Perceived mathematical ability under challenge: a longitudinal perspective on sex segregation among STEM degree fields

Science.gov (United States)

Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby

2015-01-01

Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. In this manuscript, we investigate how perceived ability under challenge—in particular in mathematics domains—influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC). Using nationally representative Education Longitudinal Study of 2002 (ELS) data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type 2 years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women's 12th grade perceptions of their ability under mathematics challenge increased their probability of selecting PEMC majors over and above biology. In addition, gender moderated the effect of growth mindset on students' selection of health science majors. Perceptions of ability under challenge in general and verbal domains also influenced retention in and declaration of certain STEM majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women

Challenges in Teaching Mathematics: Perspectives From Students’ Learning Difficulties

Directory of Open Access Journals (Sweden)

Steve Chinn

2016-04-01

Full Text Available Alcock et al (2016, this issue have set out and discussed a potential research agenda for mathematical cognition. It is timely that research topics, along with knowledge uncovered to date, should be incorporated into a coordinated agenda for further research. This commentary focuses on the perspectives that learning difficulties, and dyscalculia, reveal. These perspectives potentially add much to that research agenda. [Commentary on: Alcock, L., Ansari, D., Batchelor, S., Bisson, M.-J., De Smedt, B., Gilmore, C., . . . Weber, K. (2016. Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2, 20-41. doi:10.5964/jnc.v2i1.10

Perceived Mathematical Ability under Challenge: A Longitudinal Perspective on Sex Segregation among STEM Degree Fields

Directory of Open Access Journals (Sweden)

Samantha eNix

2015-06-01

Full Text Available Students’ perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and math (STEM degree choice. Related, students’ perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. We investigate how perceived ability under challenge – in particular in mathematics domains – influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC. Using nationally representative Education Longitudinal Study of 2002 (ELS data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type two years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women’s 12th grade perceptions of their ability under mathematics challenge increased the probability that they would select PEMC majors, increasing women's probability of selecting PEMC over and above biology. In addition, gender moderated the effect of growth mindset on students’ selection of health science majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women’s perceptions of their ability to facilitate their pathways to scientific degrees.

Opportunities and Challenges of Using Technology in Mathematics Education of Creative Technical Studies

DEFF Research Database (Denmark)

Triantafyllou, Eva; Timcenko, Olga

2014-01-01

This paper explores the opportunities and challenges of integrating technology to support mathematics teaching and learning in creative engineer- ing disciplines. We base our discussion on data from our research in the Media Technology department of Aalborg University Copenhagen, Denmark. Our ana...... analysis proposes that unlike in other engineering disciplines, technology in these disciplines should be used for contextualizing mathematics rather than in- troducing and exploring mathematical concepts....

Studies in Mathematics, Volume X. Applied Mathematics in the High School.

Science.gov (United States)

Schiffer, Max M.

This publication contains a sequence of lectures given to high school mathematics teachers by the author. Applications of mathematics emphasized are elementary algebra, geometry, and matrix algebra. Included are: (1) an introduction concerning teaching applications of mathematics; (2) Chapter 1: Mechanics for the High School Student; (3) Chapter…

Application and the Identity of Mathematics

DEFF Research Database (Denmark)

Jensen, Kasper Bjering Søby

In the paper a conceptual framework for discussing the identity of mathematics as a school subject is constructed with particular emphasize on application of mathematics. The framework is used to analyze the identity of mathematics, as it appears on two different kinds of domains: the political s...... system and the teachers. At the end it is discussed whether this frameworks gives us new insights into mathematics teaching. It is concluded that the framework can articulates important aspects.......In the paper a conceptual framework for discussing the identity of mathematics as a school subject is constructed with particular emphasize on application of mathematics. The framework is used to analyze the identity of mathematics, as it appears on two different kinds of domains: the political...

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

Science.gov (United States)

Wickstrom, Megan H.

2017-01-01

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

Loving + hating mathematics challenging the myths of mathematical life

CERN Document Server

Hersh, Reuben

2011-01-01

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

Introductory discrete mathematics

CERN Document Server

Balakrishnan, V K

2010-01-01

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

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

Science.gov (United States)

Darlington, Ellie

2014-01-01

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

The challenge of inadequate achievement in mathematics: Focus on a meta-approach

Directory of Open Access Journals (Sweden)

Kobus Maree

2009-09-01

Full Text Available As is the case elsewhere in the world, all stakeholders in South Africa are deeply concerned about the level and scope of underachievement in mathematics, not only at Grade 12 level, but, indeed, at University, University of Technology and Further Education and Training levels. These concerns assume a deeper dimension in light of the fact that inadequate achievement in mathematics inevitably will have a ripple effect on the academic situation in any country: inadequate achievement in mathematics precludes learners from applying for admission to sought-after fi elds of study, which, in turn, prevents numerous learners from realising their true potential and, eventually, from being happy and successful in careers that they might otherwise have been able to execute successfully. It goes without saying that inadequate achievement in mathematics will impact negatively on the overall economic situation in any country (even more so in a developing country such as South Africa. Truth being, achievement in mathematics amounts to equipping oneself with survival skills. In this article, the spotlight shifts from a narrow and outdated focus on problems that are associated with inadequate achievement in mathematics to possible solutions for this disconcerting situation and the implied challenge it raises. The focus is thus on three levels that collectively underpin and impact on achievement in mathematics, viz. the macro level, the meso level and the micro level. The macro level refers mainly to the input by the national government (and, by default, the National Department of Education. In the fi rst instance, it is the responsibility of the state to provide adequate schooling facilities for all learners, irrespective of where they fi nd themselves. Furthermore, it is the duty of the state to ensure that every learner has access to basic facilities, including food, water, sanitation and housing. The state (via the National Department of Education is also

Mathematics and biology: The interface, challenges and opportunities

Energy Technology Data Exchange (ETDEWEB)

Levin, S.A. (ed.) (Cornell Univ., Ithaca, NY (United States))

1992-06-01

The interface between mathematics and biology has long been a rich area of research, with mutual benefit to each supporting discipline. Traditional areas of investigation, such as population genetics, ecology, neurobiology, and 3-D reconstructions, have flourished, despite a rather meager environment for the funding of such work. In the past twenty years, the kind and scope of such interactions between mathematicians and biologists have changed dramatically, reaching out to encompass areas of both biology and mathematics that previously had not benefited. At the same time, with the closer integration of theory and experiment, and the increased reliance on high-speed computation, the costs of such research grew, though not the opportunities for funding. The perception became reinforced, both within the research community and at funding agencies, that although these interactions were expanding, they were not doing so at the rate necessary to meet the opportunities and needs. A workshop was held in Washington, DC, between April 28 and May 3, 1990 which drew together a broadly based group of researchers to synthesize conclusions from a group of working papers and extended discussions. The result is the report presented here, which we hope will provide a guide and stimulus to research in mathematical and computational biology for at least the next decade. The report identifies a number of grand challenges, representing a broad consensus among the participants.

Rescheduling nursing shifts: scoping the challenge and examining the potential of mathematical model based tools.

Science.gov (United States)

Clark, Alistair; Moule, Pam; Topping, Annie; Serpell, Martin

2015-05-01

To review research in the literature on nursing shift scheduling / rescheduling, and to report key issues identified in a consultation exercise with managers in four English National Health Service trusts to inform the development of mathematical tools for rescheduling decision-making. Shift rescheduling is unrecognised as an everyday time-consuming management task with different imperatives from scheduling. Poor rescheduling decisions can have quality, cost and morale implications. A systematic critical literature review identified rescheduling issues and existing mathematic modelling tools. A consultation exercise with nursing managers examined the complex challenges associated with rescheduling. Minimal research exists on rescheduling compared with scheduling. Poor rescheduling can result in greater disruption to planned nursing shifts and may impact negatively on the quality and cost of patient care, and nurse morale and retention. Very little research examines management challenges or mathematical modelling for rescheduling. Shift rescheduling is a complex and frequent management activity that is more challenging than scheduling. Mathematical modelling may have potential as a tool to support managers to minimise rescheduling disruption. The lack of specific methodological support for rescheduling that takes into account its complexity, increases the likelihood of harm for patients and stress for nursing staff and managers. © 2013 John Wiley & Sons Ltd.

Mathematical physics

CERN Document Server

Geroch, Robert

1985-01-01

Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the ""whys"" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle

The Challenge of Learning Physics before Mathematics: A Case Study of Curriculum Change in Taiwan

Science.gov (United States)

Chiu, Mei-Shiu

2016-01-01

The aim of this study was to identify challenges in implementing a physics-before- 10 mathematics curriculum. Obviously, students need to learn necessary mathematics skills in order to develop advanced physics knowledge. In the 2010 high school curriculum in Taiwan, however, grade 11 science students study two-dimensional motion in physics without…

Mathematical and Scientific Foundations for an Integrative Engineering Curriculum.

Science.gov (United States)

Carr, Robin; And Others

1995-01-01

Describes the Mathematical and Scientific Foundations of Engineering curriculum which emphasizes the mathematical and scientific concepts common to all engineering fields. Scientists and engineers together devised topics and experiments that emphasize the relevance of theory to real-world applications. Presents material efficiently while building…

A Hybrid Model of Mathematics Support for Science Students Emphasizing Basic Skills and Discipline Relevance

Science.gov (United States)

Jackson, Deborah C.; Johnson, Elizabeth D.

2013-01-01

The problem of students entering university lacking basic mathematical skills is a critical issue in the Australian higher-education sector and relevant globally. The Maths Skills programme at La Trobe University has been developed to address under preparation in the first-year science cohort in the absence of an institutional mathematics support…

Mathematics for physical chemistry

CERN Document Server

Mortimer, Robert G

2013-01-01

Mathematics for Physical Chemistry is the ideal supplementary text for practicing chemists and students who want to sharpen their mathematics skills while enrolled in general through physical chemistry courses. This book specifically emphasizes the use of mathematics in the context of physical chemistry, as opposed to being simply a mathematics text. This 4e includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The early chapters are constructed around a sequence of mathematical topics, wit

Influences On Pupils’ Mathematical Outcome: A Description Of Challenges

Directory of Open Access Journals (Sweden)

Lara Said

2006-12-01

Full Text Available Measures of instructional behaviour are specific process indicators reflecting teacher effectiveness. The Mathematics in Primary Schools (MIPS study poses the question of: ‘How is pupil progress and teachers’ instructional behaviour, within schools, related?’ This is conducted by tracking pupil progress in primary school mathematics from Year 1 to Year 2 and by collating a number of contextual/process variables situated at the pupil/classroom and school levels. The paper, which adopts, a multi-stage, stratified sample involves 1,786 pupils, 99 teachers and 40 schools, within the statistical framework of a 3-level hierarchical linear model. This paper also reports the findings of the pilot study. Although the paper is limited by the inability to use multilevel statistical techniques due to: the relatively small sample size of the pilot study and, the, as yet, unstandardised pupil scores on Maths 6 (NFER, the utility of this paper lies in the description of challenges faced when engaging in school effectiveness research.

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.

Mathematics and engineering in real life through mathematical competitions

Science.gov (United States)

More, M.

2018-02-01

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

Does It Help to Use Mathematically Superfluous Brackets When Teaching the Rules for the Order of Operations?

Science.gov (United States)

Gunnarsson, Robert; Sönnerhed, Wang Wei; Hernell, Bernt

2016-01-01

The hypothesis that mathematically superfluous brackets can be useful when teaching the rules for the order of operations is challenged. The idea of the hypothesis is that with brackets it is possible to emphasize the order priority of one operation over another. An experiment was conducted where expressions with mixed operations were studied,…

Teaching by Open-Approach Method in Japanese Mathematics Classroom.

Science.gov (United States)

Nohda, Nobuhiko

Mathematics educators in Japan have traditionally emphasized mathematical perspectives in research and practice. This paper features an account of changes in mathematics education in Japan that focus on the possibilities of individual students as well as their mathematical ways of thinking. Students' mathematical thinking, mathematical…

New Challenges in the Teaching of Mathematics.

Science.gov (United States)

Bourguignon, Jean Pierre

The manifold but discrete presence of mathematics in many objects or services imposes new constraints to the teaching of mathematics. If citizens need to be comfortable in various situations with a variety of mathematical tools, the learning of mathematics requires that one starts with simple concepts. This paper proposes some solutions to solve…

Teaching mathematics creatively in the junior secondary classes ...

African Journals Online (AJOL)

This paper tried to emphasize the importance of teaching mathematics with creativity in the Junior Secondary classes (JS1-3) of our education system. It was established that a mathematically creative environment like the mathematics laboratory will enhance the teaching and learning of mathematics in schools. In this study ...

Connectivity inference from neural recording data: Challenges, mathematical bases and research directions.

Science.gov (United States)

Magrans de Abril, Ildefons; Yoshimoto, Junichiro; Doya, Kenji

2018-06-01

This article presents a review of computational methods for connectivity inference from neural activity data derived from multi-electrode recordings or fluorescence imaging. We first identify biophysical and technical challenges in connectivity inference along the data processing pipeline. We then review connectivity inference methods based on two major mathematical foundations, namely, descriptive model-free approaches and generative model-based approaches. We investigate representative studies in both categories and clarify which challenges have been addressed by which method. We further identify critical open issues and possible research directions. Copyright © 2018 The Author(s). Published by Elsevier Ltd.. All rights reserved.

Loving and Hating Mathematics: Challenging the Myths of Mathematical Life

Science.gov (United States)

Hersh, Reuben; John-Steiner, Vera

2010-01-01

Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. "Loving and Hating…

Challenges of Blended E-Learning Tools in Mathematics: Students' Perspectives University of Uyo

Science.gov (United States)

Umoh, Joseph B.; Akpan, Ekemini T.

2014-01-01

An in-depth knowledge of pedagogical approaches can help improve the formulation of effective and efficient pedagogy, tools and technology to support and enhance the teaching and learning of Mathematics in higher institutions. This study investigated students' perceptions of the challenges of blended e-learning tools in the teaching and learning…

Music-Themed Mathematics Education as a Strategy for Improving Elementary Preservice Teachers' Mathematics Pedagogy and Teaching Self-Efficacy

Science.gov (United States)

An, Song A.; Tillman, Daniel A.; Paez, Carlos R.

2015-01-01

This study investigated the effects upon elementary preservice teachers' mathematics teaching self-efficacy and interdisciplinary lesson design strategies, which resulted from an educational intervention that emphasized integrated music-mathematics instruction. The participating elementary preservice teachers (n = 152) were recruited for this…

Mathematics and biology

International Nuclear Information System (INIS)

Khan, I.A.

1991-06-01

In India and in so many other countries, the science students are generally separated into two main streams: one opting mathematical sciences, the other studying biological sciences. As a result, medicos and biologists have no adequate knowledge of mathematical sciences. It causes a great drawback to them in order to be perfect and updated in their profession, due to the tremendous application of mathematics in bio-sciences, now-a-days. The main aim of this article is to emphasize on the need of the time to produce the mathematico-biologists in abundance for the better service of mankind. (author)

NCTM Principles and Standards for Mathematically Talented Students

Science.gov (United States)

Deal, Linda J.; Wismer, Michael G.

2010-01-01

The "Principles and Standards for School Mathematics" published in 2000 by the National Council of Teachers of Mathematics (NCTM) created a vision of mathematical concepts and processes to establish core educational guidelines for instruction from grades K to 12. The overall plan does emphasize higher level thinking, problem solving, and…

USING TASK LIKE PISA’S PROBLEM TO SUPPORT STUDENT’S CREATIVITY IN MATHEMATICS

Directory of Open Access Journals (Sweden)

Rita Novita

2016-01-01

Full Text Available Creativity is one of keys to success in the evolving global economy and also be a fundamental skill that is absolutely necessary in the 21st century. Also In mathematics, creativity or thinking creatively is important to be developed because creativity is an integral part of mathematics. However, limiting the use of creativity in the classroom reduces mathematics to a set of skills to master and rules to memorize. Doing so causes many children’s natural curiosity and enthusiasm for mathematics to disappear as they get older, creating a tremendous problem for mathematics educators who are trying to instil these very qualities. In order to investigate the increase in awareness of elementary school students’ creativity in solving mathematics’ problems by using task like PISA’s Question, a qualitative research emphasizing on holistic description was conducted. We used a formative evaluation type of development research as a mean to develop mathematical tasks like PISA’s question that have potential effect to support students’ creativity in mathematics. Ten elementary school students of grade 6 in Palembang were involved in this research. They judged the task given for them is very challenging and provokes their curiosity. The result showed that task like PISA’s question can encourage students to more creatively in mathematics.

Using Mathematics in Science: Working with Your Mathematics Department

Science.gov (United States)

Lyon, Steve

2014-01-01

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

Mathematics for physics with calculus

CERN Document Server

Das, Biman

2005-01-01

Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful-and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments.

