers’ attitude towards mathematics creativity. Stage II was designed to find out responses of students and...

  4. Tracing the Construction of Mathematical Activity with an Advanced Graphing Calculator to Understand the Roles of Technology Developers, Teachers and Students

    Science.gov (United States)

    Hillman, Thomas

    2014-01-01

    This article examines mathematical activity with digital technology by tracing it from its development through its use in classrooms. Drawing on material-semiotic approaches from the field of Science and Technology Studies, it examines the visions of mathematical activity that developers had for an advanced graphing calculator. It then follows the…

  5. Propensity Score Matching Helps to Understand Sources of DIF and Mathematics Performance Differences of Indonesian, Turkish, Australian, and Dutch Students in PISA

    Science.gov (United States)

    Arikan, Serkan; van de Vijver, Fons J. R.; Yagmur, Kutlay

    2018-01-01

    We examined Differential Item Functioning (DIF) and the size of cross-cultural performance differences in the Programme for International Student Assessment (PISA) 2012 mathematics data before and after application of propensity score matching. The mathematics performance of Indonesian, Turkish, Australian, and Dutch students on released items was…

  6. 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…

  7. Analysis of Student Understanding of Science Concepts Including Mathematical Representations: Ph Values and the Relative Differences of pH Values

    Science.gov (United States)

    Park, Eun-Jung; Choi, Kyunghee

    2013-01-01

    In general, mathematical representations such as formulae, numbers, and graphs are the inseparable components in science used to better describe or explain scientific phenomena or knowledge. Regardless of their necessity and benefit, science seems to be difficult for some students, as a result of the mathematical representations and problem…

  8. Logic and discrete mathematics a concise introduction

    CERN Document Server

    Conradie, Willem

    2015-01-01

    A concise yet rigorous introduction to logic and discrete mathematics. 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.  The chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical logic as well as practical applications through the easy

  9. Reprint of "Mathematics as verbal behavior".

    Science.gov (United States)

    Marr, M Jackson

    2015-05-01

    "Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. Copyright © 2015 Elsevier B.V. All rights reserved.

  10. 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.

  11. 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.

  12. God created the integers the mathematical breakthroughs that changed history

    CERN Document Server

    2007-01-01

    Bestselling author and physicist Stephen Hawking explores the "masterpieces" of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians, including Augustin Cauchy, Bernard Riemann, and Alan Turing. This extensive anthology allows readers to peer into the mind of genius by providing them with excerpts from the original mathematical proofs and results. It also helps them understand the progression of mathematical thought, and the very foundations of our present-day technologies. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication.

  13. Ideation in mathematical writing

    DEFF Research Database (Denmark)

    Misfeldt, Morten

    2007-01-01

    This paper considers idea generation during the mathematical writing process. Two contrasting explanations of the creative potential in connection to writing is presented; writing as a process of setting and obtaining rhetorical goals and writing as a process of discovery. These views...... are then related to two empirically found categories of functions that writing serves researchers in the field of mathematics, concluding that both views contributes to understanding the creative potential in relation to mathematical writing....

  14. Conceptions of Effective Mathematics Teaching within a Cultural Context: Perspectives of Teachers from China and the United States

    Science.gov (United States)

    Cai, Jinfa; Wang, Tao

    2010-01-01

    This study investigates Chinese and U.S. teachers' cultural beliefs concerning effective mathematics teaching from the teachers' perspectives. Although sharing some common beliefs, the two groups of teachers think differently about both mathematics understanding and the features of effective teaching. The sample of U.S. teachers put more emphasis…

  15. A quest towards a mathematical theory of living systems

    CERN Document Server

    Bellomo, Nicola; Gibelli, Livio; Outada, Nisrine

    2017-01-01

    This monograph aims to lay the groundwork for the design of a unified mathematical approach to the modeling and analysis of large, complex systems composed of interacting living things. Drawing on twenty years of research in various scientific fields, it explores how mathematical kinetic theory and evolutionary game theory can be used to understand the complex interplay between mathematical sciences and the dynamics of living systems. The authors hope this will contribute to the development of new tools and strategies, if not a new mathematical theory. The first chapter discusses the main features of living systems and outlines a strategy for their modeling. The following chapters then explore some of the methods needed to potentially achieve this in practice. Chapter Two provides a brief introduction to the mathematical kinetic theory of classical particles, with special emphasis on the Boltzmann equation; the Enskog equation, mean field models, and Monte Carlo methods are also briefly covered. Chapter Three...

  16. Maths Games Workshop--Part Thirteen: Types of Mathematical Games.

    Science.gov (United States)

    Kirkby, Dave

    1989-01-01

    Presented are mathematical games in six categories of mathematical objectives: learn the language of mathematics; use mathematical notation; know facts; develop skills; understand concepts; and devise strategies. Numbers of players, rules, and diagrams are provided for each problem. (YP)

  17. Mathematics for computer graphics

    CERN Document Server

    Vince, John

    2006-01-01

    Helps you understand the mathematical ideas used in computer animation, virtual reality, CAD, and other areas of computer graphics. This work also helps you to rediscover the mathematical techniques required to solve problems and design computer programs for computer graphic applications

  18. Cognitive Correlates of Performance in Advanced Mathematics

    Science.gov (United States)

    Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

    2012-01-01

    Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…

  19. 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

  20. Topological feature extraction and tracking

    International Nuclear Information System (INIS)

    Bremer, P-T; Bringa, E M; Duchaineau, M A; Gyulassy, A G; Laney, D; Mascarenhas, A; Pascucci, V

    2007-01-01

    Scientific datasets obtained by measurement or produced by computational simulations must be analyzed to understand the phenomenon under study. The analysis typically requires a mathematically sound definition of the features of interest and robust algorithms to identify these features, compute statistics about them, and often track them over time. Because scientific datasets often capture phenomena with multi-scale behaviour, and almost always contain noise the definitions and algorithms must be designed with sufficient flexibility and care to allow multi-scale analysis and noise-removal. In this paper, we present some recent work on topological feature extraction and tracking with applications in molecular analysis, combustion simulation, and structural analysis of porous materials

  1. 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.

  2. Connecting Advanced and Secondary Mathematics

    Science.gov (United States)

    Murray, Eileen; Baldinger, Erin; Wasserman, Nicholas; Broderick, Shawn; White, Diana

    2017-01-01

    There is an ongoing debate among scholars in understanding what mathematical knowledge secondary teachers should have in order to provide effective instruction. We explore connections between advanced and secondary mathematics as an entry point into this debate. In many cases, advanced mathematics is considered relevant for secondary teachers…

  3. "We Don't Understand English That Is Why We Prefer English": Primary School Students' Preference for the Language of Instruction in Mathematics

    Science.gov (United States)

    Davis, Ernest Kofi; Bishop, Alan J.; Seah, Wee Tiong

    2015-01-01

    This paper reports on a study which sought to investigate how social and political influences affect students' preference for language of instruction in mathematics in Ghana, where the language of instruction from grade 4 onwards in school is not the students' main language. 4 focus group interviews were carried out with 16 primary school…

  4. Understanding the Doctoral Experience of Asian International Students in the Science, Technology, Engineering, and Mathematics (STEM) Fields: An Exploration of One Institutional Context

    Science.gov (United States)

    Le, Tam; Gardner, Susan K.

    2010-01-01

    In this study, we explored the experience of Asian international doctoral students in the Science, Technology, Engineering, and Mathematics (STEM) fields at one research-extensive university. We found that Asian international doctoral students in the STEM fields at this institution were often isolated from their peers and faculty, faced an array…

  5. Advanced Mathematical Thinking and Students' Mathematical Learning: Reflection from Students' Problem-Solving in Mathematics Classroom

    Science.gov (United States)

    Sangpom, Wasukree; Suthisung, Nisara; Kongthip, Yanin; Inprasitha, Maitree

    2016-01-01

    Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students' inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In…

  6. 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...

  7. Mathematical narrative: from history to literature

    OpenAIRE

    Su, Yi-Wen; Horng, Wann-Sheng; Huang, Jyun-Wei; Chen, Yuh-Fen

    2016-01-01

    International audience; Mathematical narrative is a concept that has gradually been attracting the attention of school teachers and mathematics educators in especially recent years. The term ‘mathematical narrative' in this workshop proposal refers to a form of narrative that is used to communicate or construct mathematical meaning or understanding. By introducing certain metaphors, a narrator may induce or promote learners' or listeners' mathematical understanding. This teaching tool can be ...

  8. Mastering mathematics for Edexcel GCSE

    CERN Document Server

    Davis, Heather; Liggett, Linda

    2015-01-01

    Help students to develop their knowledge, skills and understanding so that they can reason mathematically, communicate mathematical information and apply mathematical techniques in solving problems; with resources developed specifically for the Edexcel GCSE 2015 specification with leading Assessment Consultant Keith Pledger and a team of subject specialists. - Supports you and your students through the new specifications, with topic explanations and new exam-style questions, to support the new assessment objectives. - Builds understanding and measures progress throughout the course with plenty

  9. 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...

  10. Authority, Identity, and Collaborative Mathematics

    Science.gov (United States)

    Langer-Osuna, Jennifer M.

    2017-01-01

    The field of mathematics education research has seen a resurgence of interest in understanding collaborative learning because students in K-12 classrooms are increasingly expected to make sense of mathematics problems together. This Research Commentary argues for the importance of understanding student authority relations in collaborative…

  11. Contributions in mathematical physics a tribute to Gerard G. Emch

    CERN Document Server

    Sinha, Kalyan

    2007-01-01

    Professor Gerard G. Emch has been one of the pioneers of the C-algebraic approach to quantum and classical statistical mechanics. In a prolific scientific career, spanning nearly five decades, Professor Emch has been one of the creative influences in the general area of mathematical physics. The present volume is a collection of tributes, from former students, colleagues and friends of Professor Emch, on the occasion of his 70th birthday. The articles featured here are a small yet representative sample of the breadth and reach of some of the ideas from mathematical physics.It is also a testimony to the impact that Professor Emch's work has had on several generations of mathematical physicists as well as to the diversity of mathematical methods used to understand them.

  12. Mathematics Connection

    African Journals Online (AJOL)

    ... and JHS teachers toward mathematics, both upper primary and JHS teachers were found to have significantly more positive attitudes toward mathematics than the lower primary teachers. The study recommended the need to encourage lower primary school teachers to develop more positive attitudes toward mathematics.

  13. Teachers' Conceptions of Mathematical Modeling

    Science.gov (United States)

    Gould, Heather

    2013-01-01

    The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…

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

    DEFF Research Database (Denmark)

    Misfeldt, Morten

    2015-01-01

    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...... guidelines and conclusions regarding the use of computer technology in mathematics education.......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...

  15. Understanding Maple

    CERN Document Server

    Thompson, Ian

    2016-01-01

    Maple is a powerful symbolic computation system that is widely used in universities around the world. This short introduction gives readers an insight into the rules that control how the system works, and how to understand, fix, and avoid common problems. Topics covered include algebra, calculus, linear algebra, graphics, programming, and procedures. Each chapter contains numerous illustrative examples, using mathematics that does not extend beyond first-year undergraduate material. Maple worksheets containing these examples are available for download from the author's personal website. The book is suitable for new users, but where advanced topics are central to understanding Maple they are tackled head-on. Many concepts which are absent from introductory books and manuals are described in detail. With this book, students, teachers and researchers will gain a solid understanding of Maple and how to use it to solve complex mathematical problems in a simple and efficient way.

  16. Adapting the mathematical task framework to design online didactic objects

    Science.gov (United States)

    Bowers, Janet; Bezuk, Nadine; Aguilar, Karen

    2011-06-01

    Designing didactic objects involves imagining how students can conceive of specific mathematical topics and then imagining what types of classroom discussions could support these mental constructions. This study investigated whether it was possible to design Java applets that might serve as didactic objects to support online learning where 'discussions' are broadly defined as the conversations students have with themselves as they interact with the dynamic mathematical representations on the screen. Eighty-four pre-service elementary teachers enrolled in hybrid mathematics courses were asked to interact with a series of applets designed to support their understanding of qualitative graphing. The results of the surveys indicate that various design features of the applets did in fact cause perturbations and opportunities for resolutions that enabled the users to 'discuss' their learning by reflecting on their in-class discussions and online activities. The discussion includes four design features for guiding future applet creation.

  17. First aid in mathematics

    CERN Document Server

    Sulley, Robert

    2014-01-01

    Achieve the best possible standard with this bestselling book of traditional practice and guidance - now in colour!. First Aid in Mathematics provides all the help and support needed for learning and practising Mathematics. It offers comprehensive coverage of core mathematical topics in clear and accessible language. It is suitable for both native English speakers and students of English as a second language and can be used in class, or as a reference and revision book. - Develops a strong basis of understanding with core topics covered in clear and accessible language. - Improves student's ab

  18. The reality of Mathematics

    Science.gov (United States)

    Ligomenides, Panos A.

    2009-05-01

    The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic [`]computation', is examined and commended upon.

  19. Mathematics and linguistics

    Energy Technology Data Exchange (ETDEWEB)

    Landauer, C.; Bellman, K.L.

    1996-12-31

    In this paper, we study foundational issues that we believe will help us develop a theoretically sound approach to constructing complex systems. The two theoretical approaches that have helped us understand and develop computational systems in the past are mathematics and linguistics. We describe some differences and strengths of the approaches, and propose a research program to combine the richness of linguistic reasoning with the precision of mathematics.

  20. Mathematical modeling with multidisciplinary applications

    CERN Document Server

    Yang, Xin-She

    2013-01-01

    Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the

  1. 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…

  2. Understanding why women are under-represented in Science, Technology, Engineering and Mathematics (STEM within Higher Education: a regional case study

    Directory of Open Access Journals (Sweden)

    Michael Christie

    Full Text Available Abstract Participation rates of women in Science, Technology, Engineering and Mathematics (STEM is comparatively low and their attrition rates high. An obvious solution is to attract more women to study such subjects. In 2016 the authors undertook research to find out why so few women enrolled in STEM subjects and investigate ways of increasing their recruitment and retention in this area. The informants in our study were enrolled in a tertiary preparation course as well as nursing and education programs. A critique of the literature was used to develop a survey that informed focus group and interview schedules which were used in collecting data. Our study found that many of the factors that hindered women from applying for STEM courses twenty years ago still apply today and recommends actions that can help increase recruitment of women into STEM and assist their retention and graduation in those areas of tertiary education.