Mathematical challenges from theoretical/computational chemistry

Energy Technology Data Exchange (ETDEWEB)

NONE

1995-12-31

The committee believes that this report has relevance and potentially valuable suggestions for a wide range of readers. Target audiences include: graduate departments in the mathematical and chemical sciences; federal and private agencies that fund research in the mathematical and chemical sciences; selected industrial and government research and development laboratories; developers of software and hardware for computational chemistry; and selected individual researchers. Chapter 2 of this report covers some history of computational chemistry for the nonspecialist, while Chapter 3 illustrates the fruits of some past successful cross-fertilization between mathematical scientists and computational/theoretical chemists. In Chapter 4 the committee has assembled a representative, but not exhaustive, survey of research opportunities. Most of these are descriptions of important open problems in computational/theoretical chemistry that could gain much from the efforts of innovative mathematical scientists, written so as to be accessible introductions to the nonspecialist. Chapter 5 is an assessment, necessarily subjective, of cultural differences that must be overcome if collaborative work is to be encouraged between the mathematical and the chemical communities. Finally, the report ends with a brief list of conclusions and recommendations that, if followed, could promote accelerated progress at this interface. Recognizing that bothersome language issues can inhibit prospects for collaborative research at the interface between distinctive disciplines, the committee has attempted throughout to maintain an accessible style, in part by using illustrative boxes, and has included at the end of the report a glossary of technical terms that may be familiar to only a subset of the target audiences listed above.

Mathematical Teaching Strategies: Pathways to Critical Thinking and Metacognition

Science.gov (United States)

Su, Hui Fang Huang; Ricci, Frederick A.; Mnatsakanian, Mamikon

2016-01-01

A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible…

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...

Math Games 180 Reproducible Activities to Motivate, Excite, and Challenge Students, Grades 6-12

CERN Document Server

Muschla, Judith A

2011-01-01

Math Games offers a dynamic collection of 180 reproducible activity sheets to stimulate and challenge your students in all areas of math - from whole numbers to data analysis - while emphasizing problem solving, critical thinking, and the use of technology for today's curriculum! Each of the book's activities can help you teach students in grades 6 through 12 how to think with numbers, recognize relationships, and make connections between mathematical concepts. You pick the activity appropriate for their needs . . . encourage the use of a calculator . . . or provide further challenges with act

Mathematical foundations of image processing and analysis

CERN Document Server

Pinoli, Jean-Charles

2014-01-01

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

Mathematical mind-benders

CERN Document Server

Winkler, Peter

2007-01-01

Peter Winkler is at it again. Following the enthusiastic reaction to Mathematical Puzzles: A Connoisseur's Collection, Peter has compiled a new collection of elegant mathematical puzzles to challenge and entertain the reader. The original puzzle connoisseur shares these puzzles, old and new, so that you can add them to your own anthology. This book is for lovers of mathematics, lovers of puzzles, lovers of a challenge. Most of all, it is for those who think that the world of mathematics is orderly, logical, and intuitive-and are ready to learn otherwise! A pdf with errata is updated by the aut

Primary Mathematics. A Saxon Teacher's Resource Booklet.

Science.gov (United States)

1997

Saxon's primary mathematics series is a "hands-on," success-oriented program which emphasizes manipulatives and mental math. The series addresses the multisensory approach to teaching. Its use enables all children to develop a solid foundation in the language and basic concepts of mathematics. Concepts are presented in carefully…

Mathematical Perspectives

Energy Technology Data Exchange (ETDEWEB)

Glimm, J.

2009-10-14

Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

Science.gov (United States)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-07-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

In-serviceMathematics and Chemistry Teachers’ Preparednessfor Mathematics and Chemistry Courses at the University of Botswana: Issues and Challenges

Directory of Open Access Journals (Sweden)

Lesego Tawana

2013-12-01

Full Text Available This research study’s aim was to track the paths of chemistry and mathematics in-service students studying for a degree at the University of Botswana who seemed to struggle with degree level concepts in their respective programmes despite holding diplomas in their fields. The authors are lecturers of both methodology and content courses in science and mathematics who became concerned about the seeminglyunderpreparedness of most in-service students for degree courses over the years. The study can be located within a social structuralist theoretical perspective where learning is viewed as a social entity, social structure referring to the ways people are interrelated or interdependent within their cultural mores as is the norm in an academic setting. The research team identified four categories of operational challenges that the students are most likely to face as university leaners, namely academic, social and emotional, economic and environmental challenges and these formed the basis on which the data collection process ensued. The qualitative methods paradigm was found to appropriate and the study was conducted within the framework of an action research approach. A qualitative research was relevant to the study because it had the capacity to enable the researchers to identify the cognitive views held by in-service students and the meanings they made of their experiences concerning their studies or the program (Hancock, 2004. The research sought to identify where the identified challenges emanated from with a view to make those involved in the academic paths of these learners to take heed of their problems. The study found that in-service learners are faced with all sorts of problems including lack of accommodation on campus, uncooperative lecturers, the university system which lumps them together with pre-service students making them academic prisoners, large class sizes which render learning a near impossibility for some, and the fast

Mathematics in the Workplace: Issues and Challenges

NARCIS (Netherlands)

Hoyles, C.; Noss, R.; Kent, P.; Bakker, A.

2013-01-01

In political and educational debate, there is contrary opinion about the mathematical needs of employees. Several influential studies report that, apart from recognizing the need for a small layer of ‘symbolic analysts’ (Reich 1992), employers do not prioritize mathematical skills (e.g., Department

Mathematics for energy

International Nuclear Information System (INIS)

Snow, D.R.

1975-01-01

This paper provides mathematicians and other persons interested in energy problems with some ideas of the kinds of mathematics being applied and a few ideas for further investigation both in the relevant mathematics and in mathematical modeling. This paper is not meant to be an extensive bibliography on the subject, but references are provided. The Conference emphasized large scale and economic considerations related to energy rather than specific technologies, but additional mathematical problems arising in current and future technologies are suggested. Several of the papers dealt with linear programming models of large scale systems related to energy. These included economic models, policy models, energy sector models for supply and demand and environmental concerns. One of the economic models utilized variational techniques including such things as the Hamiltonian, the Euler-Lagrange differential equation, transversality and natural boundary conditions

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…

Using Google Apps to Develop the Mathematical Practices

Science.gov (United States)

Layton, Rebecca D.; Cady, Jo Ann; Layton, Christopher A.

2017-01-01

Recent recommendations for the teaching of mathematics place an emphasis on the Common Core's Standards for Mathematical Practice (SMP) (CCSSI 2010). The SMPs emphasize constructing viable arguments, critiquing the ideas of others, reasoning abstractly and quantitatively, and using computational procedures. These skills, including the use of…

Two Project-Based Strategies in an Interdisciplinary Mathematical Modeling in Biology Course

Science.gov (United States)

Ludwig, Patrice; Tongen, Anthony; Walton, Brian

2018-01-01

James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…

An introduction to mathematical cryptography

CERN Document Server

Hoffstein, Jeffrey; Silverman, Joseph H

2014-01-01

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cr...

Conference Cultures of Mathematics and Logic

CERN Document Server

Löwe, Benedikt; Müller, Thomas; Xie, Yun

2016-01-01

This book gathers the proceedings of the conference "Cultures of Mathematics and Logic," held in Guangzhou, China. The event was the third in a series of interdisciplinary, international conferences emphasizing the cultural components of philosophy of mathematics and logic. It brought together researchers from many disciplines whose work sheds new light on the diversity of mathematical and logical cultures and practices. In this context, the cultural diversity can be diachronical (different cultures in different historical periods), geographical (different cultures in different regions), or sociological in nature.

Celebrate Mathematical Curiosity

Science.gov (United States)

Redford, Christine

2011-01-01

Children's mathematical questions are often based in real-world experiences, as they instinctively make connections to the world around them. In teaching math methods courses, this author recently started to emphasize the importance of fostering curiosity in, and activating the thinking of, the students. In this article, she describes how to tap…

Mathematical Literacy: A new literacy or a new mathematics?

Directory of Open Access Journals (Sweden)

Renuka Vithal

2006-10-01

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

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...

Mathematics Reform Curricula and Special Education: Identifying Intersections and Implications for Practice

Science.gov (United States)

Sayeski, Kristin L.; Paulsen, Kim J.

2010-01-01

In many general education classrooms today, teachers are using "reform" mathematics curricula. These curricula emphasize the application of mathematics in real-life contexts and include such practices as collaborative, group problem solving and student-generated algorithms. Students with learning disabilities in the area of mathematics can…

Debates on the Basic Education Curriculum Reform and Teachers' Challenges in China: The Case of Mathematics

Science.gov (United States)

Li, Qiong; Ni, Yu-jing

2012-01-01

Focusing on the case of mathematics, this paper reviews debates on China's new Basic Education Curriculum Reform program, including the status of knowledge within the reformed curriculum, the arrangement of the curriculum system, and the push toward real-life applicability and hands-on participation. It discusses the related challenges that…

Teachers' Pedagogical Mathematical Awareness in Swedish Early Childhood Education

Science.gov (United States)

Björklund, Camilla; Barendregt, Wolmet

2016-01-01

Revised guidelines for Swedish early childhood education that emphasize mathematics content and competencies in more detail than before raise the question of the status of pedagogical mathematical awareness among Swedish early childhood teachers. The purpose of this study is to give an overview of teachers' current pedagogical mathematical…

Mathematical Teaching Strategies: Pathways to Critical Thinking and Metacognition

OpenAIRE

Su, Hui Fang Huang " Ricci, Frederick A; Mnatsakanian, Mamikon

2015-01-01

A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible solutions and evaluating and justifying their reasons for the results, thereby allowing students to become confident critical thinkers. Critical th...

From the University to the Classroom: Prospective Elementary Mathematics Specialists' Pedagogical Shifts

Science.gov (United States)

Myers, Kayla D.; Swars, Susan L.; Smith, Stephanie Z.

2016-01-01

This project focuses on the development of prospective Elementary Mathematics Specialists (EMSs) in a K-5 Mathematics Endorsement Program. Program courses emphasized elementary mathematics content and pedagogy while providing opportunities for participants to evidence their learning through classroom teaching practice, all in an attempt to…

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…

What Is the Problem in Problem-Based Learning in Higher Education Mathematics

Science.gov (United States)

Dahl, Bettina

2018-01-01

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge…

USING TASK LIKE PISA’S PROBLEM TO SUPPORT STUDENT’S CREATIVITY IN MATHEMATICS

Directory of Open Access Journals (Sweden)

Rita Novita

2016-01-01

Full Text Available Creativity is one of keys to success in the evolving global economy and also be a fundamental skill that is absolutely necessary in the 21st century. Also In mathematics, creativity or thinking creatively is important to be developed because creativity is an integral part of mathematics. However, limiting the use of creativity in the classroom reduces mathematics to a set of skills to master and rules to memorize. Doing so causes many children’s natural curiosity and enthusiasm for mathematics to disappear as they get older, creating a tremendous problem for mathematics educators who are trying to instil these very qualities. In order to investigate the increase in awareness of elementary school students’ creativity in solving mathematics’ problems by using task like PISA’s Question, a qualitative research emphasizing on holistic description was conducted. We used a formative evaluation type of development research as a mean to develop mathematical tasks like PISA’s question that have potential effect to support students’ creativity in mathematics. Ten elementary school students of grade 6 in Palembang were involved in this research. They judged the task given for them is very challenging and provokes their curiosity. The result showed that task like PISA’s question can encourage students to more creatively in mathematics.Key Words: PISA, Problem Solving, Creativity in Mathematics DOI: http://dx.doi.org/10.22342/jme.7.1.2815.31-42

Partial differential equations of mathematical physics and integral equations

CERN Document Server

Guenther, Ronald B

1996-01-01

This book was written to help mathematics students and those in the physical sciences learn modern mathematical techniques for setting up and analyzing problems. The mathematics used is rigorous, but not overwhelming, while the authors carefully model physical situations, emphasizing feedback among a beginning model, physical experiments, mathematical predictions, and the subsequent refinement and reevaluation of the physical model itself. Chapter 1 begins with a discussion of various physical problems and equations that play a central role in applications. The following chapters take up the t

Developing a pedagogical problem solving view for mathematics teachers with two reflection programs

Directory of Open Access Journals (Sweden)

Bracha KRAMARSKI

2009-10-01

Full Text Available The study investigated the effects of two reflection support programs on elementary school mathematics teachers’ pedagogical problem solving view. Sixty-two teachers participated in a professional development program. Thirty teachers were assigned to the self-questioning (S_Q training and thirty two teachers were assigned to the reflection discourse (R_D training. The S_Q program was based on the IMPROVE self-questioning approach which emphasizes systematic discussion along the phases of mathematical or pedagogical problem solving as student and teacher. The R_D program emphasized discussion of standard based teaching and learning principles. Findings indicated that systematic reflection support (S_Q is effective for developing mathematics PCK, and strengthening metacognitive knowledge of mathematics teachers, more than reflection discourse (R_D. No differences were found between the groups in developing beliefs about teaching mathematics in using problem solving view.

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

GENERAL TASKS OF MATHEMATICAL EDUCATION DEVELOPMENT

Directory of Open Access Journals (Sweden)

V. A. Testov

2014-01-01

Full Text Available The paper discusses basic implementation aspects of the Mathematical Education Development Concept, adopted by the Russian Government in 2013. According to the above document, the main problems of mathematical education include: low motivation of secondary and higher school students for studying the discipline, resulted from underestimation of mathematical knowledge; and outdated educational content, overloaded by technical elements. In the author’s opinion, a number of important new mathematical fields, developed over the last years, - the graph theory, discrete mathematics, encoding theory, fractal geometry, etc – have a large methodological and applied educational potential. However, these new subdisciplines have very little representation both in the secondary and higher school mathematical curricula. As a solution for overcoming the gap between the latest scientific achievements and pedagogical practices, the author recommends integration of the above mentioned mathematical disciplines in educational curricula instead of some outdated technical issues. In conclusion, the paper emphasizes the need for qualified mathematical teachers’ training for solving the problems of students’ motivation development and content updates.

Partial differential equations of mathematical physics

CERN Document Server

Sobolev, S L

1964-01-01

Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math

Mathematics education a spectrum of work in mathematical sciences departments

CERN Document Server

Hsu, Pao-sheng; Pollatsek, Harriet

2016-01-01

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

University of Chicago School Mathematics Project 6-12 Curriculum. What Works Clearinghouse Intervention Report

Science.gov (United States)

What Works Clearinghouse, 2011

2011-01-01

The "University of Chicago School Mathematics Project ("UCSMP") 6-12 Curriculum" is a series of yearlong courses--(1) Transition Mathematics; (2) Algebra; (3) Geometry; (4) Advanced Algebra; (5) Functions, Statistics, and Trigonometry; and (6) Precalculus and Discrete Mathematics--emphasizing problem solving, real-world applications, and the use…

Mathematics for What? High School Students Reflect on Mathematics as a Tool for Social Inquiry

Science.gov (United States)

Brelias, Anastasia

2015-01-01

This study examines high school students' views of mathematics as a tool for social inquiry in light of their classroom experiences using mathematics to explore social issues. A critical theoretical perspective on mathematics literacy is used to ascertain the ways in which their views challenge or affirm the dominant image of mathematics in…

Addressing current challenges in cancer immunotherapy with mathematical and computational modelling.

Science.gov (United States)

Konstorum, Anna; Vella, Anthony T; Adler, Adam J; Laubenbacher, Reinhard C

2017-06-01

The goal of cancer immunotherapy is to boost a patient's immune response to a tumour. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumour microenvironment, immune-modulating effects of conventional treatments and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modelling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumour classification, optimal treatment scheduling and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modellers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumour-immune biology. We conclude the review with recommendations for modellers both with respect to methodology and biological direction that might help keep modellers at the forefront of cancer immunotherapy development. © 2017 The Author(s).

Nuclear medicine and mathematics

Energy Technology Data Exchange (ETDEWEB)

Pedroso de Lima, J.J. [Dept. de Biofisica e Proc. de Imagem, IBILI - Faculdade de Medicina, Coimbra (Portugal)

1996-06-01

The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: Physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently usede in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: They are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new `allies` of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking. (orig.)

Nuclear medicine and mathematics

International Nuclear Information System (INIS)

Pedroso de Lima, J.J.

1996-01-01

The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: Physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently usede in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: They are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new 'allies' of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking. (orig.)

Computer-Based Mathematics Instructions for Engineering Students

Science.gov (United States)

Khan, Mustaq A.; Wall, Curtiss E.

1996-01-01

Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.

Mathematical Models of Breast and Ovarian Cancers

Science.gov (United States)

Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron

2016-01-01

Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, since answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible, in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. PMID:27259061

International Conference on Applied Mathematics and Informatics

CERN Document Server

Vasilieva, Olga

2015-01-01

This book highlights recent compelling research results and trends in various aspects of contemporary mathematics, emphasizing applications to real-world situations. The chapters present exciting new findings and developments in situations where mathematical rigor is combined with common sense. A multi-disciplinary approach, both within each chapter and in the volume as a whole, leads to practical insights that may result in a more synthetic understanding of specific global issues—as well as their possible solutions. The volume will be of interest not only to experts in mathematics, but also to graduate students, scientists, and practitioners from other fields including physics, biology, geology, management, and medicine.

Foundation and Mathematical Uses of Higher Types

DEFF Research Database (Denmark)

Kohlenbach, Ulrich

2002-01-01

This paper addresses `1),' to which S. Feferman has contributed so profoundly. We study mathematical strong, but nevertheless PRA-reducible, systems in all finite types, emphasizing the need of third order variables already for a faithful formalization of continuous functions between Polish spaces...

The Emergence of Mathematical Structures

Science.gov (United States)

Hegedus, Stephen John; Moreno-Armella, Luis

2011-01-01

We present epistemological ruptures that have occurred in mathematical history and in the transformation of using technology in mathematics education in the twenty-first century. We describe how such changes establish a new form of digital semiotics that challenges learning paradigms and mathematical inquiry for learners today. We focus on drawing…

Pre-service teachers’ challenges in presenting mathematical problems

Science.gov (United States)

Desfitri, R.

2018-01-01

The purpose of this study was to analyzed how pre-service teachers prepare and assigned tasks or assignments in teaching practice situations. This study was also intended to discuss about kind of tasks or assignments they gave to students. Participants of this study were 15 selected pre-service mathematics teachers from mathematics education department who took part on microteaching class as part of teaching preparation program. Based on data obtained, it was occasionally found that there were hidden errors on questions or tasks assigned by pre-service teachers which might lead their students not to be able to reach a logical or correct answer. Although some answers might seem to be true, they were illogical or unfavourable. It is strongly recommended that pre-service teachers be more careful when posing mathematical problems so that students do not misunderstand the problems or the concepts, since both teachers and students were sometimes unaware of errors in problems being worked on.

Theoretical Basics of Teaching Discrete Mathematics

Directory of Open Access Journals (Sweden)

Y. A. Perminov

2012-01-01

Full Text Available  The paper deals with the research findings concerning the process of mastering the theoretical basics of discrete mathematics by the students of vocational pedagogic profile. The methodological analysis is based on the subject and functions of the modern discrete mathematics and its role in mathematical modeling and computing. The modern discrete mathematics (i.e. mathematics of the finite type structures plays the important role in modernization of vocational training. It is especially rele- vant to training students for vocational pedagogic qualifications, as in the future they will be responsible for training the middle and the senior level specialists in engineer- ing and technical spheres. Nowadays in different industries, there arise the problems which require for their solving both continual – based on the classical mathematical methods – and discrete modeling. The teaching course of discrete mathematics for the future vocational teachers should be relevant to the target qualification and aimed at mastering the mathematical modeling, systems of computer mathematics and computer technologies. The author emphasizes the fundamental role of mastering the language of algebraic and serial structures, as well as the logical, algorithmic, combinatory schemes dominating in dis- crete mathematics. The guidelines for selecting the content of the course in discrete mathematics are specified. The theoretical findings of the research can be put into practice whilst developing curricula and working programs for bachelors and masters’ training. 

Mathematical Abstraction in the Solving of Ill-Structured Problems by Elementary School Students in Korea

Science.gov (United States)

Hong, Jee Yun; Kim, Min Kyeong

2016-01-01

Ill-structured problems can be regarded as one of the measures that meet recent social needs emphasizing students' abilities to solve real-life problems. This study aimed to analyze the mathematical abstraction process in solving such problems, and to identify the mathematical abstraction level ([I] Recognition of mathematical structure through…

European Success Stories in Industrial Mathematics

CERN Document Server

Esteban, Maria J; Lery, Thibaut; Maday, Yvon

2011-01-01

This unique book presents real world success stories of collaboration between mathematicians and industrial partners, showcasing first-hand case studies, and lessons learned from the experiences, technologies, and business challenges that led to the successful development of industrial solutions based on mathematics. It shows the crucial contribution of mathematics to innovation and to the industrial creation of value, and the key position of mathematics in the handling of complex systems, amplifying innovation. Each story describes the challenge that led to the industrial cooperation, how the

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.

Turkish Primary School Students' Strategies in Solving a Non-Routine Mathematical Problem and Some Implications for the Curriculum Design and Implementation

Science.gov (United States)

Erdogan, Abdulkadir

2015-01-01

Turkish primary mathematics curriculum emphasizes the role of problem solving for teaching mathematics and pays particular attention to problem solving strategies. Patterns as a subject and the use of patterns as a non-routine problem solving strategy are also emphasized in the curriculum. The primary purpose of this study was to determine how…

Choosing High-Yield Tasks for the Mathematical Development of Practicing Secondary Teachers

Science.gov (United States)

Epperson, James A. Mendoza; Rhoads, Kathryn

2015-01-01

Many mathematics teacher educators encounter the challenge of creating or choosing mathematical tasks that evoke important mathematical insights and connections yet remain firmly grounded in school mathematics. This challenge increases substantially when trying to meet the needs of practicing secondary mathematics teachers pursuing graduate work…

Managerial Challenges Within Networks - Emphasizing the Paradox of Network Participation

DEFF Research Database (Denmark)

Jakobsen, Morten

2003-01-01

Flexibility and access to numerous resources are essential benefits associated with network participation. An important aspect of managing the network participation of a company is to maintain a dynamic portfolio of partners, and thereby keep up the strategic opportunities for development. However......, maintaining the dynamics within a network seems to be a complex challenge. There is a risk that the network ends up in The Paradox of Network Participation. The desired renewal and flexibility are not utilised because the involved parties preserve the existing networks structure consisting of the same...... and thereby sort out the paradox of network participation. Trust and information are mechanisms employed to absorb uncertainty. The relationship between trust and the requirement for information depends on the maturity of the relationship. When trust becomes too important as uncertainty absorption mechanism...

Managerial challenges within networks: emphasizing the paradox of network participation

DEFF Research Database (Denmark)

Jakobsen, Morten

Flexibility and access to numerous resources are essential benefits associated with network participation. An important aspect of managing the network participation of a company is to maintain a dynamic portfolio of partners, and thereby keep up the strategic opportunities for development. However......, maintaining the dynamics within a network seems to be a complex challenge. There is a risk that the network ends up in The Paradox of Network Participation. The desired renewal and flexibility are not utilised because the involved parties preserve the existing networks structure consisting of the same...... and thereby sort out the paradox of network participation. Trust and information are mechanisms employed to absorb uncertainty. The relationship between trust and the requirement for information depends on the maturity of the relationship. When trust becomes too important as uncertainty absorption mechanism...

The mysterious connection between mathematics and physics.

Science.gov (United States)

Kauffman, Louis H; Ul-Haq, Rukhsan

2015-12-01

The essay is in the form of a dialogue between the two authors. We take John Wheeler's idea of "It from Bit" as an essential clue and we rework the structure of the bit not to the qubit, but to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We emphasize that mathematics is a combination of calculation and concept. At the conceptual level, mathematics is structured to be independent of time and multiplicity. Mathematics in this way occurs before number and counting. From this timeless domain, mathematics and mathematicians can explore worlds of multiplicity and infinity beyond the apparent limitations of the physical world and see that among these possible worlds there are coincidences with what is observed. Copyright © 2015. Published by Elsevier Ltd.

Berkeley's Philosophy of Mathematics

CERN Document Server

Jesseph, Douglas M

1993-01-01

In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution. Jesseph begins with Berkeley's r

Pre-Service Teachers' Mathematics Language and Reflection in the Context of an Early Childhood Mathematics Methods Course

Science.gov (United States)

Boyd, Soleil

2016-01-01

Preschool teachers are expected to engage young children in challenging and supportive mathematics learning. Rich and responsive language experiences in mathematics support children's language acquisition and engagement related to mathematics, however, such engaging experiences may be minimally available to many young children. Professional…

18th European Conference on Mathematics for Industry

CERN Document Server

Capasso, Vincenzo; Nicosia, Giuseppe; Romano, Vittorio

2016-01-01

This book presents a collection of papers emphasizing applications of mathematical models and methods to real-world problems of relevance for industry, life science, environment, finance, and so on. The biannual Conference of ECMI (the European Consortium of Mathematics in Industry) held in 2014 focused on various aspects of industrial and applied mathematics. The five main topics addressed at the conference were mathematical models in life science, material science and semiconductors, mathematical methods in the environment, design automation and industrial applications, and computational finance. Several other topics have been treated, such as, among others, optimization and inverse problems, education, numerical methods for stiff pdes, model reduction, imaging processing, multi physics simulation, mathematical models in textile industry. The conference, which brought together applied mathematicians and experts from industry, provided a unique opportunity to exchange ideas, problems and methodologies...

Mathematical biology

CERN Document Server

Murray, James D

1993-01-01

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

Embedded Mathematics in Chemistry: A Case Study of Students' Attitudes and Mastery

Science.gov (United States)

Preininger, Anita M.

2017-02-01

There are many factors that shape students' attitudes toward science, technology, engineering and mathematics. This exploratory study of high school students examined the effect of enriching chemistry with math on chemistry students' attitudes toward math and careers involving math. To measure student attitudes, a survey was administered before and after the 18-week chemistry class; results from the chemistry class were compared to survey results from students in an elective science class that did not emphasize mathematics. At the end of the 18-week period, only the chemistry students exhibited more positive views toward their abilities in mathematics and careers that involve mathematics, as compared to their views at the outset of the course. To ensure that chemistry mastery was not hindered by the additional emphasis on math, and that mastery on state end-of-course examinations reflected knowledge acquired during the math-intensive chemistry class, a chemistry progress test was administered at the start and end of the term. This exploratory study suggests that emphasizing mathematical approaches in chemistry may positively influence attitudes toward math in general, as well as foster mastery of chemistry content.

Logic and discrete mathematics a concise introduction

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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

Sustaining Integrated Technology in Undergraduate Mathematics

Science.gov (United States)

Oates, Greg

2011-01-01

The effective integration of technology into the teaching and learning of mathematics remains one of the critical challenges facing contemporary tertiary mathematics. This article reports on some significant findings of a wider study investigating the use of technology in undergraduate mathematics. It first discusses a taxonomy developed to…

Interactions Between Mathematics and Physics

DEFF Research Database (Denmark)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a var......In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined...... it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction...... of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student...

Advances in mathematical economics

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Maruyama, Toru

2015-01-01

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

Advances in mathematical economics

CERN Document Server

Maruyama, Toru

2014-01-01

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

Advances in mathematical economics

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Yamazaki, Akira

2006-01-01

A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.

Mentoring in mathematics education

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Hyde, Rosalyn

2013-01-01

Designed to support both teachers and university-based tutors in mentoring pre-service and newly qualified mathematics teachers at both primary and secondary levels, Mentoring Mathematics Teachers offers straightforward practical advice that is based on practice, underpinned by research, and geared specifically towards this challenging subject area.Developed by members of The Association of Mathematics Education Teachers, the authors draw upon the most up-to-date research and theory to provide evidence-based practical guidance. Themes covered include:

Advances in mathematical economics

CERN Document Server

Yamazaki, Akira

2006-01-01

A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions.Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.

Advances in mathematical economics

CERN Document Server

Maruyama, Toru

2017-01-01

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

Advances in mathematical economics

CERN Document Server

Maruyama, Toru

2016-01-01

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

Under Threes' Mathematical Learning

Science.gov (United States)

Franzén, Karin

2015-01-01

The article focuses on mathematics for toddlers in preschool, with the aim of challenging a strong learning discourse that mainly focuses on cognitive learning. By devoting more attention to other perspectives on learning, the hope is to better promote children's early mathematical development. Sweden is one of few countries to have a curriculum…

Establishing a mathematical Lesson Study culture in Danish teacher education

DEFF Research Database (Denmark)

Skott, Charlotte Krog; Østergaard, Camilla Hellsten

Bridging theory and practice is a general challenge in mathematics teacher education. Research shows that Lesson Study (LS) is an effective way for prospective mathematics teachers to build relations between course work and field experiences......Bridging theory and practice is a general challenge in mathematics teacher education. Research shows that Lesson Study (LS) is an effective way for prospective mathematics teachers to build relations between course work and field experiences...

Mathematical Investigations for Supporting Pre-Service Primary Teachers Repeating a Mathematics Education Course

Science.gov (United States)

Bailey, Judy

2014-01-01

Preparing to become an effective primary school mathematics teacher is a challenging and complex task; and is influenced by one's past experiences, personal knowledge of, and beliefs and attitudes towards mathematics. This paper examines the experiences of a small group of pre-service teachers who did not pass their first year mathematics…

Mathematical and physical theory of turbulence

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Cannon, John

2006-01-01

Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts. These challenges call for the advancement and application of new physical concepts, mathematical modeling, and analysis techniques. Bringing together experts from physics, applied mathematics, and engineering, Mathematical and Physical Theory of Turbulence discusses recent progress and some of the major unresolved issues in two- and three-dimensional turbulence as well as scalar compressible turbulence. Containing introductory overviews as well as more specialized sections, this book examines a variety of turbulence-related topics. The authors concentrate on theory, experiments, computational, and mathematical aspects of Navier-Stokes turbulence; geophysical flows; modeling; laboratory experiments; and compressible/magnetohydrodynamic effects. The topics discussed in these areas include finite-time singularities a...

The Mathematical Intelligence Seen through the Lens of the Montessori Theory of the Human Tendencies.

Science.gov (United States)

Baker, Kay M.

1996-01-01

Contextualizes the mathematical intelligence as revealed in the human tendencies, as supported by the extended family, and facilitated by choice within a responsive environment. Reviews the function of Montessori materials, including mathematical materials, and emphasizes that the personal intelligences are integral to all activities simply…

Difference, inclusion, and mathematics education

DEFF Research Database (Denmark)

Figueiras, Lourdes; Healy, Lulu; Skovsmose, Ole

2016-01-01

The round-table discussion on Difference, Inclusion and Mathematics Education was in included in the scientific programme of VI SIPEM in recognition and celebration of the emerging body of research into the challenges of building a culture of mathematics education which values and respects the di...

Lectures on the mathematics of quantum mechanics I

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Dell'Antonio, Gianfausto

2015-01-01

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving th...

Mathematical tapas

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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.

Advanced engineering mathematics

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Jeffrey, Alan

2001-01-01

Advanced Engineering Mathematics provides comprehensive and contemporary coverage of key mathematical ideas, techniques, and their widespread applications, for students majoring in engineering, computer science, mathematics and physics. Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations. The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) th...

Situated Mathematics Teaching within Electrical Engineering Courses

Science.gov (United States)

Hennig, Markus; Mertsching, Bärbel; Hilkenmeier, Frederic

2015-01-01

The initial phase of undergraduate engineering degree programmes often comprises courses requiring mathematical expertise which in some cases clearly exceeds school mathematics, but will be imparted only later in mathematics courses. In this article, an approach addressing this challenge by way of example within a "fundamentals of electrical…

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

Science.gov (United States)

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

2016-01-01

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

Emotions in the mathematics knowledge’s desertion

Directory of Open Access Journals (Sweden)

Alfonso Jiménez Espinosa,

2010-01-01

Full Text Available The natural wearing out of students has become one of the most worrying problems for universities, but underlies another, dropping out of mathematical knowledge, which is one of the causes of the first. The mathematics learning occurs mainly in class and there is where the concept interstructuring, the network of relationships, emotions, attitudes and beliefs among the known and the new, acquire a meaning and where the student learns. This research investigates the relationship between emotions and mathematics’ learning in students at the Geological Engineering Program of the UPTC. Through the case study and the “Theoretically informed” approach is shown the intricate relationship between emotionality and the construction of mathematical structures. Weconclude that emotions, especially negative ones arise because of the inability to achieve a cognitive balance, leading the student to change his action domain, preventing the construction of mathematical knowledge. It is emphasized that these negative emotions have different origin, especially those generated by beliefs about mathematics and the unfortunate attitude of teachers.

Mathematical modeling with multidisciplinary applications

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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

Amidst Multiple Theories of Learning in Mathematics Education

Science.gov (United States)

Simon, Martin A.

2009-01-01

Currently, there are more theories of learning in use in mathematics education research than ever before (Lerman & Tsatsaroni, 2004). Although this is a positive sign for the field, it also has brought with it a set of challenges. In this article, I identify some of these challenges and consider how mathematics education researchers might think…

When Mathematics and Statistics Collide in Assessment Tasks

Science.gov (United States)

Bargagliotti, Anna; Groth, Randall

2016-01-01

Because the disciplines of mathematics and statistics are naturally intertwined, designing assessment questions that disentangle mathematical and statistical reasoning can be challenging. We explore the writing statistics assessment tasks that take into consideration potential mathematical reasoning they may inadvertently activate.

Emergent Computation Emphasizing Bioinformatics

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Simon, Matthew

2005-01-01

Emergent Computation is concerned with recent applications of Mathematical Linguistics or Automata Theory. This subject has a primary focus upon "Bioinformatics" (the Genome and arising interest in the Proteome), but the closing chapter also examines applications in Biology, Medicine, Anthropology, etc. The book is composed of an organized examination of DNA, RNA, and the assembly of amino acids into proteins. Rather than examine these areas from a purely mathematical viewpoint (that excludes much of the biochemical reality), the author uses scientific papers written mostly by biochemists based upon their laboratory observations. Thus while DNA may exist in its double stranded form, triple stranded forms are not excluded. Similarly, while bases exist in Watson-Crick complements, mismatched bases and abasic pairs are not excluded, nor are Hoogsteen bonds. Just as there are four bases naturally found in DNA, the existence of additional bases is not ignored, nor amino acids in addition to the usual complement of...