  3. 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

  4. 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

  5. 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

  6. Understand electronics

    CERN Document Server

    Bishop, Owen

    2013-01-01

    Understand Electronics provides a readable introduction to the exciting world of electronics for the student or enthusiast with little previous knowledge. The subject is treated with the minimum of mathematics and the book is extensively illustrated.This is an essential guide for the newcomer to electronics, and replaces the author's best-selling Beginner's Guide to Electronics.The step-by-step approach makes this book ideal for introductory courses such as the Intermediate GNVQ.

  7. Discrete mathematics using a computer

    CERN Document Server

    Hall, Cordelia

    2000-01-01

    Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica­ tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools su...

  8. Handbook of mathematics

    CERN Document Server

    Bronshtein, I N; Musiol, Gerhard; Mühlig, Heiner

    2015-01-01

    This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. Besides many enhancements and  new paragraphs,  new sections on Geometric and Coordinate Transformations, Quaternions and Applications, and Lie Groups and Lie Algebras were added for the sixth edition.

  9. An introduction to mathematical analysis

    CERN Document Server

    Shirali, Satish

    2014-01-01

    This book is an elementary text on the theory of functions of one real variable and is intended for students with a good understanding of calculus. It is supposed to replace traditional and outmoded courses in mathematical analysis. The book begins with material on the real number system as a Dedekind complete ordered field, continuous functions, sequences and series of constant terms as well as of functions. Pointwise and uniform convergence of series of functions, power series, treatment of trigonometric and exponential functions in terms of series are discussed. A detailed treatment of differentiation, including differentiation of uniform limits of sequences is provided. Also included is an example of a continuous nowhere differentiable function. There is an exhaustive treatment of both Riemann integration and Riemann-Stieltjes integration. Some features of this work, such as why Dedekind completeness is necessary for ensuring that nonconstant functions cannot have derivative zero everywhere on an interval...

  10. African American Mathematics Teachers as Agents in Their African American Students' Mathematics Identity Formation

    Science.gov (United States)

    Clark, Lawrence M.; Badertscher, Eden M.; Napp, Carolina

    2013-01-01

    Background/Context: Recent research in mathematics education has employed sociocultural and historical lenses to better understand how students experience school mathematics and come to see themselves as capable mathematics learners. This work has identified mathematics classrooms as places where power struggles related to students'…

  11. 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…

  12. Experimental Mathematics and Mathematical Physics

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim

    2009-06-26

    One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

  13. Comprehensive basic mathematics

    CERN Document Server

    Veena, GR

    2005-01-01

    Salient Features As per II PUC Basic Mathematics syllabus of Karnataka. Provides an introduction to various basic mathematical techniques and the situations where these could be usefully employed. The language is simple and the material is self-explanatory with a large number of illustrations. Assists the reader in gaining proficiency to solve diverse variety of problems. A special capsule containing a gist and list of formulae titled ''REMEMBER! Additional chapterwise arranged question bank and 3 model papers in a separate section---''EXAMINATION CORNER''.

  14. Concepts of mathematical modeling

    CERN Document Server

    Meyer, Walter J

    2004-01-01

    Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec

  15. Mathematics 2

    CERN Document Server

    Kodaira, Kunihiko

    1996-01-01

    This is the translation from the Japanese textbook for the grade 11 course, "General Mathematics". It is part of the easier of the three elective courses in mathematics offered at this level and is taken by about 40% of students. The book covers basic notions of probability and statistics, vectors, exponential, logarithmic, and trigonometric functions, and an introduction to differentiation and integration.

  16. Mathematical logic

    CERN Document Server

    Kleene, Stephen Cole

    1967-01-01

    Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition.

  17. 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.

  18. Mathematical problems in meteorological modelling

    CERN Document Server

    Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella

    2016-01-01

    This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...

  19. Reassembling mathematical practices: a philosophicalanthropological approach

    Directory of Open Access Journals (Sweden)

    Karen François

    2016-06-01

    Full Text Available In this paper we first explore how Wittgenstein’s philosophy provides a conceptual tools to discuss the possibility of the simultaneous existence of culturally different mathematical practices. We will argue that Wittgenstein’s later work will be a fruitful framework to serve as a philosophical background to investigate ethnomathematics (Wittgenstein 1973. We will give an overview of Wittgenstein’s later work which is referred to by many researchers in the field of ethnomathematics. The central philosophical investigation concerns Wittgenstein’s shift to abandoning the essentialist concept of language and therefore denying the existence of a universal language. Languages—or ‘language games’ as Wittgenstein calls them—are immersed in a form of life, in a cultural or social formation and are embedded in the totality of communal activities. This gives rise to the idea of rationality as an invention or as a construct that emerges in specific local contexts. In the second part of the paper we introduce, analyse and compare the mathematical aspects of two activities known as string figure-making and sand drawing, to illustrate Wittgenstein’s ideas. Based on an ethnomathematical comparative analysis, we will argue that there is evidence of invariant and distinguishing features of a mathematical rationality, as expressed in both string figure-making and sand drawing practices, from one society to another. Finally, we suggest that a philosophical-anthropological approach to mathematical practices may allow us to better understand the interrelations between mathematics and cultures. Philosophical investigations may help the reflection on the possibility of culturally determined ethnomathematics, while an anthropological approach, using ethnographical methods, may afford new materials for the analysis of ethnomathematics and its links to the cultural context. This combined approach will help us to better characterize mathematical

  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. Systematic perspectives on diverging mathematical orientations

    Directory of Open Access Journals (Sweden)

    D.F.M. Strauss

    2005-07-01

    Full Text Available The popular view that mathematics is “objective” and “neutral” in the sense that it does not know different standpoints is contradicted by the factual state of modern mathematics. In the light of the dominant one-sided trends in the history of mathe-matics, fluctuating between arithmeticism and a geometrisation of this discipline, this article explores some provisional starting-points for a different view. This third option is explored by investigating some features of an acknowledgement of the uniqueness of number and space without neglecting the inter-aspectual connections between these two modal functions. An argument is advanced regarding the inevitability of employing analogical (or elementary basic concepts, and this perspective is articulated in terms of the theory of modal aspects. Numerical and spatial terms are discussed and eventually focused on a deepened understanding of the meaning of infinity. In addition to a brief look at the circularity present in the arithmeticist claim that mathematics could be fully arithmetised (Grünbaum, attention is also asked for the agreement between Aristotle and Cantor regarding the nature of continuity – assessed in terms of the irreducibility of the numerical and spatial aspects of reality. Finally a characterisation is given of the ontological assumpt-ions of intuitionism and axiomatic formalism.

  2. Principles of mathematical modeling

    CERN Document Server

    Dym, Clive

    2004-01-01

    Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...

  3. Mathematics Competency and Situational Mathematics Anxiety: What are the Links and How Do These Links Affect Teacher Education Programs?

    Science.gov (United States)

    Cooke, Audrey; Hurst, Chris

    2012-01-01

    The issue of mathematics anxiety and its possible links to mathematical competence have long been of concern to mathematics educators, particularly with the potential of the effects of mathematics anxiety to be transmitted from teacher to student. Hence it is in the interests of teacher educators to understand the nature of mathematics anxiety and…

  4. Novice Mathematics Teachers Create Themselves

    Science.gov (United States)

    Schatz Oppenheimer, Orna; Dvir, Nurit

    2018-01-01

    This study presents a qualitative research based on three narratives written by novice mathematics teachers. We examine their unique professional world during their first year of work. The methodology of narrative framework, on which this article is based, helps to gain better understanding of the need for novice mathematics teachers to have…

  5. Mathematization in introductory physics

    Science.gov (United States)

    Brahmia, Suzanne M.

    Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in

  6. Understanding early serum hepatitis D virus and hepatitis B surface antigen kinetics during pegylated interferon-alpha therapy via mathematical modeling.

    Science.gov (United States)

    Guedj, Jeremie; Rotman, Yaron; Cotler, Scott J; Koh, Christopher; Schmid, Peter; Albrecht, Jeff; Haynes-Williams, Vanessa; Liang, T Jake; Hoofnagle, Jay H; Heller, Theo; Dahari, Harel

    2014-12-01

    There is little information on the early kinetics of hepatitis delta virus (HDV) and hepatitis B surface antigen (HBsAg) during interferon-α therapy. Here a mathematical model was developed and fitted to frequent HDV and HBsAg kinetic data from 10 patients during the first 28 weeks of pegylated-interferon-α2a (peg-IFN) therapy. Three patients achieved a complete virological response (CVR), defined as undetectable HDV 6 months after treatment stopped with loss of HBsAg and anti-HBsAg seroconversion. After initiation of therapy, a median delay of 9 days (interquartile range [IQR]: 5-15) was observed with no significant changes in HDV level. Thereafter, HDV declined in a biphasic manner, where a rapid first phase lasting for 25 days (IQR: 23-58) was followed by a slower or plateau second phase. The model predicts that the main effect of peg-IFN is to reduce HDV production/release with a median effectiveness of 96% (IQR: 93-99.8). Median serum HDV half-life (t1/2 ) was estimated as 2.9 days (IQR: 1.5-5.3) corresponding to a pretreatment production and clearance of about 10(10) (IQR: 10(9.7) -10(10.7) ) virions/day. None of the patients with flat second phase in HDV achieved CVR. HBsAg kinetics of decline paralleled the second phase of HDV decline consistent with HBsAg-productive-infected cells being the main source of production of HDV, with a median t1/2 of 135 days (IQR: 20-460). The interferon lambda-3 polymorphism (rs12979860) was not associated with kinetic parameters. Modeling results provide insights into HDV-host dynamics, the relationship between serum HBsAg levels and HBsAg-infected cells, IFN's mode of action, and its effectiveness. The observation that a flat second phase in HDV and HBsAg kinetics was associated with failure to achieve CVR provides the basis to develop early stopping rules during peg-IFN treatment in HDV-infected patients. © 2014 by the American Association for the Study of Liver Diseases. This article has been contributed to by U

  7. Vision in elementary mathematics

    CERN Document Server

    Sawyer, W W

    2003-01-01

    Sure-fire techniques of visualizing, dramatizing, and analyzing numbers promise to attract and retain students' attention and understanding. Topics include basic multiplication and division, algebra, word problems, graphs, negative numbers, fractions, many other practical applications of elementary mathematics. 1964 ed. Answers to Problems.

  8. Persian architecture and mathematics

    CERN Document Server

    2012-01-01

    This volulme features eight original papers dedicated to the theme “Persian Architecture and Mathematics,” guest edited by Reza Sarhangi. All papers were approved through a rigorous process of blind peer review and edited by an interdisciplinary scientific editorial committee. Topics range from symmetry in ancient Persian architecture to the elaborate geometric patterns and complex three-dimensional structures of standing monuments of historical periods, from the expression of mathematical ideas to architectonic structures, and from decorative ornament to the representation of modern group theory and quasi-crystalline patterns. The articles discuss unique monuments Persia, including domed structures and two-dimensional patterns, which have received significant scholarly attention in recent years. This book is a unique contribution to studies of Persian architecture in relation to mathematics.

  9. Mathematical olympiad challenges

    CERN Document Server

    Andreescu, Titu

    2000-01-01

    Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals. An important feature of the work is the comprehensive background material provided with each grouping of problems. The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-e...

  10. Mathematical omnibus thirty lectures on classic mathematics

    CERN Document Server

    Fuchs, Dmitry; Fuchs, Dmitry

    2007-01-01

    The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

  11. 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

  12. 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

  13. Relationship between Mathematics Anxiety and Mathematics ...

    African Journals Online (AJOL)

    Relationship between Mathematics Anxiety and Mathematics Achievement of Junior Secondary School Students in Maiduguri Metropolis, Borno State, Nigeria. ... Journal of Educational Foundations ... Fear of failure in mathematics test and examination was the main reason why students were anxious of mathematics.

  14. [Mathematics - astronomy - astrology special library].

    Science.gov (United States)

    Gluch, Sibylle

    2011-01-01

    About 1560 Elector August of Saxony created an unusual library--one distinguished within its period by both its specialization and location. Situated within the Kunstkammer this library was mostly dedicated to the mathematical sciences and related disciplines. It contained works by the most important authors on mathematics, astronomy, and astrology from the classical, medieval, and early modern periods. This essay traces the formation and composition of August's library, and examines its function: What kind of relationship existed between the library and the Kunstkammer? In what way did the library mirror the interests of the Elector, and to what extend does it permit inferences regarding the Elector's knowledge of mathematics? From the analysis August emerges not as a specialist with a deep understanding of mathematics, but as a particular aficionado of mathematical applications. As a practitioner and general follower of the mathematical arts he took part in a far-reaching intellectual network the center of which lay in the University of Wittenberg. Here, Melanchthon had effectively strengthened the importance of the mathematical disciplines within the university curriculum. He regarded mathematics as the foremost science, arguing that before all other disciplines its method enabled man to recognize the harmonic order of the world, and to discern divine providence. Thus, mathematics offered consoling stability and support in an often seemingly chaotic world torn by religious controversies. This kind of esteem for the mathematical sciences did not presuppose expert knowledge. Hence, the fact that August does not appear to have read the mathematical books he collected does not come as a contradiction. On the contrary, for August it sufficed to recognize the potential of the mathematical sciences, which he brought into life through the creation of a specialized library that developed a rhetoric of its own. The collection of his Kunstkammer library spoke of a

  15. Machine Learning via Mathematical Programming

    National Research Council Canada - National Science Library

    Mamgasarian, Olivi

    1999-01-01

    Mathematical programming approaches were applied to a variety of problems in machine learning in order to gain deeper understanding of the problems and to come up with new and more efficient computational algorithms...

  16. Mathematical physiology

    CERN Document Server

    Sneyd, James

    2009-01-01

    There has been a long history of interaction between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context. In this second edition the coverage of basic principles has been expanded to include such topics as stochastic differential equations, Markov models and Gibbs free energy, and the selection of models has also been expanded to include some of the basic models of fluid transport, respiration/perfusion, blood diseases, molecular motors, smooth muscle, neuroendrocine cells, the baroreceptor loop, turboglomerular oscillations, blood clotting and the retina. Owing to this extensive coverage, the second edition is published in two volumes. ...

  17. Mathematics Connection

    African Journals Online (AJOL)

    The language barrier education in Africa: The challenge of learning and teaching mathematics in a second language · EMAIL FULL TEXT EMAIL FULL TEXT DOWNLOAD FULL TEXT DOWNLOAD FULL TEXT. J Ibe, K Ekpo, O Akpan, UE Uyoata ...

  18. 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.

  19. 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.

  20. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2010-01-01

    The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...

  1. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2010-01-01

    The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...

  2. Mathematics revealed

    CERN Document Server

    Berman, Elizabeth

    1979-01-01

    Mathematics Revealed focuses on the principles, processes, operations, and exercises in mathematics.The book first offers information on whole numbers, fractions, and decimals and percents. Discussions focus on measuring length, percent, decimals, numbers as products, addition and subtraction of fractions, mixed numbers and ratios, division of fractions, addition, subtraction, multiplication, and division. The text then examines positive and negative numbers and powers and computation. Topics include division and averages, multiplication, ratios, and measurements, scientific notation and estim

  3. Mathematical statistics

    CERN Document Server

    Pestman, Wiebe R

    2009-01-01

    This textbook provides a broad and solid introduction to mathematical statistics, including the classical subjects hypothesis testing, normal regression analysis, and normal analysis of variance. In addition, non-parametric statistics and vectorial statistics are considered, as well as applications of stochastic analysis in modern statistics, e.g., Kolmogorov-Smirnov testing, smoothing techniques, robustness and density estimation. For students with some elementary mathematical background. With many exercises. Prerequisites from measure theory and linear algebra are presented.

  4. Mathematical foundation for computer science

    CERN Document Server

    Vashanti, M

    2013-01-01

    "Mathematical Foundation For Computer Science", a textbook covers mathematical logic, Normal Forms, Graphs, Trees and Relations. The emphasis in the book is on the presentation of fundamentals and theoretical concepts in an intelligible and easy to understand manner. Every topic is illustrated with a number of problems of increasing complexities which will help the beginner understand the fundamentals involved and enable them to solve various problems.

  5. Significance of Learner's Externalization and Argumentation in Research on Mathematics Education : Based on epistemology of mathematics and epistemology in mathematics education

    OpenAIRE

    松島, 充

    2013-01-01

    The purposes of this study are to investigate relation between externalization by oral language and understanding in mathematics education, and to clarify epistemology in mathematics education whichhas deep relation in a Jigsaw method. Method of this study is literature study on epistemology. Epistemology of mathematics and epistemology in mathematics education are analyzed from the standpoints of the relation between externalization by oral language and understanding in mathematics education...

  6. Mathematics for physicists

    CERN Document Server

    Dennery, Philippe

    1967-01-01

    ""A fine example of how to present 'classical' physical mathematics."" - American ScientistWritten for advanced undergraduate and graduate students, this volume provides a thorough background in the mathematics needed to understand today's more advanced topics in physics and engineering. Without sacrificing rigor, the authors develop the theoretical material at length, in a highly readable, and, wherever possible, in an intuitive manner. Each abstract idea is accompanied by a very simple, concrete example, showing the student that the abstraction is merely a generalization from easily understo

  7. Mathematical modelling of metabolism

    DEFF Research Database (Denmark)

    Gombert, Andreas Karoly; Nielsen, Jens

    2000-01-01

    Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....

  8. Understanding the Use and Impact of Social Media Features on the Educational Experiences of Higher-Education Students in Blended and Distance-Learning Environments

    Science.gov (United States)

    Scialdone, Michael John

    2014-01-01

    Students are increasingly expecting social media to be a component of their educational experiences both outside and inside of the classroom. The phenomenon of interest in this dissertation is understanding how the educational experiences of students are affected when social media are incorporated into online and blended course activities.…

  9. Response to Nieminen et al.'s Feature Article on Executive Coaching and Facilitated Multisource Feedback: Toward Better Understanding of a Growing HRD Practice

    Science.gov (United States)

    Egan, Toby

    2013-01-01

    Executive coaching is a booming, but understudied, HRD-related practice. Given the limited number of available studies that have been deployed with rigor and systematic methods, the study by Nieminen et al. adds to our understanding of the impact of executive coaching and multisource feedback on leadership development. Explored in the context of a…

  10. Fostering Mathematical Reflective Abilities through High School Teaching Activities

    Science.gov (United States)

    Zhang, Dingqiang; Zhao, Hongyuan; Yang, Hong

    2009-01-01

    The reflective ability in mathematics is a highly individual mental process, which is engaged in the course of certain types of mathematics activity. This article describes the basic meaning, characteristics, and developmental features of reflectivity in mathematics. It is suggested that reflective ability in mathematics and its relations with…

  11. Reading--Study Skills in Mathematics.

    Science.gov (United States)

    Devine, Thomas G.

    Some general suggestions for the teaching of mathematics study skills are provided in this paper. The suggestions offered are as follows: (1) teach the specialized mathematical vocabulary directly, (2) show students how the mathematical symbol system works, (3) give practice in understanding graphics, (4) give practice in spotting unstated…

  12. Why Do Spatial Abilities Predict Mathematical Performance?

    Science.gov (United States)

    Tosto, Maria Grazia; Hanscombe, Ken B.; Haworth, Claire M. A.; Davis, Oliver S. P.; Petrill, Stephen A.; Dale, Philip S.; Malykh, Sergey; Plomin, Robert; Kovas, Yulia

    2014-01-01

    Spatial ability predicts performance in mathematics and eventual expertise in science, technology and engineering. Spatial skills have also been shown to rely on neuronal networks partially shared with mathematics. Understanding the nature of this association can inform educational practices and intervention for mathematical underperformance.…

  13. Nine Actions to Build Students' Mathematics Abilities

    Science.gov (United States)

    Barger, Kenna

    2010-01-01

    The author was asked to develop a list of actions that teachers could take to build students' mathematics abilities. Too many students fail to graduate and fail to pass state assessments as a result of weak mathematics skills. Even many students who do graduate leave high school lacking sufficient understanding of mathematics to pass college…

  14. Missing the Promise of Mathematical Modeling

    Science.gov (United States)

    Meyer, Dan

    2015-01-01

    The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…

  15. Research mathematicians’ practices in selecting mathematical problems

    DEFF Research Database (Denmark)

    Misfeldt, Morten; Johansen, Mikkel Willum

    2015-01-01

    Developing abilities to create, inquire into, qualify, and choose among mathematical problems is an important educational goal. In this paper, we elucidate how mathematicians work with mathematical problems in order to understand this mathematical process. More specifically, we investigate how ma...... in problem solving and students’ conceptions of solvability and relevance of or interest in a mathematical problem are areas of research suggested by our study.......Developing abilities to create, inquire into, qualify, and choose among mathematical problems is an important educational goal. In this paper, we elucidate how mathematicians work with mathematical problems in order to understand this mathematical process. More specifically, we investigate how...... and suggest that mathematics education research could further investigate how students select and develop problems, work with multiple problems over a longer period of time, and use the solutions to problems to support the development of new problems. Furthermore, the negative emotional aspects of being stuck...

  16. Mathematics for sustainability

    CERN Document Server

    Roe, John; Jamshidi, Sara

    2018-01-01

    Designed for the 21st century classroom, this textbook poses, refines, and analyzes questions of sustainability in a quantitative environment. Building mathematical knowledge in the context of issues relevant to every global citizen today, this text takes an approach that empowers students of all disciplines to understand and reason with quantitative information. Whatever conclusions may be reached on a given topic, this book will prepare the reader to think critically about their own and other people’s arguments and to support them with careful, mathematical reasoning. Topics are grouped in themes of measurement, flow, connectivity, change, risk, and decision-making. Mathematical thinking is at the fore throughout, as students learn to model sustainability on local, regional, and global scales. Exercises emphasize concepts, while projects build and challenge communication skills. With no prerequisites beyond high school algebra, instructors will find this book a rich resource for engaging all majors in the...

  17. Basic mathematics for biochemists

    CERN Document Server

    Cornish-Bowden, Athel

    1981-01-01

    Some teachers of biochemistry think it positively beneficial for students to struggle with difficult mathematics. I do not number myself among these people, although I have derived much personal pleasure from the study of mathematics and from applying it to problems that interest me in biochemistry. On the contrary, I think that students choose courses in biochemistry out of interest in biochemistry and that they should not be encumbered with more mathematics than is absolutely required for a proper understanding of biochemistry. This of course includes physical chemistry, because a biochemist ignorant of physical chemistry is no biochemist. I have been guided by these beliefs in writing this book. I have laid heavy emphasis on those topics, such as the use of logarithms, that play an important role in biochemistry and often cause problems in teaching; I have ignored others, such as trigonometry, that one can manage without. The proper treatment of statistics has been more difficult to decide. Although it cle...

  18. Mathematics and Computation in Music

    DEFF Research Database (Denmark)

    The 5th Biennial International Conference for Mathematics and Computation in Music (MCM 2015) took place June 22–25, 2015, at Queen Mary University of London, UK, co-hosted by the School of Electronic Engineering and Computer Science (Centre for Digital Music) and the School of Mathematical...... Sciences. As the flagship conference of the Society for Mathematics and Computation in Music (SMCM), MCM 2015 provided a dedicated platform for the communication and exchange of ideas among researchers in mathematics, informatics, music theory, composition, musicology, and related disciplines. It brought...... together researchers from around the world who combine mathematics or computation with music theory, music analysis, composition, and performance. This year’s program – full details at http://mcm2015.qmul.ac.uk – featured a number of distinguished keynote speakers, including Andrée Ehresmann (who spoke...

  19. DOE Fundamentals Handbook: Mathematics, Volume 1

    International Nuclear Information System (INIS)

    1992-06-01

    The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations

  20. DOE Fundamentals Handbook: Mathematics, Volume 2

    Energy Technology Data Exchange (ETDEWEB)

    1992-06-01

    The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations.

  1. DOE Fundamentals Handbook: Mathematics, Volume 2

    International Nuclear Information System (INIS)

    1992-06-01

    The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations

  2. Mathematics for Parents: Facilitating Parents' and Children's Understanding in Mathematics.

    Science.gov (United States)

    Civil, Marta; Guevara, Cristi; Allexsaht-Snider, Martha

    The study examines ethnically and linguistically diverse parents' learning in an eight-week Math for Parents course on fractions, decimals and percentages. Analysis of classroom observations, interviews, focus groups, written feedback, videotapes, and task-based/clinical interviews provided rich data yielding findings about both parents' affective…

  3. How to read historical mathematics

    CERN Document Server

    Wardbaugh, Benjamin

    2010-01-01

    Writings by early mathematicians feature language and notations that are quite different from what we're familiar with today. Sourcebooks on the history of mathematics provide some guidance, but what has been lacking is a guide tailored to the needs of readers approaching these writings for the first time. How to Read Historical Mathematics fills this gap by introducing readers to the analytical questions historians ask when deciphering historical texts. Sampling actual writings from the history of mathematics, Benjamin Wardhaugh reveals the questions that will unlock the meaning and significa

  4. Physical mathematics

    CERN Document Server

    Cahill, Kevin

    2013-01-01

    Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.

  5. Mathematical tapas

    CERN Document Server

    Hiriart-Urruty, Jean-Baptiste

    This book contains a collection of exercises (called “tapas”) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved. The author provides some hints and (partial) answers and also puts these carefully chosen exercises into context, presents information on their origins, and comments on possible extensions. With stars marking the levels of difficulty, these tapas show or prove something interesting, challenge the reader to solve and learn, and may have surprising results. This first volume of Mathematical Tapas will appeal to mathematicians, motivated undergraduate students from science-based areas, and those generally interested in mathematics.

  6. Mathematics university teachers' perception of pedagogical content knowledge (PCK)

    Science.gov (United States)

    Khakbaz, Azimehsadat

    2016-02-01

    Teaching mathematics in university levels is one of the most important fields of research in the area of mathematics education. Nevertheless, there is little information about teaching knowledge of mathematics university teachers. Pedagogical content knowledge (PCK) provides a suitable framework to study knowledge of teachers. The purpose of this paper is to make explicit the perception of mathematics university teachers about PCK. For this purpose, a phenomenological study was done. Data resources included semi-structured interviews with 10 mathematics university teachers who were in different places of the mathematics university teaching experience spectrum. Data analysis indicated a model consisting of four cognitive themes which are mathematics syntactic knowledge, knowledge about mathematics curriculum planning, knowledge about students' mathematics learning and knowledge about creating an influential mathematics teaching-learning environment. Besides, it was found out that three contextual themes influenced on PCK for teaching mathematics in university levels which were the nature of mathematics subjects, university teachers' features and terms of learning environment.

  7. Mathematical Lives

    CERN Document Server

    Bartocci, Claudio; Guerraggio, Angelo; Lucchetti, Roberto; Williams, Kim

    2011-01-01

    Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the soci

  8. Mathematical papers

    CERN Document Server

    Green, George

    2005-01-01

    An almost entirely self-taught mathematical genius, George Green (1793 -1841) is best known for Green's theorem, which is used in almost all computer codes that solve partial differential equations. He also published influential essays, or papers, in the fields of hydrodynamics, electricity, and magnetism. This collection comprises his most significant works.The first paper, ""An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism,"" which is also the longest and perhaps the most Important, appeared In 1828. It introduced the term potential as desig

  9. 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....... Having completed this the student is able to carry out the following: Expressions and sets: Define a set; define a logic expression; negate a logic expression; combine logic expressions; construct a truth table for a logic expression; apply reduction rules for logic expressions. Apply these concepts...

  10. Motivated Mathematics

    OpenAIRE

    Aubin, J.-P.

    1983-01-01

    Mathematics seems to be treated at IIASA as if it were some sort of shameful disease, carefully hidden away in departments labelled with trendy but unrevealing names. Any debate about the role of mathematics and mathematicians at IIASA appears fated to be confused by the introduction of many seemingly unrelated issues, by the fact that many of the protagonists have their own vested interests to protect, and by the fact--why not admit it--that there are many dark fears of the more "esoteric" s...