Mathematics Teachers' Response to the Reform Agenda: Results of the 1993 National Survey of Science and Mathematics Education.

Science.gov (United States)

Weiss, Iris R.

The NCTM Standards call for the introduction of challenging mathematics content for all students beginning in the early grades. If teachers are to guide students in their exploration of mathematics concepts, they must themselves have a firm grasp of powerful mathematics concepts. This paper uses data from the 1993 National Survey of Science and…

ICT- The Educational Programs in Teaching Mathematics

Directory of Open Access Journals (Sweden)

Dance Sivakova

2017-08-01

Full Text Available The range of information and communication technology in teaching mathematics is unlimited. Despite numerous researches about the opportunities and application of the ICT in teaching mathematics and in the world, however, many aspects remain unexplored. This research comes to knowledge that will be applicable to the educational practice. The findings will serve as motivation for more frequent use of the ICT in teaching mathematics from first to fifth grade as a mean for improving of the educational process. Through application of the ICT in the educational programs in teaching mathematics the technological improved practice is investigated and discussed and it helps overcoming of the challenges that arise when trying to integrate the ICT in the educational curricula in mathematics. The biggest challenge are the findings about the possibilities of the application of the ICT in the educational programs in math from first to fifth grade as well as their dissemination, all aimed to improving of teaching mathematics from the first to the fifth grade. The application of the most ICT in the educational programs of mathematics affects the training of the students for easier adoption of the mathematical concepts and the mathematical procedures and in the easier identification and resolving problem situations.

Mathematical physiology

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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. ...

Interactions between Mathematics and Physics: The History of the Concept of Function--Teaching with and about Nature of Mathematics

Science.gov (United States)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…

What is the problem in problem-based learning in higher education mathematics

Science.gov (United States)

Dahl, Bettina

2018-01-01

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.

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.

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

Science.gov (United States)

Nagle, Courtney; Moore-Russo, Deborah

2014-01-01

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

Discrete mathematics in deaf education: a survey of teachers' knowledge and use.

Science.gov (United States)

Pagliaro, Claudia M; Kritzer, Karen L

The study documents what deaf education teachers know about discrete mathematics topics and determines if these topics are present in the mathematics curriculum. Survey data were collected from 290 mathematics teachers at center and public school programs serving a minimum of 120 students with hearing loss, grades K-8 or K-12, in the United States. Findings indicate that deaf education teachers are familiar with many discrete mathematics topics but do not include them in instruction because they consider the concepts too complicated for their students. Also, regardless of familiarity level, deaf education teachers are not familiar with discrete mathematics terminology; nor is their mathematics teaching structured to provide opportunities to apply the real-world-oriented activities used in discrete mathematics instruction. Findings emphasize the need for higher expectations of students with hearing loss, and for reform in mathematics curriculum and instruction within deaf education.

17th European Conference on Mathematics for Industry

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Günther, Michael; Marheineke, Nicole

2014-01-01

This book contains the proceedings of the 17th European Conference on Mathematics for Industry, ECMI2012, held in Lund, Sweden, July 2012, at which ECMI celebrated its 25th anniversary. It covers mathematics in a wide range of applications and methods, from circuit and electromagnetic devices, environment, fibers, flow, medicine, robotics and automotive industry, further applications to methods and education. The book includes contributions from leading figures in business, science and academia who promote the application of mathematics to industry and emphasize industrial sectors that offer the most exciting opportunities. The contributions reinforce the role of mathematics as being a catalyst for innovation as well as an overarching resource for industry and business. The book features an accessible presentation of real-world problems in industry and finance, provides insight and tools for engineers and scientists which will help them to solve similar problems, and offers modeling and simulation techniques ...

Mathematical theories of distributed sensor networks

CERN Document Server

Iyengar, Sitharama S; Balakrishnan, N

2014-01-01

Mathematical Theory of Distributed Sensor Networks demonstrates how mathematical theories can be used to provide distributed sensor modeling and to solve important problems such as coverage hole detection and repair. The book introduces the mathematical and computational structure by discussing what they are, their applications and how they differ from traditional systems. The text also explains how mathematics are utilized to provide efficient techniques implementing effective coverage, deployment, transmission, data processing, signal processing, and data protection within distributed sensor networks. Finally, the authors discuss some important challenges facing mathematics to get more incite to the multidisciplinary area of distributed sensor networks.

Mathematical manipulative models: in defense of "beanbag biology".

Science.gov (United States)

Jungck, John R; Gaff, Holly; Weisstein, Anton E

2010-01-01

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

Contributions from Sociology of Science to Mathematics Education in Brazil: Logic as a System of Beliefs

Science.gov (United States)

Novaes de Andrade, Thales Haddad; Vilela, Denise Silva

2013-01-01

In Brazil, mathematics education was associated with Jean Piaget's theory. Scholars in the field of education appropriated Piaget's work in different ways, but usually emphasized logical aspects of thought, which probably lead to an expansion of mathematics education influenced by psychology. This study attempts to extend the range of…

Mathematical methods in systems biology.

Science.gov (United States)

Kashdan, Eugene; Duncan, Dominique; Parnell, Andrew; Schattler, Heinz

2016-12-01

The editors of this Special Issue of Mathematical Biosciences and Engineering were the organizers for the Third International Workshop "Mathematical Methods in System Biology" that took place on June 15-18, 2015 at the University College Dublin in Ireland. As stated in the workshop goals, we managed to attract a good mix of mathematicians and statisticians working on biological and medical applications with biologists and clinicians interested in presenting their challenging problems and looking to find mathematical and statistical tools for their solutions.

Chern-Simons terms and cocycles in physics and mathematics

Energy Technology Data Exchange (ETDEWEB)

Jackiw, R.

1984-12-01

Contemporary topological research in Yang-Mills theory is reviewed, emphasizing the Chern-Simons terms and their relatives. Three applications of the Chern-Simons terms in physical theory are described: to help understanding gauge theories in even dimensional space-time; gauge field dynamics in odd dimensional space-time; and mathematically coherent description of even-dimensional gauge theories with chiral fermions that are apparently inconsistent due to chiral anomalies. Discussion of these applications is preceded by explanation of the mathematical preliminaries and examples in simple quantum mechanical settings. 24 refs. (LEW)

Solutions manual to accompany finite mathematics models and applications

CERN Document Server

Morris, Carla C

2015-01-01

A solutions manual to accompany Finite Mathematics: Models and Applications In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on pr

Which Preschool Mathematics Competencies Are Most Predictive of Fifth Grade Achievement?

Science.gov (United States)

Nguyen, Tutrang; Watts, Tyler W.; Duncan, Greg J.; Clements, Douglas H.; Sarama, Julie S.; Wolfe, Christopher; Spitler, Mary Elaine

2016-01-01

In an effort to promote best practices regarding mathematics teaching and learning at the preschool level, national advisory panels and organizations have emphasized the importance of children’s emergent counting and related competencies, such as the ability to verbally count, maintain one-to-one correspondence, count with cardinality, subitize, and count forward or backward from a given number. However, little research has investigated whether the kind of mathematical knowledge promoted by the various standards documents actually predict later mathematics achievement. The present study uses longitudinal data from a primarily low-income and minority sample of children to examine the extent to which preschool mathematical competencies, specifically basic and advanced counting, predict fifth grade mathematics achievement. Using regression analyses, we find early numeracy abilities to be the strongest predictors of later mathematics achievement, with advanced counting competencies more predictive than basic counting competencies. Our results highlight the significance of preschool mathematics knowledge for future academic achievement. PMID:27057084

Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory

Science.gov (United States)

Tweney, Ryan D.

2011-07-01

James Clerk Maxwell `translated' Michael Faraday's experimentally-based field theory into the mathematical representation now known as `Maxwell's Equations.' Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other results in the physics of electricity and magnetism. Examination of Maxwell's procedures opens many issues about the role of mathematical representation in physics and the learning background required for its success. Specifically, Maxwell's training in `Cambridge University' mathematical physics emphasized the use of analogous equations across fields of physics and the repeated solving of extremely difficult problems in physics. Such training develops an array of overlearned mathematical representations supported by highly sophisticated cognitive mechanisms for the retrieval of relevant information from long term memory. For Maxwell, mathematics constituted a new form of representation in physics, enhancing the formal derivational and calculational role of mathematics and opening a cognitive means for the conduct of `experiments in the mind' and for sophisticated representations of theory.

Applied & Computational MathematicsChallenges for the Design and Control of Dynamic Energy Systems

Energy Technology Data Exchange (ETDEWEB)

Brown, D L; Burns, J A; Collis, S; Grosh, J; Jacobson, C A; Johansen, H; Mezic, I; Narayanan, S; Wetter, M

2011-03-10

The Energy Independence and Security Act of 2007 (EISA) was passed with the goal 'to move the United States toward greater energy independence and security.' Energy security and independence cannot be achieved unless the United States addresses the issue of energy consumption in the building sector and significantly reduces energy consumption in buildings. Commercial and residential buildings account for approximately 40% of the U.S. energy consumption and emit 50% of CO{sub 2} emissions in the U.S. which is more than twice the total energy consumption of the entire U.S. automobile and light truck fleet. A 50%-80% improvement in building energy efficiency in both new construction and in retrofitting existing buildings could significantly reduce U.S. energy consumption and mitigate climate change. Reaching these aggressive building efficiency goals will not happen without significant Federal investments in areas of computational and mathematical sciences. Applied and computational mathematics are required to enable the development of algorithms and tools to design, control and optimize energy efficient buildings. The challenge has been issued by the U.S. Secretary of Energy, Dr. Steven Chu (emphasis added): 'We need to do more transformational research at DOE including computer design tools for commercial and residential buildings that enable reductions in energy consumption of up to 80 percent with investments that will pay for themselves in less than 10 years.' On July 8-9, 2010 a team of technical experts from industry, government and academia were assembled in Arlington, Virginia to identify the challenges associated with developing and deploying newcomputational methodologies and tools thatwill address building energy efficiency. These experts concluded that investments in fundamental applied and computational mathematics will be required to build enabling technology that can be used to realize the target of 80% reductions in energy

Peculiarities of mathematics instruction for beginners for children with disabilities in regular primary schools

Directory of Open Access Journals (Sweden)

Jablan Branka

2010-01-01

Full Text Available The paper studies the issue of education of visually impaired children, hearing impaired children and children with intellectual disabilities in regular primary schools in the context of mathematics instruction for beginners. The authors state the basic characteristics of mathematics instruction for beginners with respect to the contents studied in the first four grades of primary school, as well as the key problems and educational needs of visually impaired children, hearing impaired children and children with intellectual disabilities. The basic characteristics of inclusive education and the key role of teacher in this process are pointed out. Starting from the developmental peculiarities of children with disabilities, the authors emphasize the importance of applying an individualized approach in teaching mathematics. Possible didactic and methodical solutions are discussed, as well as different approaches in teaching this subject that can facilitate learning of mathematical contents to visually impaired children, hearing impaired children and children with intellectual disabilities. Bearing in mind the peculiarities of inclusive education, i.e. the need for the children with disabilities to participate in common activities with the other children in the class, the authors emphasize the importance of encouraging interaction and communication among children in the process of learning mathematical contents.

Mathematical Abstraction: Constructing Concept of Parallel Coordinates

Science.gov (United States)

Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

2017-09-01

Mathematical abstraction is an important process in teaching and learning mathematics so pre-service mathematics teachers need to understand and experience this process. One of the theoretical-methodological frameworks for studying this process is Abstraction in Context (AiC). Based on this framework, abstraction process comprises of observable epistemic actions, Recognition, Building-With, Construction, and Consolidation called as RBC + C model. This study investigates and analyzes how pre-service mathematics teachers constructed and consolidated concept of Parallel Coordinates in a group discussion. It uses AiC framework for analyzing mathematical abstraction of a group of pre-service teachers consisted of four students in learning Parallel Coordinates concepts. The data were collected through video recording, students’ worksheet, test, and field notes. The result shows that the students’ prior knowledge related to concept of the Cartesian coordinate has significant role in the process of constructing Parallel Coordinates concept as a new knowledge. The consolidation process is influenced by the social interaction between group members. The abstraction process taken place in this group were dominated by empirical abstraction that emphasizes on the aspect of identifying characteristic of manipulated or imagined object during the process of recognizing and building-with.

STEM Education: What Does Mathematics Have to Offer?

Science.gov (United States)

Fitzallen, Noleine

2015-01-01

The emphasis on science, technology, engineering, and mathematics (STEM) education in recent times could be perceived as business as usual or as an opportunity for innovation and change in mathematics classrooms. Either option presents challenges for mathematics educators who are expected to contribute to the foundations of a STEM literate…

Integrating Mathematics and Science: Ecology and Venn Diagrams

Science.gov (United States)

Leszczynski, Eliza; Munakata, Mika; Evans, Jessica M.; Pizzigoni, Francesca

2014-01-01

Efforts to integrate mathematics and science have been widely recognized by mathematics and science educators. However, successful integration of these two important school disciplines remains a challenge. In this article, a mathematics and science activity extends the use of Venn diagrams to a life science context and then circles back to a…

Inhibiting Intuitive Thinking in Mathematics Education

Science.gov (United States)

Thomas, Michael O. J.

2015-01-01

The papers in this issue describe recent collaborative research into the role of inhibition of intuitive thinking in mathematics education. This commentary reflects on this research from a mathematics education perspective and draws attention to some of the challenges that arise in collaboration between research fields with different cultures,…

Teachers Implementing Mathematical Problem Posing in the Classroom: Challenges and Strategies

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Leung, Shuk-kwan S.

2013-01-01

This paper reports a study about how a teacher educator shared knowledge with teachers when they worked together to implement mathematical problem posing (MPP) in the classroom. It includes feasible methods for getting practitioners to use research-based tasks aligned to the curriculum in order to encourage children to pose mathematical problems.…

A College-Level Foundational Mathematics Course: Evaluation, Challenges, and Future Directions

Science.gov (United States)

Maciejewski, Wes

2012-01-01

Recently in Ontario, Canada, the College Math Project brought to light startling data on the achievement of students in Ontario's College of Applied Arts and Technology System related to their performance in first-year mathematics courses: one-third of the students had failed their first-year mathematics course or were at risk of not completing…

Mathematical principles of signal processing Fourier and wavelet analysis

CERN Document Server

Brémaud, Pierre

2002-01-01

Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...

Third international handbook of mathematics education

CERN Document Server

Bishop, Alan; Keitel, Christine; Kilpatrick, Jeremy; Leung, Frederick

2013-01-01

This entirely new Third International Handbook of Mathematics Education comprises 31 chapters which have been written by a total of 84 different authors representing 26 nations, each a recognized expert in the field.   Comprised of four sections: Social, Political and Cultural Dimensions in Mathematics Education; Mathematics Education as a Field of Study; Technology in the Mathematics Curriculum; and International Perspectives on Mathematics Education, this Third Handbook offers essential reading for all persons interested in the future of mathematics education. The authors present challenging international perspectives on the history of mathematics education, current issues, and future directions.   What makes this Handbook unique is its structure. Each section covers past, present and future aspects of mathematics education.   The first chapter in each section identifies and analyzes historical antecedents The “middle” chapters draw attention to present-day key issues and themes The final chapter in ...

MATHEMATICS PRACTICES AND THEIR EFFECTS ON FIRST-TO-FOURTH-GRADE TEACHER EDUCATION

Directory of Open Access Journals (Sweden)

Marta Cristina Cezar Pozzobon

2012-12-01

Full Text Available Grounded on Foucauldian studies, we have attempted to understand how mathematics practices have produced effects on first-to-fourth-grade mathematics teachers. We have argued that such effects go beyond the borders of the pedagogical and the contents of this knowledge area, becoming part of a “general policy” of truth that comprehends the conceptions of scientific knowledge, mathematics and teaching of a particular time. The materials here considered were produced in a High School course in the 1990’s. We have realized that the practices of mathematics education in that period could be assessed from three emphases: a education to teach mathematics through the “concrete”, the “logical knowledge” and the “abstract”, showing mathematics teaching practices from a constructivist, science-oriented perspective, b “globalized teaching”, and c “emphasis on reality”. This has enabled us to problematize the mathematical education of first-to-fourth grade teachers produced in those practices.