  11. Mathematics for common entrance three (extension) answers

    CERN Document Server

    Alexander, Serena

    2015-01-01

    This book contains answers to all exercises featured in the accompanying textbook Mathematics for Common Entrance Three (Extension) , which provides essential preparation for Level 3 of the ISEB 13+ Mathematics exam, as well as for CASE and other scholarship exams. - Clean, clear layout for easy marking. - Includes examples of high-scoring answers with diagrams and workings. Also available to purchase from the Galore Park website www.galorepark.co.uk :. - Mathematics for Common Entrance Three (Extension). - Mathematics for Common Entrance One. - Mathematics for Common Entrance One Answers. - M

  12. Mathematical stereochemistry

    CERN Document Server

    Fujita, Shinsaku

    2015-01-01

    Chirality and stereogenicity are closely related concepts and their differentiation and description is still a challenge in chemoinformatics. A new stereoisogram approach, developed by the author, is introduced in this book, providing a theoretical framework for mathematical aspects of modern stereochemistry. The discussion covers point-groups and permutation symmetry and exemplifies the concepts using organic molecules and inorganic complexes.

  13. Mathematical quantization

    CERN Document Server

    Weaver, Nik

    2001-01-01

    With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a variety of topics.Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set correspond to operators on a Hilbert space, one can determine quantum analogs of a variety of classical structures. In particular, because topologies and measure classes on a set can be treated in terms of scalar-valued functions, we can transfer these constructions to the quantum realm, giving rise to C*- and von Neumann algebras.In the first half of the book, the author quickly builds the operator algebra setting. He uses this ...

  14. Outdoor Mathematics

    Science.gov (United States)

    Kennard, Jackie

    2007-01-01

    One of the most interesting developments in teaching has been the growing importance of the outdoor environment. Whether it be playground, garden or field, the outdoors offers a range of challenging experiences, especially in the delivery of early mathematics. Oral feedback to parents, together with photographic displays, can show them that…

  15. The Featurization of Journalism

    OpenAIRE

    Steensen, Steen

    2011-01-01

    Feature journalism has developed from being an insignificant supplement to news journalism to a family of genres that today dominates newspapers. The present article explores the growing importance of feature journalism and attempts to understand its social function, how it has changed and why it has become so important. Based on an analysis of influential textbooks on feature journalism, the paper argues that feature journalism has traditionally been dominated by a literary d...

  16. 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...

  17. 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.

  18. Psychology's Role in Mathematics and Science Education

    Science.gov (United States)

    Newcombe, Nora S.; Ambady, Nalini; Eccles, Jacquelynne; Gomez, Louis; Klahr, David; Linn, Marcia; Miller, Kevin; Mix, Kelly

    2009-01-01

    Improving mathematics and science education in the United States has been a matter of national concern for over half a century. Psychology has a vital role to play in this enterprise. In this article, the authors review the kinds of contributions that psychology can make in four areas: (a) early understanding of mathematics, (b) understanding of…

  19. An analysis of the black crusts from the Seville Cathedral: A challenge to deepen the understanding of the relationships among microstructure, microchemical features and pollution sources

    Energy Technology Data Exchange (ETDEWEB)

    Ruffolo, Silvestro A., E-mail: silvestro.ruffolo@unical.it [Università della Calabria, Dipartimento di Biologia, Ecologia e Scienze della Terra (DiBEST), Via Pietro Bucci 87036, Arcavacata di Rende, CS (Italy); Comite, Valeria [Università della Calabria, Dipartimento di Biologia, Ecologia e Scienze della Terra (DiBEST), Via Pietro Bucci 87036, Arcavacata di Rende, CS (Italy); Dipartimento di Scienze Biologiche, Geologiche e Ambientali–Sezione di Scienze della Terra, Università di Catania, Corso Italia 57, 95129 Catania (Italy); La Russa, Mauro F. [Università della Calabria, Dipartimento di Biologia, Ecologia e Scienze della Terra (DiBEST), Via Pietro Bucci 87036, Arcavacata di Rende, CS (Italy); Belfiore, Cristina M. [Università della Calabria, Dipartimento di Biologia, Ecologia e Scienze della Terra (DiBEST), Via Pietro Bucci 87036, Arcavacata di Rende, CS (Italy); Dipartimento di Scienze Biologiche, Geologiche e Ambientali–Sezione di Scienze della Terra, Università di Catania, Corso Italia 57, 95129 Catania (Italy); Barca, Donatella [Università della Calabria, Dipartimento di Biologia, Ecologia e Scienze della Terra (DiBEST), Via Pietro Bucci 87036, Arcavacata di Rende, CS (Italy); Bonazza, Alessandra [Istituto di Scienze dell' Atmosfera e del Clima, ISAC-CNR, Via Gobetti 101, 40129 Bologna (Italy); Crisci, Gino M. [Università della Calabria, Dipartimento di Biologia, Ecologia e Scienze della Terra (DiBEST), Via Pietro Bucci 87036, Arcavacata di Rende, CS (Italy); Pezzino, Antonino [Dipartimento di Scienze Biologiche, Geologiche e Ambientali–Sezione di Scienze della Terra, Università di Catania, Corso Italia 57, 95129 Catania (Italy); and others

    2015-01-01

    The Cathedral of Seville is one of the most important buildings in the whole of southern Spain. It suffers, like most of the historical buildings located in urban environments, from several degradation phenomena related to the high pollution level. Undoubtedly, the formation of black crusts plays a crucial role in the decay of the stone materials belonging to the church. Their formation occurs mainly on carbonate building materials, whose interaction with a sulfur oxide-enriched atmosphere leads to the transformation of calcium carbonate (calcite) into calcium sulfate dihydrate (gypsum) which, together with embedded carbonaceous particles, forms the black crusts on the stone surface. To better understand the composition and the formation dynamics of this degradation product and to identify the pollutant sources and evaluate their impact on the stone material, an analytical study was carried out on the black crust samples collected from different areas of the building. For a complete characterization of the black crusts, several techniques were used, including laser ablation inductively coupled plasma mass spectrometry, Fourier transform infrared spectroscopy, micro infrared spectroscopy, optical and scanning electron microscopy. This battery of tests provided information about the nature and distribution of the mineralogical phases and the elements within the crusts and the crust-substrate interface, contributing to the identification of the major pollution sources responsible for the deterioration of the monument over time. In addition, the results revealed a relation among the height of sampling, the surface exposure and the concentration of heavy metals. Finally, information has been provided about the origin of the concentration gradients of some metals. - Highlights: • Black crusts from the Cathedral of Seville have been studied. • The impact of the pollution on the Cathedral of Seville has been assessed. • A geochemical study has been performed on black

  20. Mathematical Investigations in the Reviewed Basic School Curriculum

    African Journals Online (AJOL)

    Mathematics teachers are called upon to use innovative teaching methods capable of developing mathematical understanding, inquiry, problem solving skills, and interest in children. This paper examines the role of investigations in the child's mathematical development. It looks at the nature of mathematical investigations ...

  1. The Language of Mathematics: The Importance of Teaching and Learning Mathematical Vocabulary

    Science.gov (United States)

    Riccomini, Paul J.; Smith, Gregory W.; Hughes, Elizabeth M.; Fries, Karen M.

    2015-01-01

    Vocabulary understanding is a major contributor to overall comprehension in many content areas, including mathematics. Effective methods for teaching vocabulary in all content areas are diverse and long standing. Teaching and learning the language of mathematics is vital for the development of mathematical proficiency. Students' mathematical…

  2. Science and Mathematics in Astronomy

    Science.gov (United States)

    Woolack, Edward

    2009-01-01

    A brief historical introduction to the development of observational astronomy will be presented. The close historical relationship between the successful application of mathematical concepts and advances in astronomy will be presented. A variety of simple physical demonstrations, hands-on group activities, and puzzles will be used to understand how the properties of light can be used to understand the contents of our universe.

  3. 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.

  4. Written feedback to mathematics homework

    OpenAIRE

    Žitko, Urša

    2017-01-01

    This diploma thesis is about teachers’ feedback to students’ mathematics homework. In the theoretical part I present the purpose and history of homework assignments as well as various classifications of types of homework. In general, homework assignments are intended for students to learn and refresh the subject matter they have learnt in class, to gain further understanding, to practice various mathematical processes, and to prepare the student for a forthcoming subject matter. By doing home...

  5. Applied mathematics

    International Nuclear Information System (INIS)

    Nedelec, J.C.

    1988-01-01

    The 1988 progress report of the Applied Mathematics center (Polytechnic School, France), is presented. The research fields of the Center are the scientific calculus, the probabilities and statistics and the video image synthesis. The research topics developed are: the analysis of numerical methods, the mathematical analysis of the physics and mechanics fundamental models, the numerical solution of complex models related to the industrial problems, the stochastic calculus and the brownian movement, the stochastic partial differential equations, the identification of the adaptive filtering parameters, the discrete element systems, statistics, the stochastic control and the development, the image synthesis techniques for education and research programs. The published papers, the congress communications and the thesis are listed [fr

  6. Mathematical epidemiology

    CERN Document Server

    Driessche, Pauline; Wu, Jianhong

    2008-01-01

    Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downlo...

  7. Greek or Not: The Use of Symbols and Abbreviations in Mathematics

    Science.gov (United States)

    Quinnell, Lorna; Carter, Merilyn

    2012-01-01

    The language of mathematics is unique and complex. One feature of the mathematical register is the use of symbols and abbreviations. Whilst it may be possible for a student to think mathematically in the absence of symbols, the written communication of mathematical ideas cannot be achieved concisely without the use of mathematical symbols.…

  8. A readable introduction to real mathematics

    CERN Document Server

    Rosenthal, Daniel; Rosenthal, Peter

    2014-01-01

    Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. Topics covered include: * mathematical induction * modular arithmetic * the fundamental theorem of arithmetic * Fermat's little theorem * RSA encryption * the Euclidean algorithm * rational and irrational numbers * complex numbers * cardinality * Euclidean pl...

  9. A mathematics sampler topics for the liberal arts

    CERN Document Server

    Berlinghoff, William P; Skrien, Dale

    2001-01-01

    Now in its fifth edition, A Mathematics Sampler presents mathematics as both science and art, focusing on the historical role of mathematics in our culture. It uses selected topics from modern mathematics-including computers, perfect numbers, and four-dimensional geometry-to exemplify the distinctive features of mathematics as an intellectual endeavor, a problem-solving tool, and a way of thinking about the rapidly changing world in which we live. A Mathematics Sampler also includes unique LINK sections throughout the book, each of which connects mathematical concepts with areas of interest th

  10. 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…

  11. Listening to their voices: Exploring mathematics-science identity development of African American males in an urban school community

    Science.gov (United States)

    Wilson, Kimi Leemar

    National data continues to show an underrepresentation of African American males pursuing science, technology, engineering and mathematics (STEM) majors, careers and professions in the United States. Whites and Asian Americans are continuously positioned as the face of STEM education and participation. And while research has provided ways to support mathematics and science learning for African American males, there still remains a gap in understanding how their formed mathematics-science identities in K-12 public schooling influences STEM participation. The research undertaken in this study explores this gap, and uses an integrative identity framework to understand mathematics-science identity development which goes beyond personal identity, and explores the relational, collective and material components of identity. Specifically, this research seeks to answer the following research questions: What are the shared lived experiences that exist between a group of African American male students developing a mathematics-science identity, and how these shared lived experiences shape their mathematics-science identity development? Therefore, by analyzing African American males lived experiences employing an integrative identity framework fosters a greater understanding of how mathematics-science identity is formed in K-12 public schools, which impacts STEM education and participation. The high school aged youth featured in this study consist of four African American males, who live in a moderate size city in California. Data for this study consists of observations, phenomenological interviews, and policy document analysis that took place over six months. Data has been analyzed to describe and interpret the young men's mathematics and science experiences, as revealed in their K-12 public school education. This inquiry sought to make meaning of how African American males experience mathematics and science teaching and learning within K-12 public schooling and how these

  12. Mathematical paradigms of climate science

    CERN Document Server

    Cannarsa, Piermarco; Jones, Christopher; Portaluri, Alessandro

    2016-01-01

    This book, featuring a truly interdisciplinary approach, provides an overview of cutting-edge mathematical theories and techniques that promise to play a central role in climate science. It brings together some of the most interesting overview lectures given by the invited speakers at an important workshop held in Rome in 2013 as a part of MPE2013 (“Mathematics of Planet Earth 2013”). The aim of the workshop was to foster the interaction between climate scientists and mathematicians active in various fields linked to climate sciences, such as dynamical systems, partial differential equations, control theory, stochastic systems, and numerical analysis. Mathematics and statistics already play a central role in this area. Likewise, computer science must have a say in the efforts to simulate the Earth’s environment on the unprecedented scale of petabytes. In the context of such complexity, new mathematical tools are needed to organize and simplify the approach. The growing importance of data assimilation te...

  13. Mathematical modelling of scour: A review

    DEFF Research Database (Denmark)

    Sumer, B. Mutlu

    2007-01-01

    A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers...

  14. Challenging mathematical problems with elementary solutions

    CERN Document Server

    Yaglom, A M

    1987-01-01

    Volume I of a two-part series, this book features a broad spectrum of 100 challenging problems related to probability theory and combinatorial analysis. The problems, most of which can be solved with elementary mathematics, range from relatively simple to extremely difficult. Suitable for students, teachers, and any lover of mathematics. Complete solutions.

  15. Using statistics to understand the environment

    CERN Document Server

    Cook, Penny A

    2000-01-01

    Using Statistics to Understand the Environment covers all the basic tests required for environmental practicals and projects and points the way to the more advanced techniques that may be needed in more complex research designs. Following an introduction to project design, the book covers methods to describe data, to examine differences between samples, and to identify relationships and associations between variables.Featuring: worked examples covering a wide range of environmental topics, drawings and icons, chapter summaries, a glossary of statistical terms and a further reading section, this book focuses on the needs of the researcher rather than on the mathematics behind the tests.

  16. 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'…

  17. 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…

  18. 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…

  19. Fundamentals of modern mathematics a practical review

    CERN Document Server

    MacNeil, David B

    2013-01-01

    Students and others wishing to know more about the practical side of mathematics will find this volume a highly informative resource. Accessible explanations of important concepts feature worked examples and diagrams. 1963 edition.