Mathematical models for lymphatic filariasis transmission and control: Challenges and prospects

Directory of Open Access Journals (Sweden)

Kaliannagounder Krishnamoorthy

2008-02-01

Full Text Available Abstract Background Mathematical models developed for describing the dynamics of transmission, infection, disease and control of lymphatic filariasis (LF gained momentum following the 1997 World Health Assembly resolution and the launching of the Global Programme to Eliminate Lymphatic Filariasis (GPELF in 2000. Model applications could provide valuable inputs for making decisions while implementing large scale programmes. However these models need to be evaluated at different epidemiological settings for optimization and fine-tuning with new knowledge and understanding on infection/disease dynamics. Discussion EPIFIL and LYMFASIM are the two mathematical simulation models currently available for lymphatic filariasis transmission and control. Both models have been used for prediction and evaluation of control programmes under research settings. Their widespread application in evaluating large-scale elimination programmes warrants validation of assumptions governing the dynamics of infection and disease in different epidemiological settings. Furthermore, the predictive power of the models for decision support can be enhanced by generating knowledge on some important issues that pose challenges and incorporating such knowledge into the models. We highlight factors related to the efficacy of the drugs of choice, their mode of action, and the possibility that drug resistance may develop; the role of vector-parasite combinations; the magnitude of transmission thresholds; host-parasite interactions and their effects on the dynamics of infection and immunity; parasite biology, and progression to LF-associated disease. Summary The two mathematical models developed offer potential decision making tools for transmission and control of LF. In view of the goals of the GPELF, the predictive power of these models needs to be enhanced for their wide-spread application in large scale programmes. Assimilation and translation of new information into the models is

Lectures on the mathematics of quantum mechanics II selected topics

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Dell'Antonio, Gianfausto

2016-01-01

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving th...

Freedom in mathematics

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Cartier, Pierre; Heinzmann, Gerhard; Villani, Cédric

2016-01-01

This book challenges the views put forward by Pierre Cartier, one of the anchors of the famous Bourbaki group, and Cédric Villani, one of the most brilliant mathematicians of his generation, who received the Fields Medal in 2010. Jean Dhombres, mathematician and science historian, and Gerhard Heinzmann, philosopher of science and also a specialist in mathematics engage in a fruitful dialogue with the two mathematicians, prompting readers to reflect on mathematical activity and its social consequences in history as well as in the modern world. Cédric Villani’s popular success proves once again that a common awareness has developed, albeit in a very confused way, of the major role of mathematics in the construction and efficiency of natural sciences, which are at the origin of our technologies. Despite this, the idea that mathematics cannot be shared remains firmly entrenched, a perceived failing that has even been branded a lack of culture by vocal forces in the media as well as cultural and political esta...

The competitive challenge in banking

NARCIS (Netherlands)

Boot, A.W.A.; Schmeits, A.

2005-01-01

The increasingly competitive environment poses challenges to bankers. This paper emphasizes relationship banking as a prime source of the banks' comparative advantage. The proliferation of transaction-oriented banking (trading and financial market activities) does however seriously challenge

Discrete mathematics in the high school curriculum

NARCIS (Netherlands)

Anderson, I.; Asch, van A.G.; van Lint, J.H.

2004-01-01

In this paper we present some topics from the field of discrete mathematics which might be suitable for the high school curriculum. These topics yield both easy to understand challenging problems and important applications of discrete mathematics. We choose elements from number theory and various

Note-Taking in a Mathematics Classroom

Science.gov (United States)

Hoong, Leong Yew; Guan, Tay Eng; Seng, Quek Khiok; Fwe, Yap Sook; Luen, Tong Cherng; Toh, Wei Yeng Karen; Chia, Alexander; Teck, Ong Yao

2014-01-01

The authors are a team of teachers and teacher educators who are deeply interested in helping mathematically-challenged students improve in their learning of mathematics. In Singapore, depending on their performance at the end of a nationwide Year 6 examination, students are channelled into three ability streams for Years 7 to 10: Express (60%),…

Students’ Representation in Mathematical Word Problem-Solving: Exploring Students’ Self-efficacy

Science.gov (United States)

Sahendra, A.; Budiarto, M. T.; Fuad, Y.

2018-01-01

This descriptive qualitative research aims at investigating student represented in mathematical word problem solving based on self-efficacy. The research subjects are two eighth graders at a school in Surabaya with equal mathematical ability consisting of two female students with high and low self-efficacy. The subjects were chosen based on the results of test of mathematical ability, documentation of the result of middle test in even semester of 2016/2017 academic year, and results of questionnaire of mathematics word problem in terms of self-efficacy scale. The selected students were asked to do mathematical word problem solving and be interviewed. The result of this study shows that students with high self-efficacy tend to use multiple representations of sketches and mathematical models, whereas students with low self-efficacy tend to use single representation of sketches or mathematical models only in mathematical word problem-solving. This study emphasizes that teachers should pay attention of student’s representation as a consideration of designing innovative learning in order to increase the self-efficacy of each student to achieve maximum mathematical achievement although it still requires adjustment to the school situation and condition.

Some mathematical methods of physics

CERN Document Server

Goertzel, Gerald

2014-01-01

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

First course in mathematical logic

CERN Document Server

Suppes, Patrick

2010-01-01

In modern mathematics, both the theory of proof and the derivation of theorems from axioms bear an unquestioned importance. The necessary skills behind these methods, however, are frequently underdeveloped. This book counters that neglect with a rigorous introduction that is simple enough in presentation and context to permit relatively easy comprehension. It comprises the sentential theory of inference, inference with universal quantifiers, and applications of the theory of inference developed to the elementary theory of commutative groups. Throughout the book, the authors emphasize the perva

Preparing Mathematics Teachers for Technology-Rich Environments

Science.gov (United States)

Sturdivant, Rodney X.; Dunham, Penelope; Jardine, Richard

2009-01-01

This article describes key elements for faculty development programs to prepare mathematics teachers for technology-rich environments. We offer practical examples from our experiences in teaching mathematics with technology and in teaching others to incorporate technology-based pedagogies. We address challenges faced by faculty using technology,…

The Mathematics of Mixing Things Up

Science.gov (United States)

Diaconis, Persi

2011-08-01

How long should a Markov chain Monte Carlo algorithm be run? Using examples from statistical physics (Ehrenfest urn, Ising model, hard discs) as well as card shuffling, this tutorial paper gives an overview of a body of mathematical results that can give useful answers to practitioners (viz: seven shuffles suffice for practical purposes). It points to new techniques (path coupling, geometric inequalities, and Harris recurrence). The discovery of phase transitions in mixing times (the cutoff phenomenon) is emphasized.

Difference, inclusion, and mathematics education

DEFF Research Database (Denmark)

Figueiras, Lourdes; Healy, Lulu; Skovsmose, Ole

2016-01-01

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

International Conference on Quantum Mathematical Physics : a Bridge between Mathematics and Physics

CERN Document Server

Kleiner, Johannes; Röken, Christian; Tolksdorf, Jürgen

2016-01-01

Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fu...

Enhancing Teacher Education in Primary Mathematics with Mobile Technologies

Science.gov (United States)

Schuck, Sandy

2016-01-01

A challenge of teacher education is to produce graduate primary school teachers who are confident and competent teachers of mathematics. Various approaches to primary school teacher education in mathematics have been investigated, but primary teacher education graduates still tend to be diffident in their teaching of mathematics. In an age where…

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

Mathematical stereochemistry

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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.

Frontiers in mathematical biology

CERN Document Server

1994-01-01

Volume 100, which is the final volume of the LNBM series serves to commemorate the acievements in two decades of this influential collection of books in mathematical biology. The contributions, by the leading mathematical biologists, survey the state of the art in the subject, and offer speculative, philosophical and critical analyses of the key issues confronting the field. The papers address fundamental issues in cell and molecular biology, organismal biology, evolutionary biology, population ecology, community and ecosystem ecology, and applied biology, plus the explicit and implicit mathematical challenges. Cross-cuttting issues involve the problem of variation among units in nonlinear systems, and the related problems of the interactions among phenomena across scales of space, time and organizational complexity.

Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra

Science.gov (United States)

Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

2016-01-01

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…

Mayr, mathematics and the study of evolution

Directory of Open Access Journals (Sweden)

Crow James F

2009-02-01

Full Text Available Abstract In 1959 Ernst Mayr challenged the relevance of mathematical models to evolutionary studies and was answered by JBS Haldane in a witty and convincing essay. Fifty years on, I conclude that the importance of mathematics has in fact increased and will continue to do so.

Mathematical modelling in engineering: A proposal to introduce linear algebra concepts

Directory of Open Access Journals (Sweden)

Andrea Dorila Cárcamo

2016-03-01

Full Text Available The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasize the development of mathematical abilities primarily associated with modelling and interpreting, which aren´t limited only to calculus abilities. Considering this, an instructional design was elaborated based on mathematic modelling and emerging heuristic models for the construction of specific linear algebra concepts:  span and spanning set. This was applied to first year engineering students. Results suggest that this type of instructional design contributes to the construction of these mathematical concepts and can also favour first year engineering students understanding of key linear algebra concepts and potentiate the development of higher order skills.

Can Instructional Reform in Urban Middle Schools Help Students Narrow the Mathematics Performance Gap? Some Evidence from the QUASAR Project.

Science.gov (United States)

Silver, Edward A.; Lane, Suzanne

1995-01-01

Compared mathematical performance of middle school students in low-income communities involved in the QUASAR project to those of a demographically similar school and of a nationally representative sample. QUASAR mathematics instruction emphasizes reasoning, problem-solving, and understanding. Quasar students outperformed NAEP's disadvantaged urban…

Mathematical reasoning analogies, metaphors, and images

CERN Document Server

English, Lyn D

2013-01-01

How we reason with mathematical ideas continues to be a fascinating and challenging topic of research--particularly with the rapid and diverse developments in the field of cognitive science that have taken place in recent years. Because it draws on multiple disciplines, including psychology, philosophy, computer science, linguistics, and anthropology, cognitive science provides rich scope for addressing issues that are at the core of mathematical learning. Drawing upon the interdisciplinary nature of cognitive science, this book presents a broadened perspective on mathematics and mat

Acknowledging individual responsibility while emphasizing social determinants in narratives to promote obesity-reducing public policy: a randomized experiment.

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Jeff Niederdeppe

Full Text Available This study tests whether policy narratives designed to increase support for obesity-reducing public policies should explicitly acknowledge individual responsibility while emphasizing social, physical, and economic (social determinants of obesity. We use a web-based, randomized experiment with a nationally representative sample of American adults (n = 718 to test hypotheses derived from theory and research on narrative persuasion. Respondents exposed to narratives that acknowledged individual responsibility while emphasizing obesity's social determinants were less likely to engage in counterargument and felt more empathy for the story's main character than those exposed to a message that did not acknowledge individual responsibility. Counterarguing and affective empathy fully mediated the relationship between message condition and support for policies to reduce rates of obesity. Failure to acknowledge individual responsibility in narratives emphasizing social determinants of obesity may undermine the persuasiveness of policy narratives. Omitting information about individual responsibility, a strongly-held American value, invites the public to engage in counterargument about the narratives and reduces feelings of empathy for a character that experiences the challenges and benefits of social determinants of obesity.

Acknowledging individual responsibility while emphasizing social determinants in narratives to promote obesity-reducing public policy: a randomized experiment.

Science.gov (United States)

Niederdeppe, Jeff; Roh, Sungjong; Shapiro, Michael A

2015-01-01

This study tests whether policy narratives designed to increase support for obesity-reducing public policies should explicitly acknowledge individual responsibility while emphasizing social, physical, and economic (social) determinants of obesity. We use a web-based, randomized experiment with a nationally representative sample of American adults (n = 718) to test hypotheses derived from theory and research on narrative persuasion. Respondents exposed to narratives that acknowledged individual responsibility while emphasizing obesity's social determinants were less likely to engage in counterargument and felt more empathy for the story's main character than those exposed to a message that did not acknowledge individual responsibility. Counterarguing and affective empathy fully mediated the relationship between message condition and support for policies to reduce rates of obesity. Failure to acknowledge individual responsibility in narratives emphasizing social determinants of obesity may undermine the persuasiveness of policy narratives. Omitting information about individual responsibility, a strongly-held American value, invites the public to engage in counterargument about the narratives and reduces feelings of empathy for a character that experiences the challenges and benefits of social determinants of obesity.

Authentic Teaching Experiences in Secondary Mathematics Methods

Science.gov (United States)

Stickles, Paula R.

2015-01-01

Often secondary mathematics methods courses include classroom peer teaching, but many pre-service teachers find it challenging to teach their classmate peers as there are no discipline issues and little mathematical discourse as the "students" know the content. We will share a recent change in our methods course where pre-service…

Building mathematics cellular phone learning communities

Directory of Open Access Journals (Sweden)

Wajeeh M. Daher

2011-04-01

Full Text Available Researchers emphasize the importance of maintaining learning communities and environments. This article describes the building and nourishment of a learning community, one comprised of middle school students who learned mathematics out-of-class using the cellular phone. The building of the learning community was led by three third year pre-service teachers majoring in mathematics and computers. The pre-service teachers selected thirty 8th grade students to learn mathematics with the cellular phone and be part of a learning community experimenting with this learning. To analyze the building and development stages of the cellular phone learning community, two models of community building stages were used; first the team development model developed by Tuckman (1965, second the life cycle model of a virtual learning community developed by Garber (2004. The research findings indicate that a learning community which is centered on a new technology has five 'life' phases of development: Pre-birth, birth, formation, performing, and maturity. Further, the research finding indicate that the norms that were encouraged by the preservice teachers who initiated the cellular phone learning community resulted in a community which developed, nourished and matured to be similar to a community of experienced applied mathematicians who use mathematical formulae to study everyday phenomena.

Mathematics Turned Inside Out: The Intensive Faculty Versus the Extensive Faculty

OpenAIRE

Grcar, Joseph F.

2011-01-01

Research universities in the United States have larger mathematics faculties outside their mathematics departments than inside. Members of this "extensive" faculty conduct most mathematics research, their interests are the most heavily published areas of mathematics, and they teach this mathematics in upper division courses independent of mathematics departments. The existence of this de facto faculty challenges the pertinence of institutional and national policies for higher education in mat...

The Use of GBL to Teach Mathematics in Higher Education

Science.gov (United States)

Naik, Nitin

2017-01-01

Innovation in learning and teaching is an everyday requirement in contemporary higher education (HE), especially in challenging subjects such as mathematics. Teaching mathematics to students with limited experience of formal mathematical instruction is a good example of a demanding pedagogical undertaking where innovatory practice can help HE…

SIMULTANEOUS INTEGRATION OF WATER AND ENERGY: ACHIEVEMENTS AND CHALLENGES

Directory of Open Access Journals (Sweden)

Junior Lorenzo Llanes

2016-01-01

Full Text Available Process Integration (PI is a tool that for over forty years has demonstrated its strength to provide optimal solutions to complex problems. The interaction of exchange systems of energy and water networks is a typical case of such problems. The gradual increase in the consumption of water and energy has determined the development of methodologies that take into account the simultaneous integration of these resources. This paper aims to present a literature review related to the simultaneous integration of water and energy. First, general items related to this research field are presented, emphasizing the approaches to simultaneous integration (Pinch Analysis and Mathematical Programming. Some recent cases of studies, demonstrating the strength of these tools mainly focus to sugar industry, are also presented. Finally some of the challenges to be faced by the simultaneous integration of water and energy for the diversification of the Cuban sugar industry are presented.

Mathematical and conceptual foundations of 20th-century physics

International Nuclear Information System (INIS)

Emch, G.G.

1984-01-01

This volume presents a unified mathematical account of the conceptual foundations of 20th-century Physics. Part 1 provides a survey of classical physics divided in separate chapters on mechanics, thermodynamics and statistical mechanics, and electromagnetism. This study provides opportunities to place in perspective the successive advents of calculus, of probability and statistics, of differential and sympletic geometry, and of classical functional analysis. Relativity is presented in part 2 of this book and quantum theory in part 3. The motivation provided by physical problems in the development of mathematical disciplines such as, for instance, pseudo-Riemannian geometries, Hilbert spaces and operator algebras, are emphasized. (H.W.). refs.; figs.; schemes

Single Sex Mathematics Classes: A Critical Analysis of the Impact at a Secondary School

OpenAIRE

Seifert, Angelique; Pugalee, David K.

2012-01-01

Single sex classes have recently been emphasized as an effective way to promote mathematics learning. Despite their popularity, the research on the effectiveness of such programs is mixed underscoring the need for additional research and discussion. This research is set in one of the twenty-five largest public school systems in the United States, where schools have recently been allowed to begin instructional initiatives with same sex classes in mathematics. Preliminary data on the effecti...

Indicators that influence prospective mathematics teachers representational and reasoning abilities

Science.gov (United States)

Darta; Saputra, J.

2018-01-01

Representational and mathematical reasoning ability are very important ability as basic in mathematics learning process. The 2013 curriculum suggests that the use of a scientific approach emphasizes higher order thinking skills. Therefore, a scientific approach is required in mathematics learning to improve ability of representation and mathematical reasoning. The objectives of this research are: (1) to analyze representational and reasoning abilities, (2) to analyze indicators affecting the ability of representation and mathematical reasoning, (3) to analyze scientific approaches that can improve the ability of representation and mathematical reasoning. The subject of this research is the students of mathematics prospective teachers in the first semester at Private Higher Education of Bandung City. The research method of this research was descriptive analysis. The research data were collected using reasoning and representation tests on sixty-one students. Data processing was done by descriptive analysis specified based on the indicators of representation ability and mathematical reasoning that influenced it. The results of this first-year study showed that students still had many weaknesses in reasoning and mathematical representation that were influenced by the ability to understand the indicators of both capabilities. After observing the results of the first-year research, then in the second and third year, the development of teaching materials with a scientific approach in accordance with the needs of prospective students was planned.