  20. Research in collegiate mathematics education VI

    CERN Document Server

    Selden, Annie; Harel, Guershon; Hauk, Shandy

    2006-01-01

    The sixth volume of Research in Collegiate Mathematics Education presents state-of-the-art research on understanding, teaching, and learning mathematics at the postsecondary level. The articles advance our understanding of collegiate mathematics education while being readable by a wide audience of mathematicians interested in issues affecting their own students. This is a collection of useful and informative research regarding the ways our students think about and learn mathematics. The volume opens with studies on students' experiences with calculus reform and on the effects of concept-based

  1. Understanding physics

    CERN Document Server

    Cassidy, David; Rutherford, James

    2002-01-01

    Understanding Physics provides a thorough grounding in contemporary physics while placing physics into its social and historical context Based in large part on the highly respected Project Physics Course developed by two of the authors, it also integrates the results of recent pedagogical research The text thus - teaches about the basic phenomena in the physical world and the concepts developed to explain them - shows that science is a rational human endeavor with a long and continuing tradition, involving many different cultures and people - develops facility in critical thinking, reasoned argumentation, evaluation of evidence, mathematical modeling, and ethical values The treatment emphasizes not only what we know but also how we know it, why we believe it, and what effects that knowledge has - Why do we believe the Earth and planets revolve around the Sun? - Why do we believe that matter is made of atoms? - How do relativity theory and quantum mechanics alter our conception of Nature and in what ways do th...

  2. 11th Biennial Conference on Emerging Mathematical Methods, Models and Algorithms for Science and Technology

    CERN Document Server

    Manchanda, Pammy; Bhardwaj, Rashmi

    2015-01-01

    The present volume contains invited talks of 11th biennial conference on “Emerging Mathematical Methods, Models and Algorithms for Science and Technology”. The main message of the book is that mathematics has a great potential to analyse and understand the challenging problems of nanotechnology, biotechnology, medical science, oil industry and financial technology. The book highlights all the features and main theme discussed in the conference. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world.

  3. Generalized dynamics of soft-matter quasicrystals mathematical models and solutions

    CERN Document Server

    Fan, Tian-You

    2017-01-01

    The book systematically introduces the mathematical models and solutions of generalized hydrodynamics of soft-matter quasicrystals (SMQ). It provides methods for solving the initial-boundary value problems in these systems. The solutions obtained demonstrate the distribution, deformation and motion of the soft-matter quasicrystals, and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. Mathematical solutions for solid and soft-matter quasicrystals are compared, to help readers to better understand the featured properties of SMQ.

  4. Symbolic feature detection for image understanding

    Science.gov (United States)

    Aslan, Sinem; Akgül, Ceyhun Burak; Sankur, Bülent

    2014-03-01

    In this study we propose a model-driven codebook generation method used to assign probability scores to pixels in order to represent underlying local shapes they reside in. In the first version of the symbol library we limited ourselves to photometric and similarity transformations applied on eight prototypical shapes of flat plateau , ramp, valley, ridge, circular and elliptic respectively pit and hill and used randomized decision forest as the statistical classifier to compute shape class ambiguity of each pixel. We achieved90% accuracy in identification of known objects from alternate views, however, we could not outperform texture, global and local shape methods, but only color-based method in recognition of unknown objects. We present a progress plan to be accomplished as a future work to improve the proposed approach further.

  5. Unexpected Expectations The Curiosities of a Mathematical Crystal Ball

    CERN Document Server

    Wapner, Leonard M

    2012-01-01

    Unexpected Expectations: The Curiosities of a Mathematical Crystal Ball explores how paradoxical challenges involving mathematical expectation often necessitate a reexamination of basic premises. The author takes you through mathematical paradoxes associated with seemingly straightforward applications of mathematical expectation and shows how these unexpected contradictions may push you to reconsider the legitimacy of the applications. The book requires only an understanding of basic algebraic operations and includes supplemental mathematical background in chapter appendices. After a history o

  6. The Impact of Technology on High School Mathematics Curriculum

    OpenAIRE

    Alacacı, Cengiz; McDonald, Gaby

    2014-01-01

    The infusion of technology into school mathematics has intensified in the last two decades. This article discusses the effects of this infusion on the mathematics curriculum. After a review of the different roles technology plays in mathematics and the diversity of the tools and their functions in teaching and learning mathematics, an epistemological perspective is offered to understand how technology could affect our cognition and perception while doing mathematics. With this background, spe...

  7. 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....

  8. Mathematical Rigor in Introductory Physics

    Science.gov (United States)

    Vandyke, Michael; Bassichis, William

    2011-10-01

    Calculus-based introductory physics courses intended for future engineers and physicists are often designed and taught in the same fashion as those intended for students of other disciplines. A more mathematically rigorous curriculum should be more appropriate and, ultimately, more beneficial for the student in his or her future coursework. This work investigates the effects of mathematical rigor on student understanding of introductory mechanics. Using a series of diagnostic tools in conjunction with individual student course performance, a statistical analysis will be performed to examine student learning of introductory mechanics and its relation to student understanding of the underlying calculus.

  9. The use of mathematical models in teaching wastewater treatment engineering

    DEFF Research Database (Denmark)

    Morgenroth, Eberhard Friedrich; Arvin, Erik; Vanrolleghem, P.

    2002-01-01

    Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models...

  10. Early predictors of high school mathematics achievement.

    Science.gov (United States)

    Siegler, Robert S; Duncan, Greg J; Davis-Kean, Pamela E; Duckworth, Kathryn; Claessens, Amy; Engel, Mimi; Susperreguy, Maria Ines; Chen, Meichu

    2012-07-01

    Identifying the types of mathematics content knowledge that are most predictive of students' long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students' knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that elementary school students' knowledge of fractions and of division uniquely predicts those students' knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education. Implications of these findings for understanding and improving mathematics learning are discussed.

  11. 9th International Congress on Mathematical Education

    CERN Document Server

    Hashimoto, Yoshihiko; Hodgson, Bernard; Lee, Peng; Lerman, Stephen; Sawada, Toshio

    2004-01-01

    Mathematics as a discipline has a long history, emerging from many cultures, with a truly universal character. Mathematicians throughout the world have a fundamentally common understanding of the nature of mathematics and of its central problems and methods. Research mathematicians in any part of the world are part of a cohesive intellectual community that communicates fluently. Mathematics education in contrast has a variable and culturally based character, and this is certainly true of educational organization and practice. Educational research is both an applied social science and a multidisciplinary domain of theoretical scholarship. Among organizations devoted to mathematics education, The International Commission on Mathematical Instruction (ICMI) is distinctive because of its close ties to the mathematics community. The great challenges now facing mathematics education around the world demand a deeper and more sensitive involvement of disciplinary mathematicians than we now have, both in the work of ed...

  12. The mathematics behind biological invasions

    CERN Document Server

    Lewis, Mark A; Potts, Jonathan R

    2016-01-01

    This book investigates the mathematical analysis of biological invasions. Unlike purely qualitative treatments of ecology, it draws on mathematical theory and methods, equipping the reader with sharp tools and rigorous methodology. Subjects include invasion dynamics, species interactions, population spread, long-distance dispersal, stochastic effects, risk analysis, and optimal responses to invaders. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes. Applications to real biological invasions are included throughout. Ultimately, the book imparts a powerful principle: that by bringing ecology and mathematics together, researchers can uncover new understanding of, and effective response strategies to, biological invasions. It is suitable for graduate students and established researchers in mathematical ecolo...

  13. The Language of Mathematics Utilizing Math in Practice

    CERN Document Server

    Baber, Robert L

    2011-01-01

    A new and unique way of understanding the translation of concepts and natural language into mathematical expressions Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process-not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and i

  14. 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)

  15. Core-Plus Mathematics. What Works Clearinghouse Intervention Report

    Science.gov (United States)

    What Works Clearinghouse, 2010

    2010-01-01

    "Core-Plus Mathematics" is a four-year curriculum that replaces the traditional sequence with courses that each feature interwoven strands of algebra and functions, statistics and probability, geometry and trigonometry, and discrete mathematics. The first three courses in the series provide a common core of broadly useful mathematics,…

  16. Teaching Teaching & Understanding Understanding

    DEFF Research Database (Denmark)

    2006-01-01

    "Teaching Teaching & Understanding Understanding" is a 19-minute award-winning short-film about teaching at university and higher-level educational institutions. It is based on the "Constructive Alignment" theory developed by Prof. John Biggs. The film delivers a foundation for understanding what...

  17. Mathematics++ selected topics beyond the basic courses

    CERN Document Server

    Kantor, Ida; Šámal, Robert

    2015-01-01

    Mathematics++ is a concise introduction to six selected areas of 20th century mathematics providing numerous modern mathematical tools used in contemporary research in computer science, engineering, and other fields. The areas are: measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, the authors introduce basic notions, examples, and results. The presentation is clear and accessible, stressing intuitive understanding, and it includes carefully selected exercises as an integral part. Theory is comp

  18. 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…

  19. Exploring mathematics problems prepares children to learn from instruction.

    Science.gov (United States)

    DeCaro, Marci S; Rittle-Johnson, Bethany

    2012-12-01

    Both exploration and explicit instruction are thought to benefit learning in many ways, but much less is known about how the two can be combined. We tested the hypothesis that engaging in exploratory activities prior to receiving explicit instruction better prepares children to learn from the instruction. Children (159 second- to fourth-grade students) solved relatively unfamiliar mathematics problems (e.g., 3+5=4+□) before or after they were instructed on the concept of mathematical equivalence. Exploring problems before instruction improved understanding compared with a more conventional "instruct-then-practice" sequence. Prompts to self-explain did not improve learning more than extra practice. Microgenetic analyses revealed that problem exploration led children to more accurately gauge their competence, attempt a larger variety of strategies, and attend more to problem features-better preparing them to learn from instruction. Copyright © 2012 Elsevier Inc. All rights reserved.

  20. FEATURE ARTICLES

    African Journals Online (AJOL)

    2008-06-01

    Jun 1, 2008 ... data or results in a novel application of methods developed in another field. The University of Ibadan, since 1968, as employed a medical statistician with background in mathematical statistics in its medical school and this has improved tremendously, the quality of medical research as collaboration ...

  1. AI and Mathematical Education

    Directory of Open Access Journals (Sweden)

    Angel Garrido

    2012-01-01

    Full Text Available From ancient times, the history of human beings has developed by a succession of steps and sometimes jumps, until reaching the relative sophistication of the modern brain and culture. Researchers are attempting to create systems that mimic human thinking, understand speech, or beat the best human chess player. Understanding the mechanisms of intelligence, and creating intelligent artifacts are the twin goals of Artificial Intelligence (AI. Great mathematical minds have played a key role in AI in recent years; to name only a few: Janos Neumann (also known as John von Neumann, Konrad Zuse, Norbert Wiener, Claude E. Shannon, Alan M. Turing, Grigore Moisil, Lofti A. Zadeh, Ronald R. Yager, Michio Sugeno, Solomon Marcus, or Lászlo A. Barabási. Introducing the study of AI is not merely useful because of its capability for solving difficult problems, but also because of its mathematical nature. It prepares us to understand the current world, enabling us to act on the challenges of the future.

  2. Mathematical methods of electromagnetic theory

    CERN Document Server

    Friedrichs, Kurt O

    2014-01-01

    This text provides a mathematically precise but intuitive introduction to classical electromagnetic theory and wave propagation, with a brief introduction to special relativity. While written in a distinctive, modern style, Friedrichs manages to convey the physical intuition and 19th century basis of the equations, with an emphasis on conservation laws. Particularly striking features of the book include: (a) a mathematically rigorous derivation of the interaction of electromagnetic waves with matter, (b) a straightforward explanation of how to use variational principles to solve problems in el

  3. Reassembling mathematical practices: a philosophical-anthropological approach

    Directory of Open Access Journals (Sweden)

    Karen François

    2016-01-01

    Full Text Available In this paper we first explore h ow Wittgenstein ’ s philosophy provides a conceptual tools to discuss the possibility of the simultaneous existence of culturally different mathematical practices. We will argue that Wittgenstein ’ s later work will be a fruitful framework to serve as a philosophical background to investigate ethnomathematics ( Wittgenstein 1973 . W e will give an overview of Wittgenstein’s later work which is referred to by many researchers in the field of ethnomathematics . The central philosophical investigation concerns Wittgenstein’s shift to abandon ing the essentialist concept of language and therefore deny ing the existence of a universal language. Languages — or ‘language games’ as Wittgenstein calls them — are immersed in a form of life, in a cultural or social formation and are embedded in the totality o f communal activities. This gives rise to the idea of rationality as an invention or as a construct that emerges in specific local contexts. In the second part of the paper we introduce, analyse and compare the mathematical aspects of two activities known as string figure - making and sand drawing, to illustrate Wittgenstein ’s ideas . Base d on an ethnomathematical comparative analysis , we will argue that there is evidence of invariant and distinguishing features of a mathematical rationality , as expressed in both string figure - making and sand drawing practices, from one society to another . Finally, w e suggest that a philosop hical - anthropological approach to mathematical practices may allow us to better understand the interrelations between mathematics and cul tures. Philoso phical investigations may help the reflection on the possibility of culturally determined ethnomathematics, while an anthropological approach, using ethnographical methods, may afford new materials for the analysis of ethnomathematics and its links to the cultural context. This combined approach will help us to better

  4. Chance Encounters: Probability in Games and Simulations. Seeing and Thinking Mathematically in the Middle Grades.

    Science.gov (United States)

    Kleiman, Glenn; Zweig, Karen

    With the Seeing and Thinking Mathematically materials, students learn mathematics by doing mathematics, by using and connecting mathematical ideas, and by actively constructing their own understandings. In this unit students learn to see probability through a mathematical lens by exploring and creating games and simulations and by applying the…

  5. Calling for Research Collaborations and the Use of Dis/ability Studies in Mathematics Education

    Science.gov (United States)

    Tan, Paulo; Kastberg, Signe

    2017-01-01

    In this commentary, the authors find that despite discussions of "mathematics for all," opportunities that support the development of mathematical reasoning and understanding of mathematics as a human endeavor often do not exist for mathematics learners identified in schools as having dis/abilities. Indeed, mathematics for all is…

  6. Determination of the Processes Driving the Acquisition of Immunity to Malaria Using a Mathematical Transmission Model

    OpenAIRE

    Filipe, Jo?o A. N; Riley, Eleanor M; Drakeley, Christopher J; Sutherland, Colin J; Ghani, Azra C

    2007-01-01

    Acquisition of partially protective immunity is a dominant feature of the epidemiology of malaria among exposed individuals. The processes that determine the acquisition of immunity to clinical disease and to asymptomatic carriage of malaria parasites are poorly understood, in part because of a lack of validated immunological markers of protection. Using mathematical models, we seek to better understand the processes that determine observed epidemiological patterns. We have developed an age-s...