Challenge Beginning Teacher Beliefs

Science.gov (United States)

Lannin, John K.; Chval, Kathryn B.

2013-01-01

As beginning teachers start to recognize the complexity of teaching mathematics in elementary school classrooms and how their new vision for teaching mathematics creates new challenges, they experience discomfort--a healthy awareness that much is to be learned. Brousseau (1997) notes that changes in the roles that are implicitly assigned to the…

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...

Deleuze and the history of mathematics in defence of the 'new'

CERN Document Server

Duffy, Simon

2013-01-01

Gilles Deleuze's engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges are an opportunity to reconfigure particular philosophical problems - for example, the problem of individuation - and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction of Deleuze's philosophy, as well as addressing the undervalued

Special Education Teachers' Views on Using Technology in Teaching Mathematics

Science.gov (United States)

Baglama, Basak; Yikmis, Ahmet; Demirok, Mukaddes Sakalli

2017-01-01

Individuals with special needs require support in acquiring various academic and social skills and mathematical skills are one of the most important skills in which individuals with special needs need to acquire in order to maintain their daily lives. Current approaches in education emphasize the importance of integrating technology into special…

Low and High Achivers in Mathematics

DEFF Research Database (Denmark)

Overgaard, Steffen; Tonnesen, Pia Beck

2016-01-01

achievers - within their first years of schooling think mathematically, as background to initiate more effective teaching of the two groups of students. In autumn 2014, 328 Grade 2 students (born in 2006) received an individual special teaching, early intervention, based on the same model and material, 20...... to enhance the teaching of low and high mathematics achievers so as to increase their mathematical knowledge and confidence.......Every mathematics teacher has a challenge in coping with the gap between low and high achievers in the classroom. The purpose of the the project, Early Math Intervention for Marginalized Students, TMTM 2014, is to bring forth knowledge of how these marginalized students - low as well as high...

Unpacking the Male Superiority Myth and Masculinization of Mathematics at the Intersections: A Review of Research on Gender in Mathematics Education

Science.gov (United States)

Leyva, Luis A.

2017-01-01

Gender research in mathematics education has experienced methodological and theoretical shifts over the past 45 years. Although achievement studies have used assessment tools to explore and subsequently challenge the assumption of male superiority on mathematics assessments, research on participation has unpacked these studies' sex-based…

Logic as a Key to Interdisciplinary Integration for Students in the Mathematical Sciences

Directory of Open Access Journals (Sweden)

Thomas Marlowe

2017-08-01

Full Text Available We describe the creation and development of a course on mathematical logic and its extensions and limitations, in which coverage of technical material is interleaved with and related to discussion of relevant historical, linguistic, philosophical, and theological issues and of individuals of note. The new course, Logic, Limitations to Knowledge, and Christianity, presents an overview of topics in and related to logic, including development of formal logic and an axiomatic first-order logic. It explores the history of mathematics and logic in the Catholic Intellectual and wider Western Traditions, as well as the mutual interactions of mathematics, philosophy, language, and religion. It then considers extensions of first-order logic, and provable limits to knowledge: the three unsolvable problems of Euclidean geometry, and examples from Gödel, Turing, Arrow, quantum physics, and others. Epistemological issues will be emphasized throughout the course. The translation between natural language and expression in logical and reasoning formalisms is emphasized throughout. As a Core Curriculum course at Seton Hall University, fundamental questions such as "What is logic?" and "What are its limits?" will be considered within the framework of Christianity's broader view of the human person and human intelligence.

Perspectives on instructor modeling in mathematics teacher education

OpenAIRE

Brown, Cassondra

2009-01-01

Teachers' instructional practices are greatly shaped by their own learning experiences as students in K-12 and college classrooms, which for most teachers was traditional, teacher-centered instruction. One of the challenges facing mathematics education reform is that, traditional teaching is in contrast to reform student- centered instruction. If teachers learn from their experiences as mathematics students, mathematics teacher educators are encouraged to model practices they would like teach...

Building innovative and creative character through mathematics

Science.gov (United States)

Suyitno, Hardi; Suyitno, Amin

2018-03-01

21st century is predicted as the century with rapid development in all aspects of life. People require creative and innovative character to exist. Specifically, mathematics has been given to students from the kindergarten until the middle school. Thus, building character through mathematics should begin since the early age. The problem is how to build creative and innovative character through mathematics education? The goal expected from this question is to build innovative and creative characters to face the challenges of the 21st century. This article discusses the values of mathematics, the values in mathematics education, innovative and creative character, and the integration of these values in teaching mathematics that support the innovative and creative character building, and applying the values in structurely programmed, measurable, and applicable learning activities.

A Water-Service Challenge

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Roman, Harry T.

2011-01-01

It is important to let students see the value of mathematics in design--and how mathematics lends perspective to problem solving. In this article, the author describes a water-service challenge which enables students to design a water utility system that uses surface runoff into an open reservoir as the potable water source. This challenge…

Teachers' Views of the Challenges of Teaching Grade 9 Applied Mathematics in Toronto Schools

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Stoilescu, Dorian; McDougall, Douglas; Egodawatte, Gunawardena

2016-01-01

Mathematics teachers, mathematics department heads, curriculum leaders, and administrators from 11 schools in four school boards from Toronto, Ontario, Canada, participated in a project to improve the teaching and learning in grade 9 mathematics classrooms. In each of these schools, an implementation team was created, so that at least three…

The QUASAR Project: The "Revolution of the Possible" in Mathematics Instructional Reform in Urban Middle Schools.

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Silver, Edward A.; Stein, Mary Kay

1996-01-01

Examines critical features of the QUASAR Project, a mathematics instruction program oriented toward helping students develop a meaningful understanding of mathematical ideas through challenging mathematical tasks, and discusses findings regarding the positive impact it has had on students. Challenges and obstacles in implementing the project are…

Perceptions and Lived Experiences of Traditional Community College Developmental Mathematics Students

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Mathai, Mince John

2014-01-01

Many students graduate from high school without adequate proficiency in mathematics, which is necessary to successfully undertake the challenges of college-level mathematics courses. As the underprepared students pursue postsecondary education, these institutions are required to provide remediation in mathematics to equip them with basic…

9th International Congress on Mathematical Education

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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...

Technology-Enhanced Mathematics Education for Creative Engineering Studies

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Triantafyllou, Eva; Timcenko, Olga

2014-01-01

This project explores the opportunities and challenges of integrating digital technologies in mathematics education in creative engineering studies. Students in such studies lack motivation and do not perceive the mathematics the same way as mathematics students do. Digital technologies offer new...... are conceptualized. Then, we are going to apply this field data in designing learning technologies, which will be introduced in university classrooms. The effect of this introduction will be evaluated through educational design experiments....

Mindset Matters: Supporting Student Persistence Through The Developmental Mathematics Pipeline

OpenAIRE

Kiser, Tracey Nicole

2016-01-01

Abstract of the DissertationMindset Matters: Supporting Student Persistence Through The Developmental Mathematics PipelinebyTracey Nicole KiserDoctor of Education in Teaching and LearningUniversity of California, San Diego, 2016Christopher P. Halter, ChairDevelopmental mathematics is one of the most challenging leaks in the mathematics K-20 pipeline. Few students enter two-year colleges prepared to successfully engage in college-level mathematics classes. Many of students who place into devel...

Developing Digital Technologies for Undergraduate University Mathematics

DEFF Research Database (Denmark)

Triantafyllou, Eva; Timcenko, Olga

2013-01-01

Our research effort presented in this paper relates with developing digital tools for mathematics education at undergraduate university level. It focuses specifically on studies where mathematics is not a core subject but it is very important in order to cope with core subjects. For our design, we...... requirements for the development of digital tools that support mathematics teaching and learning at university level....... during lectures and exercise time. During these observations we were able to investigate how the applets were used in practice but also to get insight in the challenges that the students face during mathematics learning. These findings together with student feedback inspire the next round of design...

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

Science.gov (United States)

Røykenes, Kari

2016-01-01

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

Mathematics Connection - Vol 10 (2011)

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 ...

Mathematization in introductory physics

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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

School mathematical discourse in a learning landscape

DEFF Research Database (Denmark)

Valero, Paola; Meaney, Tamsin; Alrø, Helle

By bringing our research work together, we are able to discuss the potential of combining the notions of the learning landscape and school mathematical discourse. We do so in a search for concepts and methodological tools to challenge the simplification of issues in regard to mathematics learning...... in multicultural settings, when adopting restricted perspectives on issues of bilingualism. In the paper we discuss the relationship between the learning landscape and school mathematical discourse. We then use these notions to analyse two case studies in Danish and New Zealand schools. Our conclusion raises...... possibilities about how these notions can be used when researching mathematics education in multicultural settings....

Cultivating Parabolas in the Parlor Garden: Reconciling Mathematics Education and Feminine Ideals in Nineteenth-Century America

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Fiss, Andrew

2014-02-01

This article introduces the justification problem for mathematics, which it explores through the case study of 1820s-1840s rationales for the teaching of mathematics to women in the United States. It argues that, while educators in the 1820s justified women's studies through mental discipline (a common reason for men's study), those of the 1830s-1840s increasingly relied on separate, gendered justifications, tied to emerging ideals of middle-class femininity. This article therefore emphasizes the contingency of the justification problem, which serves to break the present-day cycle of gender stereotypes regarding mathematics.

Variational analysis and aerospace engineering mathematical challenges for the aerospace of the future

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Mohammadi, Bijan; Pironneau, Olivier; Cipolla, Vittorio

2016-01-01

This book presents papers surrounding the extensive discussions that took place from the ‘Variational Analysis and Aerospace Engineering’ workshop held at the Ettore Majorana Foundation and Centre for Scientific Culture in 2015. Contributions to this volume focus on advanced mathematical methods in aerospace engineering and industrial engineering such as computational fluid dynamics methods, optimization methods in aerodynamics, optimum controls, dynamic systems, the theory of structures, space missions, flight mechanics, control theory, algebraic geometry for CAD applications, and variational methods and applications. Advanced graduate students, researchers, and professionals in mathematics and engineering will find this volume useful as it illustrates current collaborative research projects in applied mathematics and aerospace engineering.

Mathematical models of blast induced TBI: current status, challenges and prospects

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Raj K Gupta

2013-05-01

Full Text Available Blast induced traumatic brain injury (TBI has become a signature wound of recent military activities and is the leading cause of death and long-term disability among U.S. soldiers. The current limited understanding of brain injury mechanisms impedes the development of protection, diagnostic and treatment strategies. We believe mathematical models of blast wave brain injury biomechanics and neurobiology, complemented with in vitro and in vivo experimental studies, will enable a better understanding of injury mechanisms and accelerate the development of both protective and treatment strategies. The goal of this paper is to review the current state of the art in mathematical and computational modeling of blast induced TBI, identify research gaps and recommend future developments. A brief overview of blast wave physics, injury biomechanics and the neurobiology of brain injury is used as a foundation for a more detailed discussion of multiscale mathematical models of primary biomechanics and secondary injury and repair mechanisms. The paper also presents a discussion of model development strategies, experimental approaches to generate benchmark data for model validation and potential applications of the model for prevention and protection against blast wave TBI.

Computational intelligence in wireless sensor networks recent advances and future challenges

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Falcon, Rafael; Koeppen, Mario

2017-01-01

This book emphasizes the increasingly important role that Computational Intelligence (CI) methods are playing in solving a myriad of entangled Wireless Sensor Networks (WSN) related problems. The book serves as a guide for surveying several state-of-the-art WSN scenarios in which CI approaches have been employed. The reader finds in this book how CI has contributed to solve a wide range of challenging problems, ranging from balancing the cost and accuracy of heterogeneous sensor deployments to recovering from real-time sensor failures to detecting attacks launched by malicious sensor nodes and enacting CI-based security schemes. Network managers, industry experts, academicians and practitioners alike (mostly in computer engineering, computer science or applied mathematics) benefit from the spectrum of successful applications reported in this book. Senior undergraduate or graduate students may discover in this book some problems well suited for their own research endeavors. USP: Presents recent advances and fu...

How Does Students’ Sense of Self-Worth Influence Their Goal Orientation in Mathematics Achievement?

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Gulseren Sekreter

2017-12-01

Full Text Available In learning mathematics, students are naturally motivated to protect their self-worth by maintaining a belief that they are competent in this area. However, there is an important question which educators have to answer: “Why do students often confuse ability with worth?” The most important reason is that in our society students are widely considered to be worthy according to their ability to achieve in the given tasks in mathematics. Irrespective the contributions of the Multiple Intelligence Theory of intelligence in education, unfortunately mathematics is still regarded as predicting students’ overall ability to learn. Educators should realize that the need in order to protect self-worth arises primarily from fear of failure. Therefore, if this fear of failure is strong, some students will not try and gradually they will produce failure- avoiding strategies to avoid certain tasks in order not to look bad or receive negative assessments from others to protect his/her self-worth. It is important to make sure that the performance goals do not promote failure-avoidance (performance-avoidance-oriented behavior, such as avoiding unfavorable judgments of capabilities and looking incompetent when the student encounters greater challenges. The main purpose of this qualitative study, therefore, is to explore students’ achievement goal motivation, their self-worth and how these motivational factors impact their learning goals in mathematics. This study hypothesizes that self- worth protection in math has also been considered from a performance-avoidance goal viewpoint.This study emphasizes that educators, who consider true self-worth as the student’s inherent value, should avoid comparing their students’ ability, capability relative to others as well as students’ academic performance and outcomes with others in class context.

The Mathematics of "Star Trek"--An Honors Colloquium

Science.gov (United States)

Karls, Michael A.

2011-01-01

After the success of a course on cryptography for a general audience, based on Simon Singh's "The Code Book" [49], I decided to try again and create a mathematics course for a general audience based on "The Physics of Star Trek" by Lawrence Krauss [32]. This article looks at the challenges of designing a physics-based mathematics course "from…

Special Educators and Mathematics Phobia: An Initial Qualitative Investigation

Science.gov (United States)

Humphrey, Michael; Hourcade, Jack J.

2010-01-01

Special educators are uniquely challenged to be content experts in all curricular areas, including mathematics, because students in their caseloads may require academic instruction in any area. However, special educators with math phobia may be limited in their ability to provide effective instruction to their students with mathematical deficits…

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...

The affordances of using a flipped classroom approach in the teaching of mathematics: a case study of a grade 10 mathematics class

Science.gov (United States)

Muir, Tracey; Geiger, Vince

2016-03-01

Teaching secondary mathematics has a number of challenges, including the expectations that teachers cover the prescribed curriculum, help students learn difficult concepts, prepare students for future studies, and, increasingly, that they do so incorporating digital technologies. This study investigates a teacher's, and his students', perceptions of the benefits or otherwise of a flipped classroom approach in meeting these challenges, within a prescribed curriculum context. Data collection instruments included a survey designed to investigate the nature of students' engagement with the flipped approach and semi-structured student and teacher interviews. Analysis of these data indicated that the teacher and students were positive about their experiences with a flipped classroom approach and that students were motivated to engage with the teacher-created online mathematics resources. The study adds to the limited research literature related to student and teacher perceptions of the affordances of the flipped classroom approach and has implications for secondary mathematics teachers who face the challenge of the twin demands of covering the prescribed curriculum and catering for a range of students' learning needs.

Perception of mathematics teachers on cooperative learning method in the 21st century

Science.gov (United States)

Taufik, Nurshahira Alwani Mohd; Maat, Siti Mistima

2017-05-01

Mathematics education is one of the branches to be mastered by students to help them compete with the upcoming challenges that are very challenging. As such, all parties should work together to help increase student achievement in Mathematics education in line with the Malaysian Education Blueprint (MEB) 2010-2025. Teaching methods play a very important role in attracting and fostering student understanding and interested in learning Mathematics. Therefore, this study was conducted to identify the perceptions of teachers in carrying out cooperative methods in the teaching and learning of mathematics. Participants of this study involving 4 teachers who teach Mathematics in primary schools around the state of Negeri Sembilan. Interviews are used as a method for gathering data. The findings indicate that cooperative methods help increasing interest and understanding in the teaching and learning of mathematics. In conclusion, the teaching methods affect the interest and understanding of students in the learning of Mathematics in the classroom.

Mathematical models in biology bringing mathematics to life

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Ferraro, Maria; Guarracino, Mario

2015-01-01

This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy.  The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...

Attitudes of Pre-Service Mathematics Teachers towards Modelling: A South African Inquiry

Science.gov (United States)

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

This study explores the attitudes of mathematics pre-service teachers, based on their initial exposure to a model-eliciting challenge. The new Curriculum and Assessment Policy Statement determines that mathematics students should be able to identify, investigate and solve problems via modelling. The unpreparedness of mathematics teachers in…

International Conference on Mathematics and Computing

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Giri, Debasis; Saxena, P; Srivastava, P

2014-01-01

This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in computer science are of vital importance to a broad range of communities, including mathematicians and computing p...