  7. Cultural horizons for mathematics

    Science.gov (United States)

    Owens, Kay; Paraides, Patricia; Jannok Nutti, Ylva; Johansson, Gunilla; Bennet, Maria; Doolan, Pat; Peckham, Ray; Hill, John; Doolan, Frank; O'Sullivan, Dominic; Murray, Libbey; Logan, Patricia; McNair, Melissa; Sunnari, Vappu; Murray, Beatrice; Miller, Alissa; Nolan, John; Simpson, Alca; Ohrin, Christine; Doolan, Terry; Doolan, Michelle; Taylor, Paul

    2011-06-01

    As a result of a number of government reports, there have been numerous systemic changes in Indigenous education in Australia revolving around the importance of partnerships with the community. A forum with our local Dubbo community established the importance of working together and developed a model which placed the child in an ecological perspective that particularly noted the role of Elders and the place of the child in the family. However, there was also the issue of curriculum and mathematics education to be addressed. It was recognised that a colonised curriculum reduces the vision of what might be the potential for Indigenous mathematics education. This paper reports on the sharing that developed between our local community and some researchers and teachers from Sweden, Papua New Guinea and New Zealand. It has implications for recognising the impact of testing regimes, the teaching space, understanding the ways children learn, the curriculum, and teacher education. As a result of these discussions, a critical pedagogy that considers culture and place is presented as an ecocultural perspective on mathematics education. This perspective was seen as critical for the curriculum and learning experiences of Indigenous children.

  8. Mathematical foundations of biomechanics.

    Science.gov (United States)

    Niederer, Peter F

    2010-01-01

    The aim of biomechanics is the analysis of the structure and function of humans, animals, and plants by means of the methods of mechanics. Its foundations are in particular embedded in mathematics, physics, and informatics. Due to the inherent multidisciplinary character deriving from its aim, biomechanics has numerous connections and overlapping areas with biology, biochemistry, physiology, and pathophysiology, along with clinical medicine, so its range is enormously wide. This treatise is mainly meant to serve as an introduction and overview for readers and students who intend to acquire a basic understanding of the mathematical principles and mechanics that constitute the foundation of biomechanics; accordingly, its contents are limited to basic theoretical principles of general validity and long-range significance. Selected examples are included that are representative for the problems treated in biomechanics. Although ultimate mathematical generality is not in the foreground, an attempt is made to derive the theory from basic principles. A concise and systematic formulation is thereby intended with the aim that the reader is provided with a working knowledge. It is assumed that he or she is familiar with the principles of calculus, vector analysis, and linear algebra.

  9. Mathematics and Maxwell's equations

    International Nuclear Information System (INIS)

    Boozer, Allen H

    2010-01-01

    The universality of mathematics and Maxwell's equations is not shared by specific plasma models. Computations become more reliable, efficient and transparent if specific plasma models are used to obtain only the information that would otherwise be missing. Constraints of high universality, such as those from mathematics and Maxwell's equations, can be obscured or lost by integrated computations. Recognition of subtle constraints of high universality is important for (1) focusing the design of control systems for magnetic field errors in tokamaks from perturbations that have little effect on the plasma to those that do, (2) clarifying the limits of applicability to astrophysics of computations of magnetic reconnection in fields that have a double periodicity or have B-vector =0 on a surface, as in a Harris sheet. Both require a degree of symmetry not expected in natural systems. Mathematics and Maxwell's equations imply that neighboring magnetic field lines characteristically separate exponentially with distance along a line. This remarkably universal phenomenon has been largely ignored, though it defines a trigger for reconnection through a critical magnitude of exponentiation. These and other examples of the importance of making distinctions and understanding constraints of high universality are explained.

  10. IGCSE core mathematics

    CERN Document Server

    Wall, Terry

    2013-01-01

    Give your core level students the support and framework they require to get their best grades with this book dedicated to the core level content of the revised syllabus and written specifically to ensure a more appropriate pace. This title has been written for Core content of the revised Cambridge IGCSE Mathematics (0580) syllabus for first teaching from 2013. ? Gives students the practice they require to deepen their understanding through plenty of practice questions. ? Consolidates learning with unique digital resources on the CD, included free with every book. We are working with Cambridge

  11. Understanding analysis

    CERN Document Server

    Abbott, Stephen

    2015-01-01

    This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-sty...

  12. 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.

  13. Attitudes towards Graphing Calculators in Developmental Mathematics

    Science.gov (United States)

    Rajan, Shaun Thomas

    2013-01-01

    The purpose of this exploratory study was to examine instructor and student attitudes towards the use of the graphing calculator in the developmental mathematics classroom. A focus of the study was to see if instructors or students believed there were changes in the conceptual understanding of mathematics as a result of graphing calculator…

  14. Electromagnetic Concepts in Mathematical Representation of Physics.

    Science.gov (United States)

    Albe, Virginie; Venturini, Patrice; Lascours, Jean

    2001-01-01

    Addresses the use of mathematics when studying the physics of electromagnetism. Focuses on common electromagnetic concepts and their associated mathematical representation and arithmetical tools. Concludes that most students do not understand the significant aspects of physical situations and have difficulty using relationships and models specific…

  15. Mathematics Didn't Just Happen.

    Science.gov (United States)

    Lightner, James E.

    2001-01-01

    Examines several periods of world history including Greece, the middle ages, and the 17th century to gain a better understanding of the development of mathematics and share this information with students so that they can learn mathematics as a product of the people who lived their lives surrounded by the cultural influences and distractions of…

  16. Teaching Mathematics and Language to English Learners

    Science.gov (United States)

    Leith, Chad; Rose, Elena; King, Tony

    2016-01-01

    To create a classroom learning community in which all students are engaged and inspired, a mathematics teacher's mastery of the content must be matched by an awareness of the needs of individual students and an understanding of the instructional strategies that will enable all learners to develop their mathematical knowledge and skills. Yet when…

  17. Emotion and Disaffection with School Mathematics

    Science.gov (United States)

    Lewis, Gareth

    2013-01-01

    This paper reports some initial findings from research designed to understand more deeply the motivational and emotional landscape of disaffection with school mathematics. A context is described in which there has been significant concern expressed about a number of aspects of mathematics education, but where affect is seen as salient to these…

  18. Turning Origami into the Language of Mathematics

    Science.gov (United States)

    Cipoletti, Beth; Wilson, Nancy

    2004-01-01

    The National Council of Teachers of Mathematics (1989) proposes using everyday objects, such as paper, to enable students to explore geometric relationships and vocabulary. Paper-folding and other types of hands-on activities have been found to increase students' ability to communicate mathematically and foster their understanding of mathematical…

  19. Affective Productions of Mathematical Experience

    Science.gov (United States)

    Walshaw, Margaret; Brown, Tony

    2012-01-01

    In underscoring the affective elements of mathematics experience, we work with contemporary readings of the work of Spinoza on the politics of affect, to understand what is included in the cognitive repertoire of the Subject. We draw on those resources to tell a pedagogical tale about the relation between cognition and affect in settings of…

  20. 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

  1. Mathematics for Life: Sustainable Mathematics Education

    Science.gov (United States)

    Renert, Moshe

    2011-01-01

    Ecological sustainability has not been a major focus of mathematics education research, even though it has attracted considerable attention in other areas of educational research in the past decade. The connections between mathematics education and ecological sustainability are not readily apparent. This paper explores how mathematics educators…

  2. 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…

  3. Mathematics make microbes beautiful, beneficial, and bountiful.

    Science.gov (United States)

    Jungck, John R

    2012-01-01

    Microbiology is a rich area for visualizing the importance of mathematics in terms of designing experiments, data mining, testing hypotheses, and visualizing relationships. Historically, Nobel Prizes have acknowledged the close interplay between mathematics and microbiology in such examples as the fluctuation test and mutation rates using Poisson statistics by Luria and Delbrück and the use of graph theory of polyhedra by Caspar and Klug. More and more contemporary microbiology journals feature mathematical models, computational algorithms and heuristics, and multidimensional visualizations. While revolutions in research have driven these initiatives, a commensurate effort needs to be made to incorporate much more mathematics into the professional preparation of microbiologists. In order not to be daunting to many educators, a Bloom-like "Taxonomy of Quantitative Reasoning" is shared with explicit examples of microbiological activities for engaging students in (a) counting, measuring, calculating using image analysis of bacterial colonies and viral infections on variegated leaves, measurement of fractal dimensions of beautiful colony morphologies, and counting vertices, edges, and faces on viral capsids and using graph theory to understand self assembly; (b) graphing, mapping, ordering by applying linear, exponential, and logistic growth models of public health and sanitation problems, revisiting Snow's epidemiological map of cholera with computational geometry, and using interval graphs to do complementation mapping, deletion mapping, food webs, and microarray heatmaps; (c) problem solving by doing gene mapping and experimental design, and applying Boolean algebra to gene regulation of operons; (d) analysis of the "Bacterial Bonanza" of microbial sequence and genomic data using bioinformatics and phylogenetics; (e) hypothesis testing-again with phylogenetic trees and use of Poisson statistics and the Luria-Delbrück fluctuation test; and (f) modeling of

  4. The history of mathematics a brief course

    CERN Document Server

    Cooke, Roger

    2005-01-01

    This new edition brings the fascinating and intriguing history of mathematics to life. The Second Edition of this internationally acclaimed text has been thoroughly revised, updated, and reorganized to give readers a fresh perspective on the evolution of mathematics. Written by one of the world's leading experts on the history of mathematics, the book details the key historical developments in the field, providing an understanding and appreciation of how mathematics influences today's science, art, music, literature, and society. In the first edition, each chapter was devoted to a single cultu

  5. Mathematics Intervention Supporting Allen, a Latino EL: A Case Study

    Directory of Open Access Journals (Sweden)

    Marialuisa Di Stefano

    2017-05-01

    Full Text Available This research discusses a single case study of a first-grade Latino English Learner (EL student, Allen (pseudonym, from a larger inquiry-based intervention on inversion and mental reversibility development. The purpose of this case study was to develop a better understanding of the relationship between Allen’s English language proficiency and his ability to solve inversion and compensation mathematics tasks. The integration of multiple paradigms confronting radical constructivism and sociocultural theory of learning via culturally relevant pedagogy provided us with a multi-faceted set of perspectives in understanding the interconnection between Allen’s cultural and linguistic background and his development of algebraic reasoning. Through conceptual and retrospective analyses, we found that Allen’s language features are highly correlated with the development of his thinking strategies and his ability to solve mathematics tasks. Implications of this study include the development of teaching strategies that address critical issues in mathematics, such as the individual differences of learners, specifically ELs from Latino background. We suggest further research is needed in the field of language acquisition and access to STEM related concepts.

  6. Ones and zeros understanding Boolean algebra digital circuits and the logic of sets

    CERN Document Server

    Gregg, John

    1998-01-01

    "Ones and Zeros explains, in lay terms, Boolean algebra, the suprisingly simple system of mathematical logic used in digital computer circuitry. Ones and Zeros follows the development of this logic system from its origins in Victorian England to its rediscovery in this century as the foundation of all modern computing machinery. Readers will learn about the interesting history of the development of symbolic logic in particular, and the often misunderstood process of mathematical invention and scientific discovery, in general. Ones and Zeros also features practical exercises with answers, real-world examples of digital circuit design, and a reading list." "Ones and Zeros will be of particular interest to software engineers who want to gain a comprehensive understanding of computer hardware." "Outstanding features include: a history of mathematical logic, an explanation of the logic of digital circuits, and hands-on exercises and examples."--Jacket.

  7. Mathematical modelling in science and mathematics education

    Science.gov (United States)

    Teodoro, Vítor Duarte; Neves, Rui Gomes

    2011-01-01

    Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high school and university curricula in science and mathematics. In this paper, it is discussed the relevance of mathematical modelling and illustrated how a computer modelling tool (Modellus, a free tool available on the Internet and developed at FCTUNL) can be used to embed modelling in high school and undergraduate courses. Modellus allows students to create and explore mathematical models using functions, differential and iterative equations, and visualize the behaviour of mathematical objects.

  8. Sport and Mathematics: A Definition and Delineation.

    Science.gov (United States)

    Schutz, Robert W.

    1980-01-01

    There are many areas within sport studies that require using mathematical analyses, which would foster a fuller understanding of the structure and strategy of sport and the development of quantitatively viable theories of motor development. (CJ)

  9. General relativity, strings, and mathematical physics

    CERN Document Server

    Porrati, Massimo

    1999-01-01

    We give a historical review of some aspects of string theory relevant to our present understanding of general relativity, and connected with Einstein's unification program. We also point out to various mathematical fallouts of $9 string theory. (31 refs).

  10. Learning to Calculate and Learning Mathematics.

    Science.gov (United States)

    Fearnley-Sander, Desmond

    1980-01-01

    A calculator solution of a simple computational problem is discussed with emphasis on its ramifications for the understanding of some fundamental theorems of pure mathematics and techniques of computing. (Author/MK)

  11. Cognitive correlates of performance in advanced mathematics.

    Science.gov (United States)

    Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

    2012-03-01

    Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic). To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. We recruited 80 undergraduates from four universities in Beijing. The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications. ©2011 The British Psychological Society.

  12. Ethnomathematics: the cultural aspects of mathematics

    Directory of Open Access Journals (Sweden)

    Milton Rosa

    2011-01-01

    Full Text Available Ethnomathematics studies the cultural aspects of mathematics. It presents mathematical concepts of the school curriculum in a way in which these concepts are related to the students¿ cultural and daily experiences, thereby enhancing their abilities to elaborate meaningful connections and deepening their understanding of mathematics. Ethnomathematical approaches to mathematics curriculum are intended to make school mathematics more relevant and meaningful for students and to promote the overall quality of their education. In this context, the implementation of an ethnomathematical perspective in the school mathematics curriculum helps to develop students' intellectual, social, emotional, and political learning by using their own unique cultural referents to impart their knowledge, skills, and attitudes. This kind of curriculum provides ways for students to maintain their identity while succeeding academically.

  13. Supporting students' strategic competence: a case of a sixth-grade mathematics classroom

    Science.gov (United States)

    Özdemir, İ. Elif Yetkin; Pape, Stephen J.

    2012-06-01

    Mathematics education research has documented several classroom practices that might influence student self-regulation. We know little, however, about the ways these classroom practices could be structured in real classroom settings. In this exploratory case study, we purposefully selected a sixth-grade mathematics teacher who had participated in a professional development program focussed on NCTM standards and SRL in the mathematics classroom for extensive classroom observation. The purpose was to explore how and to what extend she structured classroom practices to support strategic competence in her students. Four features of classroom practices were found as evidence for how strategic competence was potentially supported in this classroom: (a) allowing autonomy and shared responsibility during the early stages of learning, (b) focusing on student understanding, (c) creating contexts for students to learn about strategic learning and to exercise strategic behaviour, and (d) helping students to personalise strategies by recognising their ideas and strategic behaviours.

  14. 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.

  15. The mathematics of various entertaining subjects

    CERN Document Server

    Rosenhouse, Jason

    Volume 1 : The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books exploring puzzles and brainteasers, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects brings together authors from a variety of specialties to present fascinating problems and solutions in recreational mathematics. Contributors to the book show how sophisticated mathematics can help construct mazes that look like famous people, how the analysis of crossword puzzles has much in common with understanding epidemics, and how the theory of electrical circuits is useful in understanding the classic Towers of Hanoi puzzle. The card game SET is related to the theory of error-correcting codes, and simple tic-tac-toe tak...

  16. Mathematics Connection: Editorial Policies

    African Journals Online (AJOL)

    MATHEMATICS CONNECTION aims at providing a forum to promote the development of Mathematics Education in Ghana. Articles that seek to enhance the teaching and/or learning of mathematics ... Faculty of Social Sciences, Methodist University, Accra Prof. B. K. Gordor, Department of Mathematics (UCC), Cape Coast ...

  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. World Mathematical Year 2000

    Indian Academy of Sciences (India)

    2001-08-10

    World Mathematical Year 2000. (July 23 to August 10, 2001) at Indian Institute of Science, Bangalore 560 012 sponsored by National Board for Higher Mathematics, organised by Department of Mathematics and. TIFR Centre, Indian Institute of Science. Prof. J L Bona, Department of Mathematics, University of Texas at ...

  20. Chanting as mathematical enculturation

    Directory of Open Access Journals (Sweden)

    Anne Watson

    2004-10-01

    Full Text Available Unison response is a major teaching strategy in mathematics throughout the world. The spoken word is the dominant source of mathematical stimulus, the dominant shaper of the mathematical environment in which school learners construct mathematical meaning. The teachers’ utterances are intended to be expert, and the creation of learner responses is intended to involve learning of some kind.

  1. It's all just mathematics

    Science.gov (United States)

    Tegmark, Max

    2014-02-01

    The world can be described using mathematical equations and numbers, but why does maths do it so well? In his new book Our Mathematical Universe, a section of which is abridged and edited here, Max Tegmark makes the radical proposal that our reality isn't just described by mathematics - it is mathematics.

  2. Visual Representations in Mathematics Teaching: An Experiment with Students

    Science.gov (United States)

    Debrenti, Edith

    2015-01-01

    General problem-solving skills are of central importance in school mathematics achievement. Word problems play an important role not just in mathematical education, but in general education as well. Meaningful learning and understanding are basic aspects of all kinds of learning and it is even more important in the case of learning mathematics. In…

  3. Reflective Awareness in Mathematics Teachers' Learning and Teaching

    Science.gov (United States)

    Chapman, Olive

    2015-01-01

    The nature of mathematics teachers' knowledge specific to teaching mathematics [MTK] is of ongoing concern in mathematics education research. This article contributes to our under-standing of this knowledge with particular focus on reflective awareness. It discusses MTK based on ways it has been used in research. It highlights reflective awareness…

  4. Using Five-Frames in Preschool Mathematics Instruction

    Science.gov (United States)

    Rizer, Jennifer

    2017-01-01

    Mathematics education is a critical part of instruction for students around the globe. The foundation for understanding basic mathematical concepts begins early in life. Preschool classrooms can provide the early skills in mathematical reasoning that will be needed later in life. In this study, the author sought to determine if the use of…

  5. Tutorials in mathematical biosciences

    CERN Document Server

    2008-01-01

    The book offers an easy introduction to fast growing research areas in evolution of species, population genetics, ecological models, and population dynamics. The first two chapters review the concept and methodologies of phylogenetic trees; computational schemes and illustrations are given, including applications such as tracing the origin of SARS and influenza. The third chapter introduces the reader to ecological models, including predator-prey models. This chapter includes and introduction to reaction-diffusion equations, which are used to analyze the ecological models. The next chapter reviews a broad range of ongoing research in population dynamics, including evolution of dispersal models; it also features interesting mathematical theorems and lists open problems. The final chapter deals with gene frequencies under the action of migration and selection. The book is addressed to readers at the level of grad students and researchers. A background in PDEs is provided.

  6. Succeeding at teaching secondary mathematics your first year

    CERN Document Server

    Roddick, Cheryl D

    2010-01-01

    This practical resource helps beginning secondary mathematics teachers design a curriculum that is meaningful, differentiate instruction, engage students, meet standards, assess student understanding, and more.

  7. A discrete transition to advanced mathematics

    CERN Document Server

    Richmond, Bettina

    2009-01-01

    As the title indicates, this book is intended for courses aimed at bridging the gap between lower-level mathematics and advanced mathematics. The text provides a careful introduction to techniques for writing proofs and a logical development of topics based on intuitive understanding of concepts. The authors utilize a clear writing style and a wealth of examples to develop an understanding of discrete mathematics and critical thinking skills. While including many traditional topics, the text offers innovative material throughout. Surprising results are used to motivate the reader. The last thr

  8. Identity as an Analytical Tool to Explore Students’ Mathematical Writing

    DEFF Research Database (Denmark)

    Iversen, Steffen Møllegaard

    Learning to communicate in, with and about mathematics is a key part of learning mathematics (Niss & Højgaard, 2011). Therefore, understanding how students’ mathematical writing is shaped is important to mathematics education research. In this paper the notion of ‘writer identity’ (Ivanič, 1998......; Burgess & Ivanič, 2010) is introduced and operationalised in relation to students’ mathematical writing and through a case study it is illustrated how this analytic tool can facilitate valuable insights when exploring students’ mathematical writing....

  9. Site Features

    Data.gov (United States)

    U.S. Environmental Protection Agency — This dataset consists of various site features from multiple Superfund sites in U.S. EPA Region 8. These data were acquired from multiple sources at different times...

  10. Feature Extraction

    CERN Multimedia

    CERN. Geneva

    2015-01-01

    Feature selection and reduction are key to robust multivariate analyses. In this talk I will focus on pros and cons of various variable selection methods and focus on those that are most relevant in the context of HEP.

  11. Solar Features

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — Collection includes a variety of solar feature datasets contributed by a number of national and private solar observatories located worldwide.

  12. Quantum Gravity Mathematical Models and Experimental Bounds

    CERN Document Server

    Fauser, Bertfried; Zeidler, Eberhard

    2007-01-01

    The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas which evolved while developing a theory of quantum gravity require highly advanced mathematical methods. This book presents different mathematical approaches to formulate a theory of quantum gravity. It represents a carefully selected cross-section of lively discussions about the issue of quantum gravity which took place at the second workshop "Mathematical and Physical Aspects of Quantum Gravity" in Blaubeuren, Germany. This collection covers in a unique way aspects of various competing approaches. A unique feature of the book is the presentation of different approaches to quantum gravity making comparison feasible. This feature is supported by an extensive index. The book is mainly addressed to mathematicians and physicists who are interested in questions related to mathematical physics. It allows the reader to obtain a broad and up-to-date overview on ...

  13. Forms of Mathematical Interaction in Different Social Settings: Examples from Students' Teachers' and Teacher-Students' Communication about Mathematics

    Science.gov (United States)

    Nuhrenborger, Marcus; Steinbring, Heinz

    2009-01-01

    The study presented in this article investigates forms of "mathematical" interaction in different social settings. One major interest is to better understand mathematics teachers' joint professional discourse while observing and analysing young students mathematical interaction followed by teacher's intervention. The teachers' joint professional…

  14. Comparative Studies on U. S. and Chinese Mathematics Learning and the Implications for Standards-Based Mathematics Teaching Reform

    Science.gov (United States)

    Wang, Jian; Lin, Emily

    2005-01-01

    Chinese students often outperform U.S. students on international tests in mathematics. Chinese students' mathematics performances are assumed to be related directly to their teachers' deep mathematics understanding and ability to represent concepts flexibly in their classrooms, which, in turn, are thought to be influenced by Chinese mathematics…

  15. Computer Algebra Recipes for Mathematical Physics

    CERN Document Server

    Enns, Richard H

    2005-01-01

    Over two hundred novel and innovative computer algebra worksheets or "recipes" will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they encounter in their mathematical physics studies. While the aim of this text is to illustrate applications, a brief synopsis of the fundamentals for each topic is presented, the topics being organized to correlate with those found in traditional mathematical physics texts. The recipes are presented in the form of stories and anecdotes, a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn. Key features: * Uses the MAPLE computer algebra system to allow the reader to easily and quickly change the mathematical models and the parameters and then generate new answers * No prior knowledge of MAPLE is assumed; the relevant MAPLE commands are introduced on a need-to-know basis * All MAPLE commands are indexed for easy reference * A classroom-tested story/anecdote format is use...

  16. International Conference on Mathematical Fluid Dynamics

    CERN Document Server

    Suzuki, Yukihito

    2016-01-01

    This volume presents original papers ranging from an experimental study on cavitation jets to an up-to-date mathematical analysis of the Navier-Stokes equations for free boundary problems, reflecting topics featured at the International Conference on Mathematical Fluid Dynamics, Present and Future, held 11–14 November 2014 at Waseda University in Tokyo. The contributions address subjects in one- and two-phase fluid flows, including cavitation, liquid crystal flows, plasma flows, and blood flows. Written by internationally respected experts, these papers highlight the connections between mathematical, experimental, and computational fluid dynamics. The book is aimed at a wide readership in mathematics and engineering, including researchers and graduate students interested in mathematical fluid dynamics.

  17. 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...

  18. Mathematical modeling in realistic mathematics education

    Science.gov (United States)

    Riyanto, B.; Zulkardi; Putri, R. I. I.; Darmawijoyo

    2017-12-01

    The purpose of this paper is to produce Mathematical modelling in Realistics Mathematics Education of Junior High School. This study used development research consisting of 3 stages, namely analysis, design and evaluation. The success criteria of this study were obtained in the form of local instruction theory for school mathematical modelling learning which was valid and practical for students. The data were analyzed using descriptive analysis method as follows: (1) walk through, analysis based on the expert comments in the expert review to get Hypothetical Learning Trajectory for valid mathematical modelling learning; (2) analyzing the results of the review in one to one and small group to gain practicality. Based on the expert validation and students’ opinion and answers, the obtained mathematical modeling problem in Realistics Mathematics Education was valid and practical.

  19. Mathematical methods for physicists and engineers

    CERN Document Server

    Collins, Royal Eugene

    2011-01-01

    This practical, highly readable text provides physics and engineering students with the essential mathematical tools for thorough comprehension of their disciplines. Featuring all the necessary topics in applied mathematics in the form of programmed instruction, the text can be understood by advanced undergraduates and beginning graduate students without any assistance from the instructor. Topics include elementary vector calculus, matrix algebra, and linear vector operations; the many and varied methods of solving linear boundary value problems, including the more common special functions o

  20. Enabling collaboration on semiformal mathematical knowledge by semantic web integration

    CERN Document Server

    Lange, C

    2011-01-01

    Mathematics is becoming increasingly collaborative, but software does not sufficiently support that: Social Web applications do not currently make mathematical knowledge accessible to automated agents that have a deeper understanding of mathematical structures. Such agents exist but focus on individual research tasks, such as authoring, publishing, peer-review, or verification, instead of complex collaboration workflows. This work effectively enables their integration by bridging the document-oriented perspective of mathematical authoring and publishing, and the network perspective of threaded

  1. The Stages of Student Mathematical Imagination in Solving Mathematical Problems

    Science.gov (United States)

    Wibowo, Teguh; Sutawidjaja, Akbar; As'ari, Abdur Rahman; Sulandra, I. Made

    2017-01-01

    This research is a qualitative study that aimed to describe the stages of students mathematical imagination in solving mathematical problems. There are three kinds of mathematical imagination in solving mathematical problems, namely sensory mathematical imagination, creative mathematical imagination and recreative mathematical imagination.…

  2. Mathematical methods for physicists a comprehensive guide

    CERN Document Server

    Arfken, George B; Harris, Frank E

    2012-01-01

    Now in its 7th edition, Mathematical Methods for Physicists continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining the key features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples. Taking a problem-solving-skills approach to incorporating theorems with applications, the book's improved focus w

  3. The best writing on mathematics 2014

    CERN Document Server

    Pitici, Mircea

    2014-01-01

    This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2014 makes available to a wide audience many articles not easily found anywhere else-and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest math

  4. The Best Writing on Mathematics 2011

    CERN Document Server

    Pitici, Mircea

    2011-01-01

    This anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2011 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematica

  5. The mathematical theory of general relativity

    CERN Document Server

    Katkar, L N

    2014-01-01

    This book is prepared for M. Sc. Students of Mathematics and Physics. The aim of writing this book is to give the reader a feeling for the necessity and beauty of the laws of general relativity. The contents of the book will attract both mathematicians and physicists which provides motivation and applications of many ideas and powerful mathematical methods of modern analysis and differential geometry. An attempt has been made to make the presentation comprehensive, rigorous and yet simple. Most calculations and transformations have been carried out in great detail. KEY FEATURE: Numerous solved examples using the well known mathematical techniques viz., the tensors and the differential forms in each chapter.