Advances in mathematical economics

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Yamazaki, Akira

2005-01-01

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. The editorial board of this series comprises the following prominent economists and mathematicians: Managing Editors: S. Kusuoka (Univ. Tokyo), T. Maruyama (Keio Univ.). Editors: R. Anderson (U.C. Berkeley), C. Castaing (Univ. Montpellier), F.H. Clarke (Univ. Lyon I), G. Debreu (U.C. Berkeley), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Okayama Univ.), J.-M. Grandmont...

Advanced mathematics communication beyond modality of sight

Science.gov (United States)

Sedaghatjou, Mina

2018-01-01

This study illustrates how mathematical communication and learning are inherently multimodal and embodied; hence, sight-disabled students are also able to conceptualize visuospatial information and mathematical concepts through tactile and auditory activities. Adapting a perceptuomotor integration approach, the study shows that the lack of access to visual fields in an advanced mathematics course does not obstruct a blind student's ability to visualize, but transforms it. The goal of this study is not to compare the visually impaired student with non-visually impaired students to address the 'differences' in understanding; instead, I discuss the challenges that a blind student, named Anthony, has encountered and the ways that we tackled those problems. I also demonstrate how the proper and precisely crafted tactile materials empowered Anthony to learn mathematical functions.

Explorations in Elementary Mathematical Modeling

Directory of Open Access Journals (Sweden)

Mazen Shahin

2010-06-01

Full Text Available In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and cooperative learning into this inquiry-based learning course where students work in small groups on carefully designed activities and utilize available software to support problem solving and understanding of real life situations. We emphasize the use of graphical and numerical techniques, rather than theoretical techniques, to investigate and analyze the behavior of the solutions of the difference equations.As an illustration of our approach, we will show a nontraditional and efficient way of introducing models from finance and economics. We will also present an interesting model of supply and demand with a lag time, which is called the cobweb theorem in economics. We introduce a sample of a research project on a technique of removing chaotic behavior from a chaotic system.

The Applied Mathematics for Power Systems (AMPS)

Energy Technology Data Exchange (ETDEWEB)

Chertkov, Michael [Los Alamos National Laboratory

2012-07-24

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

An approach critical in mathematics education: Opportunities and interaction theory-practice-through critical mathematics education

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Itamar Miranda da Silva

2011-06-01

Full Text Available This paper discusses the possibilities of articulation of theory-and-practice in the teaching, by means of critical mathematics education as a proposal for the teacher facing the challenges of daily life in the classroom. The discussion is based on the literature through which was estudied and analyzed several books, articles and dissertations on the subject, as well as our experiences and reflections resulting from the process of teacher education we experienced. From the readings and analysis was possible to construct a teaching proposal that suggests to address critical mathematics education as an alternative link between theory and practice and to assign to the teaching of mathematics a greater dynamism, with the prospect of developing knowledge and pedagogical practices that contribute to a broader training, which prepares for citizenship and for being critical students and teachers in the training process. Conjectures were raised about possible contributions of critical mathematics education as a differentiated alternative as opposed to reproductivist teaching. We believe therefore that this article could help with the reflections on the importance of mathematics education in teacher education which enables the realization that beyond disciplinary knowledge (content, are necessary pedagogical knowledge, curriculum and experiential to address the problems that relate to the teaching of mathematics

Connecting Pre-Service Teachers with Contemporary Mathematics Practices: Selecting and Sequencing Students' Work Samples

Science.gov (United States)

Livy, Sharyn; Muir, Tracey; Downton, Ann

2017-01-01

One of the challenges facing teacher educators is providing our pre-service teachers (PSTs) with authentic experiences that cross the boundaries between Initial Teacher Education (ITE) and the classroom. An additional challenge facing the mathematics teacher educator, is addressing and deepening PSTs' mathematical content knowledge (MCK), which…

The philosophical aspect of learning inverse problems of mathematical physics

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Виктор Семенович Корнилов

2018-12-01

Full Text Available The article describes specific questions student learning inverse problems of mathematical physics. When teaching inverse problems of mathematical physics to the understanding of the students brought the information that the inverse problems of mathematical physics with a philosophical point of view are the problems of determining the unknown causes of known consequences, and the search for their solutions have great scientific and educational potential. The reasons are specified in the form of unknown coefficients, right side, initial conditions of the mathematical model of inverse problems, and as a consequence are functionals of the solution of this mathematical model. In the process of learning the inverse problems of mathematical physics focuses on the philosophical aspects of the phenomenon of information and identify cause-effect relations. It is emphasized that in the process of logical analysis applied and humanitarian character, students realize that information is always related to the fundamental philosophical questions that the analysis applied and the humanitarian aspects of the obtained results the inverse problem of mathematical physics allows students to make appropriate inferences about the studied process and to, ultimately, new information, to study its properties and understand its value. Philosophical understanding of the notion of information opens up to students a new methodological opportunities to comprehend the world and helps us to reinterpret existing science and philosophy of the theory related to the disclosure of the interrelationship of all phenomena of reality.

Game Design and Development as Mathematical Activities

DEFF Research Database (Denmark)

Jensen, Erik Ottar; Hanghøj, Thorkild; Misfeldt, Morten

2016-01-01

education which have mostly been tied to students making learning games involving specific mathematical content. Game design activities are reported to have a motivational pull for students. A challenge seems to be that the students are mostly motivated by the game design or the programming activities...... between user and goal through the computational artifacts being used. The framework serves as a lens for making sense of computer game design as a context for learning mathematics....

Gendered Pathways: How Mathematics Ability Beliefs Shape Secondary and Postsecondary Course and Degree Field Choices

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Perez-Felkner, Lara; Nix, Samantha; Thomas, Kirby

2017-01-01

Do mathematics ability beliefs explain gender gaps in the physical science, engineering, mathematics, and computer science fields (PEMC) and other science fields? We leverage U.S. nationally representative longitudinal data to estimate gendered differences in girls' and boys' perceptions of mathematics ability with the most difficult or challenging material. Our analyses examine the potentially interacting effects of gender and these ability beliefs on students' pathways to scientific careers. Specifically, we study how beliefs about ability with challenging mathematics influence girls' and boys' choices to pursue PEMC degrees, evaluating educational milestones over a 6-year period: advanced science course completion in secondary school and postsecondary major retention and selection. Our findings indicate even at the same levels of observed ability, girls' mathematics ability beliefs under challenge are markedly lower than those of boys. These beliefs matter over time, potentially tripling girls' chances of majoring in PEMC sciences, over and above biological science fields, all else being equal. Implications and potential interventions are discussed. PMID:28428762

Experimentally supported mathematical modeling of continuous baking processes

DEFF Research Database (Denmark)

Stenby Andresen, Mette

and temperature) and control the process (air flow, temperature, and humidity) are therefore emphasized. The oven is furthermore designed to work outside the range of standard tunnel ovens, making it interesting for manufacturers of both baking products and baking equipment. A mathematical model describing......The scope of the PhD project was to increase knowledge on the process-to-product interactions in continuous tunnel ovens. The work has focused on five main objectives. These objectives cover development of new experimental equipment for pilot plant baking experiments, mathematical modeling of heat...... and mass transfer in a butter cookie product, and evaluation of quality assessment methods. The pilot plant oven is a special batch oven designed to emulate continuous convection tunnel oven baking. The design, construction, and validation of the oven has been part of the project and is described...

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

Science.gov (United States)

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

2013-01-01

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

Mathematical methods in biology and neurobiology

CERN Document Server

Jost, Jürgen

2014-01-01

Mathematical models can be used to meet many of the challenges and opportunities offered by modern biology. The description of biological phenomena requires a range of mathematical theories. This is the case particularly for the emerging field of systems biology. Mathematical Methods in Biology and Neurobiology introduces and develops these mathematical structures and methods in a systematic manner. It studies:   • discrete structures and graph theory • stochastic processes • dynamical systems and partial differential equations • optimization and the calculus of variations.   The biological applications range from molecular to evolutionary and ecological levels, for example:   • cellular reaction kinetics and gene regulation • biological pattern formation and chemotaxis • the biophysics and dynamics of neurons • the coding of information in neuronal systems • phylogenetic tree reconstruction • branching processes and population genetics • optimal resource allocation • sexual recombi...

Exploring Iconic Interpretation and Mathematics Teacher Development through Clinical Simulations

Science.gov (United States)

Dotger, Benjamin; Masingila, Joanna; Bearkland, Mary; Dotger, Sharon

2015-01-01

Field placements serve as the traditional "clinical" experience for prospective mathematics teachers to immerse themselves in the mathematical challenges of students. This article reports data from a different type of learning experience, that of a clinical simulation with a standardized individual. We begin with a brief background on…

Framing the structural role of mathematics in physics lectures: A case study on electromagnetism

Directory of Open Access Journals (Sweden)

Ricardo Karam

2014-05-01

Full Text Available Physics education research has shown that students tend to struggle when trying to use mathematics in a meaningful way in physics (e.g., mathematizing a physical situation or making sense of equations. Concerning the possible reasons for these difficulties, little attention has been paid to the way mathematics is treated in physics instruction. Starting from an overall distinction between a technical approach, which involves an instrumental (tool-like use of mathematics, and a structural one, focused on reasoning about the physical world mathematically, the goal of this study is to characterize the development of the latter in didactic contexts. For this purpose, a case study was conducted on the electromagnetism course given by a distinguished physics professor. The analysis of selected teaching episodes with the software Videograph led to the identification of a set of categories that describe different strategies used by the professor to emphasize the structural role of mathematics in his lectures. As a consequence of this research, an analytic tool to enable future comparative studies between didactic approaches regarding the way mathematics is treated in physics teaching is provided.

Connecting Slope, Steepness, and Angles

Science.gov (United States)

Nagle, Courtney R.; Moore-Russo, Deborah

2013-01-01

All teachers, especially high school teachers, face the challenge of ensuring that students have opportunities to relate and connect the various representations and notions of mathematics concepts developed over the course of the pre-K-12 mathematics curriculum. NCTM's (2000) Representation Standard emphasizes the importance of students being…

Type classes for mathematics in type theory

OpenAIRE

Spitters, Bas; Van der Weegen, Eelis

2011-01-01

The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage of their unique features to make practical a particularly flexible approach formerly thought infeasible. Thus, we address both traditional proof engineering challenges as well as new ones resulting from our ambition to build upon this development a library...

Good Questions: Great Ways to Differentiate Mathematics Instruction. Second Edition

Science.gov (United States)

Small, Marian

2012-01-01

Expanded to include connections to Common Core State Standards, as well as National Council of Teachers of Mathematics (NCTM) standards, this critically acclaimed book will help every teacher and coach to meet the challenges of differentiating mathematics instruction in the K-8 classroom. In this bestseller, math education expert Marian Small…

More than Numbers: Teaching ELLs Mathematical Language in Primary Grades

Science.gov (United States)

Sistla, Michelle; Feng, Jay

2014-01-01

Teaching English Language Learners (ELL) academics while they are acquiring English language skills is a challenge for teachers. This action research examines the use of Response To Intervention (RTI) in teaching ELLs mathematical language and its effect on students' math achievement in primary grades. It shows that when mathematical language…

2nd International Conference on Mathematics and Computing

CERN Document Server

Chowdhury, Dipanwita; Giri, Debasis

2015-01-01

This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. This is the second conference on mathematics and computing organized at Haldia Institute of Technology, India. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in com...

A student's guide to the study, practice, and tools of modern mathematics

CERN Document Server

Bindner, Donald

2010-01-01

A Student's Guide to the Study, Practice, and Tools of Modern Mathematics provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to Mathematica® and Maple™ to MATLAB® and R. Along with a color insert, the text includes exercises and challenges to stimulate creativity and improve problem solving abilities.The first section of the book covers issues pertaining to studying mathematics. The authors explain how to write mathematical proofs and papers, how to perform

Contributions from sociology of science to mathematics education in Brazil: logic as a system of beliefs

Science.gov (United States)

de Andrade, Thales Haddad Novaes; Vilela, Denise Silva

2013-09-01

In Brazil, mathematics education was associated with Jean Piaget's theory. Scholars in the field of education appropriated Piaget's work in different ways, but usually emphasized logical aspects of thought, which probably lead to an expansion of mathematics education influenced by psychology. This study attempts to extend the range of interlocutions and pose a dialogue between the field of mathematics education in Brazil and the sociology of science proposed by David Bloor. The main point of Bloor's theory is that logical-mathematical knowledge is far from being true and universal and is socially conditioned. In particular we will be discussing the first principle of the strong program, which deals with conditions that generate beliefs promoted by education policies in Brazil, such as the MEC/USAID treaties. In this case the "naturalization of logic" was stimulated by a widespread diffusion of both Piaget studies and the Modern Mathematics Movement.

Developing a Maori Language Mathematics Lexicon: Challenges for Corpus Planning in Indigenous Language Contexts

Science.gov (United States)

Trinick, Tony; May, Stephen

2013-01-01

Over the last 25 years, there has been significant modernisation and elaboration of the Maori language mathematics lexicon and register to support the teaching of (Western) mathematics as a component of Maori-medium schooling. These developments are situated within the wider Maori language revitalisation movement in Aotearoa/New Zealand, of which…

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

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Mumcu, Hayal Yavuz

2016-01-01

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

Engaging Life-Sciences Students with Mathematical Models: Does Authenticity Help?

Science.gov (United States)

Poladian, Leon

2013-01-01

Compulsory mathematics service units for the life sciences present unique challenges: even students who learn some specific skills maintain a negative attitude to mathematics and do not see the relevance of the unit towards their degree. The focus on authentic content and the presentation and teaching of global or qualitative methods before…

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

The Preparation Experiences of Elementary Mathematics Specialists: Examining Influences on Beliefs, Content Knowledge, and Teaching Practices

Science.gov (United States)

Swars, Susan L.; Smith, Stephanie Z.; Smith, Marvin E.; Carothers, Jody; Myers, Kayla

2018-01-01

Many in the field of mathematics education call for elementary schools to have elementary mathematics specialists (EMSs) who provide needed mathematical expertise and support for children and teachers. EMSs serve as a reasonable, immediate alternative to the challenges generated by elementary teachers needing improved mathematical knowledge for…

Hong Kong and U.S. Teachers' Perceptions of Mathematical Disagreements and Their Resolution Processes

Science.gov (United States)

Barlow, Angela T.; Huang, Rongjin; Law, Huk-Yuen; Chan, Yip Cheung; Zhang, Qiaoping; Baxter, Wesley A.; Gaddy, Angeline K.

2016-01-01

Mathematical disagreements occur when students challenge each other's ideas related to a mathematical concept. In this research, we examined Hong Kong and U.S. elementary teachers' perceptions of mathematical disagreements and their resolutions using a video-stimulated survey. Participants were directed to give particular attention to the…

Using Assessment for Learning Mathematics with Mobile Tablet Based Solutions

Directory of Open Access Journals (Sweden)

Ghislain Maurice Norbert Isabwe

2014-03-01

Full Text Available This article discusses assessment for learning in mathematics subjects. Teachers of large classes face the challenge of regularly assessing studentsཿ ongoing mathematical learning achievements. Taking the complexity of assessment and feedback for learning as a background, we have developed a new approach to the assessment for learning mathematics at university level. We devised mobile tablet technology supported assessment processes, and we carried out user studies in both Rwanda and Norway. Results of our study indicated that students found it fruitful to be involved in assessing other studentsཿ mathematics work, i.e. assessing fellow studentsཿ answers to mathematical tasks. By being involved in the assessment process, the students expected mathematical learning gains. Their providing and obtaining of feedback to/from their fellow students using technology supported tools were highly appreciated as regards their own mathematical learning process.

The changing emphases in health physics

International Nuclear Information System (INIS)

Denham, D.H.; Kathren, R.L.

1987-11-01

This paper explores the changing emphases in health physics as evidenced by the subject matter of published papers in four primary English language journals of interest to health physicists. Articles from each journal were first grouped by subject and date of publication and were then compiled according to the list of professional domains practiced by health physicists. Five domains of practice were examined, measurements including dosimetry and environmental monitoring; regulations and standards; facilities and equipment including shielding, ventilation, and instrumentation; operations and procedures; and education and training. 2 tabs

Applied Mathematics at the U.S. Department of Energy: Past, Present and a View to the Future

International Nuclear Information System (INIS)

Brown, D.L; Bell, J.; Estep, D.; Gropp, W.; Hendrickson, B.; Keller-McNulty, S.; Keyes, D.; Oden, J.T.; Petzold, L.; Wright, M.