  6. The best writing on mathematics 2013

    CERN Document Server

    Pitici, Mircea

    2014-01-01

    This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2013 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mat

  7. 2015 Association for Women in Mathematics Symposium

    CERN Document Server

    Lauter, Kristin; Chambers, Erin; Flournoy, Nancy; Grigsby, Julia; Martin, Carla; Ryan, Kathleen; Trivisa, Konstantina

    2016-01-01

    Presenting the latest findings in topics from across the mathematical spectrum, this volume includes results in pure mathematics along with a range of new advances and novel applications to other fields such as probability, statistics, biology, and computer science. All contributions feature authors who attended the Association for Women in Mathematics Research Symposium in 2015: this conference, the third in a series of biennial conferences organized by the Association, attracted over 330 participants and showcased the research of women mathematicians from academia, industry, and government.

  8. 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.

  9. Teaching Statistics in Middle School Mathematics Classrooms: Making Links with Mathematics but Avoiding Statistical Reasoning

    Science.gov (United States)

    Savard, Annie; Manuel, Dominic

    2015-01-01

    Statistics is a domain that is taught in Mathematics in all school levels. We suggest a potential in using an interdisciplinary approach with this concept. Thus the development of the understanding of a situation might mean to use both mathematical and statistical reasoning. In this paper, we present two case studies where two middle school…

  10. Just-in-Time Mathematics: Integrating the Teaching of Finance Theory and Mathematics.

    Science.gov (United States)

    Prichett, Gordon D.; Feinstein, Steven P.

    1999-01-01

    Describes a course that integrates the teaching of finance theory and mathematics. Concludes that this marriage of mathematics and finance reflects the current state of the investments profession and produces a deeper understanding of both fields. Contains 18 references. (Author/ASK)

  11. Mathematics and Mathematics Education as Triadic Communication? A Semiotic Framework Exemplified

    Science.gov (United States)

    Ongstad, Sigmund

    2006-01-01

    The article investigates in the first part critically dyadic and essentialist understanding of signs and utterances in mathematics and mathematics education as opposed to a triadic view. However even Peircean semiotics, giving priority to triadic, dynamic sign may face challenges, such as explaining the sign as a pragmatic act and how signs are…

  12. The third approach to the history of mathematics in China

    OpenAIRE

    Qu, Anjing

    2003-01-01

    The first approach to the history of mathematics in China led by Li Yan (1892--1963) and Qian Baocong (1892--1974) featured discovering {\\it what} mathematics had been done in China's past. From the 1970s on, Wu Wen-tsun and others shifted this research paradigm to one of recovering {\\it how} mathematics was done in ancient China. Both approaches, however, focus on the same problem, that is mathematics in history. The theme of the third approach is supposed to be {\\it why} mathematics was don...

  13. What counts in teaching mathematics adding value to self and content

    CERN Document Server

    Schuck, Sandy

    2011-01-01

    This synthesis of current practice and research in mathematics teacher education and mathematics education features contributions from recognised scholars. It examines the role of 'critical friends' in reflective practice and the emerging issues in the field.

  14. Undergraduate Students' Perceptions of the Mathematics Courses Included in the Primary School Teacher Education Program

    Science.gov (United States)

    Serin, Mehmet Koray; Incikabi, Semahat

    2017-01-01

    Mathematics educators have reported on many issues regarding students' mathematical education, particularly students who received mathematics education at different departments such as engineering, science or primary school, including their difficulties with mathematical concepts, their understanding of and preferences for mathematical concepts.…

  15. Differences in the Mathematics-Vocabulary Knowledge of Fifth-Grade Students with and without Learning Difficulties

    Science.gov (United States)

    Forsyth, Suzanne R.; Powell, Sarah R.

    2017-01-01

    The purpose of this pilot study was to explore the impact of mathematics and reading learning difficulties on the mathematics-vocabulary understanding of fifth-grade students. Students (n = 114) completed three measures: mathematics computation, general vocabulary, and mathematics vocabulary. Based on performance on the mathematics computation and…

  16. Mathematics for Language, Language for Mathematics

    Science.gov (United States)

    Prochazkova, Lenka Tejkalova

    2013-01-01

    The author discusses the balance and mutual influence of the language of instruction and mathematics in the context of CLIL, Content and Language Integrated Learning. Different aspects of the relationship of language and Mathematics teaching and learning are discussed: the benefits of using a foreign language of instruction, as well as the…

  17. Understanding health insurance plans

    Science.gov (United States)

    ... medlineplus.gov/ency/patientinstructions/000879.htm Understanding health insurance plans To use the sharing features on this ... for you and your family. Types of Health Insurance Plans Depending on how you get your health ...

  18. Understanding cardiovascular disease

    Science.gov (United States)

    ... page: //medlineplus.gov/ency/patientinstructions/000759.htm Understanding cardiovascular disease To use the sharing features on this page, ... lead to heart attack or stroke. Types of Cardiovascular Disease Coronary heart disease (CHD) is the most common ...

  19. Understanding the DASH diet

    Science.gov (United States)

    ... medlineplus.gov/ency/patientinstructions/000784.htm Understanding the DASH diet To use the sharing features on this page, please enable JavaScript. The DASH diet is low in salt and rich in fruits, ...

  20. Understanding your hospital bill

    Science.gov (United States)

    ... medlineplus.gov/ency/patientinstructions/000881.htm Understanding your hospital bill To use the sharing features on this ... help you save money. Charges Listed on Your Hospital Bill A hospital bill will list the major ...

  1. Mathematics education and the dignity of being

    DEFF Research Database (Denmark)

    Valero, Paola; García, Gloria; Camelo, Francisco

    2012-01-01

    the dilemma of how the historical insertion of school mathematics in relation to the Colonial project of assimilation of Latin American indigenous peoples into the episteme of the Enlightenment and Modernity is in conflict with the possibility of the promotion of a social subjectivity in mathematics...... classrooms. We illustrate a pedagogical possibility to move towards a mathematics education for social subjectivity with our work in reassembling the notion of geometrical space in the Colombian secondary school mathematics curriculum with notions of space from critical geography and the problem......On the grounds of our work as researchers, teacher educators and teachers engaging with a socio-political approach in mathematics education in Colombia, we propose to understand democracy in terms of the possibility of constructing a social subjectivity for the dignity of being. We address...

  2. A course in mathematical methods for physicists

    CERN Document Server

    Herman, Russell L

    2014-01-01

    Based on the author’s junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics. The book offers: •A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra •Classroom-tested explanations of complex and Fourier analysis for trigonometric and special functions •Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems •Sections on nonlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functions

  3. Mathematics education and the dignity of being

    Directory of Open Access Journals (Sweden)

    Paola Valero

    2012-11-01

    Full Text Available On the grounds of our work as researchers, teacher educators and teachers engaging with a socio-political approach in mathematics education in Colombia, we propose to understand democracy in terms of the possibility of constructing a social subjectivity for the dignity of being. We address the dilemma of how the historical insertion of school mathematics in relation to the Colonial project of assimilation of Latin American indigenous peoples into the episteme of the Enlightenment and Modernity is in conflict with the possibility of the promotion of a social subjectivity in mathematics classrooms. We illustrate a pedagogical possibility to move towards a mathematics education for social subjectivity with our work in reassembling the notion of geometrical space in the Colombian secondary school mathematics curriculum with notions of space from critical geography and the problem of territorialisation, and Latin American epistemology with the notion of intimate space as an important element of social subjectivity.

  4. Ethnomathematics: the cultural aspects of mathematics

    Directory of Open Access Journals (Sweden)

    Milton Rosa

    2011-09-01

    Full Text Available Ethnomathematics studies the cultural aspects of mathematics. It presents mathematical concepts of the school curriculum in a way in which these concepts are related to the students’ cultural and daily experiences, thereby enhancing their abilities to elaborate meaningful connections and deepening their understanding ofmathematics. Ethnomathematical approaches to mathematics curriculum are intended to make school mathematics more relevant and meaningful for students and to promote the overall quality of their education.In this context, the implementation of an ethnomathematical perspective in the school mathematics curriculum helps to develop students’ intellectual, social, emotional, and political learning by using their own unique cultural referents to impart their knowledge, skills, and attitudes. This kind of curriculum providesways for students to maintain their identity while succeeding academically.

  5. Mathematics education and the dignity of being

    Directory of Open Access Journals (Sweden)

    Paola Valero

    2012-08-01

    Full Text Available On the grounds of our work as researchers, teacher educators and teachers engaging with a socio-political approach in mathematics education in Colombia, we propose to understand democracy in terms of the possibility of constructing a social subjectivity for the dignity of being. We address the dilemma of how the historical insertion of school mathematics in relation to the Colonial project of assimilation of Latin American indigenous peoples into the episteme of the Enlightenment and Modernity is in conflict with the possibility of the promotion of a social subjectivity in mathematics classrooms. We illustrate a pedagogical possibility to move towards a mathematics education for social subjectivity with our work in reassembling the notion of geometrical space in the Colombian secondary school mathematics curriculum with notions of space from critical geography and the problem of territorialisation, and Latin American epistemology with the notion of intimate space as an important element of social subjectivity.

  6. University Science and Mathematics Education in Transition

    DEFF Research Database (Denmark)

    Skovsmose, Ole; Valero, Paola; Christensen, Ole Ravn

    of science and mathematics education in the current information society and provides insight essential for developing possibilities to improve science and mathematics education in universities all around the world. The uniquely broad treatment offered by University Science and Mathematics Education...... configuration poses to scientific knowledge, to universities and especially to education in mathematics and science. Traditionally, educational studies in mathematics and science education have looked at change in education from within the scientific disciplines and in the closed context of the classroom....... Although educational change is ultimately implemented in everyday teaching and learning situations, other parallel dimensions influencing these situations cannot be forgotten. An understanding of the actual potentialities and limitations of educational transformations are highly dependent on the network...

  7. Developing My Mathematics Identity

    Science.gov (United States)

    Gonzalez, Lidia

    2016-01-01

    Assuming the role of storyteller, the author uses her experiences as a graduate student and beginning teacher to reflect critically on issues related to mathematics, mathematics education, gender, and diversity.

  8. Journal of applied mathematics

    National Research Council Canada - National Science Library

    2001-01-01

    "[The] Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics...

  9. 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....

  10. The argument of mathematics

    CERN Document Server

    Aberdein, Andrew

    2014-01-01

    This book presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. It offers large array of examples ranging from the history of mathematics to formal proof verification.

  11. Mathematical knowledge in teaching

    CERN Document Server

    Rowland, Tim

    2011-01-01

    This book examines issues of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing approaches to characterizing, assessing and developing mathematical knowledge for teaching.

  12. Mathematics for the nonmathematician

    CERN Document Server

    Kline, Morris

    1967-01-01

    Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems.

  13. Modern mathematics made simple

    CERN Document Server

    Murphy, Patrick

    1982-01-01

    Modern Mathematics: Made Simple presents topics in modern mathematics, from elementary mathematical logic and switching circuits to multibase arithmetic and finite systems. Sets and relations, vectors and matrices, tesselations, and linear programming are also discussed.Comprised of 12 chapters, this book begins with an introduction to sets and basic operations on sets, as well as solving problems with Venn diagrams. The discussion then turns to elementary mathematical logic, with emphasis on inductive and deductive reasoning; conjunctions and disjunctions; compound statements and conditional

  14. Mathematical modeling using Maple

    OpenAIRE

    Beauchamp, Robert Edward.

    1996-01-01

    The area of higher mathematics begins with successive courses in calculus; however, rarely does the calculus student recognize the applications or impetus for the mathematical skills that are taught. Giordano and Weir produced A First Course in Mathematical Modeling, the first text which addressed this shortcoming in the curriculum of every science and engineering field. With the advent of powerful classroom computers, Fox, Maddox, Giordano and Weir produced Mathematical Modeling With Minitab...

  15. Our Mathematical Universe?

    OpenAIRE

    Butterfield, Jeremy

    2014-01-01

    This is a discussion of some themes in Max Tegmark's recent book, Our Mathematical Universe. It was written as a review for Plus Magazine, the online magazine of the UK's national mathematics education and outreach project, the Mathematics Millennium Project. Since some of the discussion (about symmetry breaking, and Pythagoreanism in the philosophy of mathematics) went beyond reviewing Tegmark's book, the material was divided into three online articles. This version combines those three arti...

  16. The Importance of Dialogic Processes to Conceptual Development in Mathematics

    Science.gov (United States)

    Kazak, Sibel; Wegerif, Rupert; Fujita, Taro

    2015-01-01

    We argue that dialogic theory, inspired by the Russian scholar Mikhail Bakhtin, has a distinct contribution to the analysis of the genesis of understanding in the mathematics classroom. We begin by contrasting dialogic theory to other leading theoretical approaches to understanding conceptual development in mathematics influenced by Jean Piaget…

  17. Manipulative Apps to Support Students with Disabilities in Mathematics

    Science.gov (United States)

    Bouck, Emily C.; Working, Christopher; Bone, Erin

    2018-01-01

    Understanding mathematical concepts is important for all students, although often challenging for many students with disabilities. Historically, educators have used concrete manipulatives to support and build conceptual understanding. Mobile devices provide a valuable option to support students with disabilities in mathematics through app-based…

  18. 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.

  19. Mathematics of Risk Taking

    Indian Academy of Sciences (India)

    Author Affiliations. K B Athreya1 2 M G Nadkarni3. Department of Mathematics Iowa State University, Ames, Iowa; I M I, Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India. Department of Mathematics, University of Mumbai Kalina, Mumbai, 400098, India.

  20. Mathematical Sciences in Australia

    Science.gov (United States)

    Thomas, Jan; Muchatuta, Michelle; Wood, Leigh

    2009-01-01

    This article investigates enrolment trends in mathematical sciences in Australian universities. Data has been difficult to extract and the coding for mathematical disciplines has made investigation challenging. We show that the number of mathematics major undergraduates in Australia is steadily declining though the number studying…