2008-01-01

mathematical developments required to meet the future science and engineering needs of the DOE. It is important to emphasize that the panelists were not asked to speculate only on advances that might be made in their own research specialties. Instead, the guidance this panel was given was to consider the broad science and engineering challenges that the DOE faces and identify the corresponding advances that must occur across the field of mathematics for these challenges to be successfully addressed. As preparation for the meeting, each panelist was asked to review strategic planning and other informational documents available for one or more of the DOE Program Offices, including the Offices of Science, Nuclear Energy, Fossil Energy, Environmental Management, Legacy Management, Energy Efficiency and Renewable Energy, Electricity Delivery and Energy Reliability and Civilian Radioactive Waste Management as well as the National Nuclear Security Administration. The panelists reported on science and engineering needs for each of these offices, and then discussed and identified mathematical advances that will be required if these challenges are to be met. A review of DOE challenges in energy, the environment and national security brings to light a broad and varied array of questions that the DOE must answer in the coming years. A representative subset of such questions includes: (1) Can we predict the operating characteristics of a clean coal power plant? (2) How stable is the plasma containment in a tokamak? (3) How quickly is climate change occurring and what are the uncertainties in the predicted time scales? (4) How quickly can an introduced bio-weapon contaminate the agricultural environment in the US? (5) How do we modify models of the atmosphere and clouds to incorporate newly collected data of possibly of new types? (6) How quickly can the United States recover if part of the power grid became inoperable? (7) What are optimal locations and communication protocols for sensing

Persisting mathematics and science high school teachers: A Q-methodology study

Science.gov (United States)

Robbins-Lavicka, Michelle M.

There is a lack of qualified mathematics and science teachers at all levels of education in Arkansas. Lasting teaching initiative programs are needed to address retention so qualified teachers remain in the classroom. The dearth of studies regarding why mathematics and science teachers persist in the classroom beyond the traditional 5-year attrition period led this Q-methodological study to evaluate the subjective perceptions of persistent mathematics and science teachers to determine what makes them stay. This study sought to understand what factors persisting mathematics and science teachers used to explain their persistence in the classroom beyond 5 years and what educational factors contributed to persisting mathematics and science teachers. Q-methodology combines qualitative and quantitative techniques and provided a systematic means to investigate personal beliefs by collecting a concourse, developing a Q-sample and a person-sample, conducting a Q-sorting process, and analyzing the data. The results indicated that to encourage longevity within mathematics and science classrooms (a) teachers should remain cognizant of their ability to influence student attitudes toward teaching; (b) administrators should provide support for teachers and emphasize the role and importance of professional development; and (c) policy makers should focus their efforts and resources on developing recruitment plans, including mentorship programs, while providing and improving financial compensation. Significantly, the findings indicate that providing mentorship and role models at every level of mathematics and science education will likely encourage qualified teachers to remain in the mathematics and science classrooms, thus increasing the chance of positive social change.

Advertising energy saving programs: The potential environmental cost of emphasizing monetary savings.

Science.gov (United States)

Schwartz, Daniel; Bruine de Bruin, Wändi; Fischhoff, Baruch; Lave, Lester

2015-06-01

Many consumers have monetary or environmental motivations for saving energy. Indeed, saving energy produces both monetary benefits, by reducing energy bills, and environmental benefits, by reducing carbon footprints. We examined how consumers' willingness and reasons to enroll in energy-savings programs are affected by whether advertisements emphasize monetary benefits, environmental benefits, or both. From a normative perspective, having 2 noteworthy kinds of benefit should not decrease a program's attractiveness. In contrast, psychological research suggests that adding external incentives to an intrinsically motivating task may backfire. To date, however, it remains unclear whether this is the case when both extrinsic and intrinsic motivations are inherent to the task, as with energy savings, and whether removing explicit mention of extrinsic motivation will reduce its importance. We found that emphasizing a program's monetary benefits reduced participants' willingness to enroll. In addition, participants' explanations about enrollment revealed less attention to environmental concerns when programs emphasized monetary savings, even when environmental savings were also emphasized. We found equal attention to monetary motivations in all conditions, revealing an asymmetric attention to monetary and environmental motives. These results also provide practical guidance regarding the positioning of energy-saving programs: emphasize intrinsic benefits; the extrinsic ones may speak for themselves. (c) 2015 APA, all rights reserved).

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

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 lines broaden the concept of fractions for students who are tied to the more general part-whole representations of area models. We also discuss how number lines, compared to other representations, are a superior and more mathematically correct way to explain fraction concepts.

Student reflections on learning with challenging tasks: `I think the worksheets were just for practice, and the challenges were for maths'

Science.gov (United States)

Russo, James; Hopkins, Sarah

2017-09-01

The current study considered young students' (7 and 8 years old) experiences and perceptions of mathematics lessons involving challenging (i.e. cognitively demanding) tasks. We used the Constant Comparative Method to analyse the interview responses ( n = 73) regarding what work artefacts students were most proud of creating and why. Five themes emerged that characterised student reflections: enjoyment, effort, learning, productivity and meaningful mathematics. Overall, there was evidence that students embraced struggle and persisted when engaged in mathematics lessons involving challenging tasks and, moreover, that many students enjoyed the process of being challenged. In the second section of the paper, the lesson structure preferences of a subset of participants ( n = 23) when learning with challenging tasks are considered. Overall, more students preferred the teach-first lesson structure to the task-first lesson structure, primarily because it activated their cognition to prepare them for work on the challenging task. However, a substantial minority of students (42 %) instead endorsed the task-first lesson structure, with several students explaining they preferred this structure precisely because it was so cognitively demanding. Other reasons for preferring the task-first structure included that it allowed the focus of the lesson to be on the challenging task and the subsequent discussion of student work. A key implication of these combined findings is that, for many students, work on challenging tasks appeared to remain cognitively demanding irrespective of the structure of the lesson.

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 ...

A certain ambiguity a mathematical novel

CERN Document Server

Suri, Gaurav

2010-01-01

While taking a class on infinity at Stanford in the late 1980s, Ravi Kapoor discovers that he is confronting the same mathematical and philosophical dilemmas that his mathematician grandfather had faced many decades earlier--and that had landed him in jail. Charged under an obscure blasphemy law in a small New Jersey town in 1919, Vijay Sahni is challenged by a skeptical judge to defend his belief that the certainty of mathematics can be extended to all human knowledge--including religion. Together, the two men discover the power--and the fallibility--of what has long been considered the pinn

Developing Culturally Responsive Mathematics Teachers: Secondary Teachers' Evolving Conceptions of Knowing Students

Science.gov (United States)

Parker, Frieda; Bartell, Tonya Gau; Novak, Jodie D.

2017-01-01

Research advances in teaching, learning, curriculum, and assessment have not changed the continued underperformance of marginalized students in mathematics education. Culturally responsive teaching is a means of addressing the needs of these students. It is sometimes challenging, however, to convince secondary mathematics teachers about the…

Connecting Theory and Practice: Preservice Teachers' Construction of Practical Tools for Teaching Mathematics

Science.gov (United States)

Jacobbe, Tim; Ross, Dorene D.; Caron, D. Alvarez; Barko, Timothy; Busi, Rich

2014-01-01

The National Council of Teachers of Mathematics (NCTM) has called for changes in mathematics teaching from a procedural to conceptual focus since 1980, yet the way mathematics is taught in many classrooms continues to contradict the recommended practices. The pervasiveness of this challenge has led some educators to suggest changes in university…

Mathematics-Literacy Checklists: A Pedagogical Innovation to Support Teachers as They Implement the Common Core

Science.gov (United States)

del Prado Hill, Pixita; Friedland, Ellen S.; McMillen, Susan

2016-01-01

This article presents two innovative tools--the Mathematics-Literacy Planning Framework and Mathematics-Literacy Implementation Checklist--which are designed to help instructional coaches and specialists support teachers to meet the challenges of the mathematics-literacy integration goals of the Common Core. Developed with teacher input, these…

Mathematics education, democracy and development: Exploring connections

Directory of Open Access Journals (Sweden)

Renuka Vithal

2012-12-01

Full Text Available Mathematics education and its links to democracy and development are explored in this article, with specific reference to the case of South Africa. This is done by engaging four key questions. Firstly, the question of whether mathematics education can be a preparation for democracy and include a concern for development, is discussed by drawing on conceptual tools of critical mathematics education and allied areas in a development context. Secondly, the question of how mathematics education is distributed in society and participates in shaping educational possibilities in addressing its development needs and goals is used to examine the issues emerging from mathematics performance in international studies and the national Grade 12 examination; the latter is explored specifically in respect of the South African mathematics curriculum reforms and teacher education challenges. Thirdly, the question of whether a mathematics classroom can be a space for democratic living and learning that equally recognises the importance of issues of development in contexts like South Africa, as a post-conflict society still healing from its apartheid wounds, continuing inequality and poverty, is explored through pedagogies of conflict, dialogue and forgiveness. Finally the question of whether democracy and development can have anything to do with mathematics content matters, is discussed by appropriating, as a metaphor, South Africa’s Truth and Reconciliation Commission’s framework of multiple ‘truths’, to seek links within and across the various forms and movements in mathematics and mathematics education that have emerged in the past few decades.

CULTUROLOGICAL APPROACH AS METHODOLOGICAL BASIS OF MATHEMATICAL EDUCATION

Directory of Open Access Journals (Sweden)

Ye. A. Perminov

2017-01-01

literacy have the extreme humanitarian importance, since their existence either indirectly or sometimes directly influences quality of life of any person and society in general. The most in-demand, significant and obligatory thematic and methodological components of mathematical education are highlighted: mathematical modeling, discrete mathematics and computing processes. The principle of a cultural conformity and a harmonious combination of the culturological and artfundamentals of mathematical education are emphasized as the basic educational principles, the use of which is capable to improve and raise the level of mathematical culture of the Russian society on a new, higher position.The evidence from this study points towards the idea that effective functioning of the system of mathematical education is impossible without the qualified, well prepared staff who are not only professionals in the subject sphere, but also bearers of high pedagogical culture. Moral and ethical, communicative and individual, and personal components of pedagogical culture of a teacher-mathematician are characterized.Practical significance. The author is convinced that introduction of the proposed concept of mathematical education based on culturological approach to its contents and the organization will help to overcome the disproportions existing today in mathematical education between integration and subject differentiation of a training material, technologization of educational process and preservation of traditional methods of training, fundamentalization of knowledge and competence-based approach to it, etc.Materials of the publication can be useful for future and practising teachers of mathematics and allied sciences, as well as for other categories of the educators engaged in the organization and advance of mathematical education and promotion of mathematical knowledge.

Mathematical oncology 2013

CERN Document Server

Gandolfi, Alberto

2014-01-01

With chapters on free boundaries, constitutive equations, stochastic dynamics, nonlinear diffusion–consumption, structured populations, and applications of optimal control theory, this volume presents the most significant recent results in the field of mathematical oncology. It highlights the work of world-class research teams, and explores how different researchers approach the same problem in various ways. Tumors are complex entities that present numerous challenges to the mathematical modeler. First and foremost, they grow. Thus their spatial mean field description involves a free boundary problem. Second, their interiors should be modeled as nontrivial porous media using constitutive equations. Third, at the end of anti-cancer therapy, a small number of malignant cells remain, making the post-treatment dynamics inherently stochastic. Fourth, the growth parameters of macroscopic tumors are non-constant, as are the parameters of anti-tumor therapies. Changes in these parameters may induce phenomena that a...

Ancient Paradoxes Can Extend Mathematical Thinking

Science.gov (United States)

Czocher, Jennifer A.; Moss, Diana L.

2017-01-01

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

Methods of applied mathematics with a software overview

CERN Document Server

Davis, Jon H

2016-01-01

This textbook, now in its second edition, provides students with a firm grasp of the fundamental notions and techniques of applied mathematics as well as the software skills to implement them. The text emphasizes the computational aspects of problem solving as well as the limitations and implicit assumptions inherent in the formal methods. Readers are also given a sense of the wide variety of problems in which the presented techniques are useful. Broadly organized around the theme of applied Fourier analysis, the treatment covers classical applications in partial differential equations and boundary value problems, and a substantial number of topics associated with Laplace, Fourier, and discrete transform theories. Some advanced topics are explored in the final chapters such as short-time Fourier analysis and geometrically based transforms applicable to boundary value problems. The topics covered are useful in a variety of applied fields such as continuum mechanics, mathematical physics, control theory, and si...

Mathematics Diagnostic Testing in Engineering: An International Comparison between Ireland and Portugal

Science.gov (United States)

Carr, M.; Fidalgo, C.; Bigotte de Almeida, M. E.; Branco, J. R.; Santos, V.; Murphy, E.; Ní Fhloinn, E.

2015-01-01

Concern has been expressed throughout Europe about the significant deficiencies in the basic mathematical skills of many engineering undergraduates. Mathematics diagnostic tests in the UK, Ireland and Portugal have shown these shortcomings, which provide a challenge to those striving to introduce more innovative educational practices into…

Tablet Technology to Facilitate Improved Interaction and Communication with Students Studying Mathematics at a Distance

Science.gov (United States)

Galligan, Linda; Hobohm, Carola; Loch, Birgit

2012-01-01

Teaching and learning of mathematics is challenging when lecturer and students are separated geographically. While student engagement and interaction with the course, with other students and with the lecturer is vital to mathematics learning, it is difficult to facilitate this electronically, because of the nature of mathematics. With tablet…

A Voyage of Mathematical and Cultural Awareness for Students of Upper Secondary School

Science.gov (United States)

Panagiotou, Evangelos N.

2014-01-01

Many papers have emphasized the need for and importance of particular examples and the underlying rationale for introducing a historical dimension in mathematics education. This article presents the development and implementation of a project, based on original sources, in a situation where the existing curriculum does not include history. The subject was conic sections and the motivating problems and original work which eventually found resolution in modern concepts. The project was carried out during the school year 2006-2007 with 18 students of a Greek experimental high school 2nd class (11th degree). It was devised as a series of worksheets, separate readings and oral presentations and written essays so that students might appreciate that mathematics evolves under the influence of factors intrinsic and extrinsic to it. Both epistemological and disciplinary issues are taken into account. Even though this work is just one case study, we have found that exposing students directly to primary sources in mathematics contributes greatly to motivation and understanding, and illustrates the nature of mathematics as a discipline and as a human endeavour.

Mathematical methods for students of physics and related fields

CERN Document Server

Hassani, Sadri

2000-01-01

Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics This new edition has been made more user-friendly through organization into convenient, shorter chapters Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms Some praise for the previous edi...

Mathematical Methods For Students of Physics and Related Fields

CERN Document Server

Hassani, Sadri

2009-01-01

Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms. Some praise for the previo...

Destrezas de Matematica: Curriculo Basico. Guia para el Maestro (Mathematics Skills: Basic Curriculum. Teacher's Guide).

Science.gov (United States)

Puerto Rico State Dept. of Education, Hato Rey. Office of Special Education.

The fundamental importance of basic mathematics to daily life is emphasized in this teacher's guide for special education teachers in Puerto Rico. While it is necessary for the teacher to determine the needs and abilities of each student and adapt the curriculum accordingly, this guide presents, in Spanish, a set of lesson plans, each with an…

Linking Teaching in Mathematics and the Subjects of Natural Science

DEFF Research Database (Denmark)

Michelsen, Claus

2017-01-01

teaching programs. This is partly due to the lack of a framework for integrating productive ideas across the disciplines. This paper focus on how to grasp the challenges of an interdisciplinary approach to teaching in mathematics and the subjects of natural science. Based on contemporary mathematics...... and science education we design a didactical framework for interdisciplinary teaching centered on modeling activities across mathematics and the disciplines of natural science. To exemplify the potential of the framework we present a case study of an intensive in-service teacher-training program...... for mathematics and biology teachers. The teachers were presented to the didactical framework and in pairs of two, one mathematics teacher and one biology teacher; they designed and implemented interdisciplinary mathematicsbiology teaching sequences. The teachers’ reports on their development and implementation...

Mathematical methods for mathematicians, physical scientists and engineers

CERN Document Server

Dunning-Davies, J

2003-01-01

This practical introduction encapsulates the entire content of teaching material for UK honours degree courses in mathematics, physics, chemistry and engineering, and is also appropriate for post-graduate study. It imparts the necessary mathematics for use of the techniques, with subject-related worked examples throughout. The text is supported by challenging problem exercises (and answers) to test student comprehension. Index notation used in the text simplifies manipulations in the sections on vectors and tensors. Partial differential equations are discussed, and special functions introduced

Using GeoGebra for Mathematics Education at University Undergraduate Level

DEFF Research Database (Denmark)

Triantafyllou, Eva; Timcenko, Olga

Our research effort presented in this talk relates with developing digital tools for mathematics education at undergraduate university level. It focuses specifically on studies where mathematics is not a core subject but it is very important in order to cope with core subjects. For our design, we...... feedback inspire the next round of design requirements for the development of digital tools that support mathematics teaching and learning at university level....... conducted observations of teachers and students during lectures and exercise time. During these observations we were able to investigate how the applets were used in practice but also to get insight in the challenges that the students face during mathematics learning. These findings together with student...

Graphic Organizer in Action: Solving Secondary Mathematics Word Problems

Directory of Open Access Journals (Sweden)

Khoo Jia Sian

2016-09-01

Full Text Available Mathematics word problems are one of the most challenging topics to learn and teach in secondary schools. This is especially the case in countries where English is not the first language for the majority of the people, such as in Brunei Darussalam. Researchers proclaimed that limited language proficiency and limited Mathematics strategies are the possible causes to this problem. However, whatever the reason is behind difficulties students face in solving Mathematical word problems, it is perhaps the teaching and learning of the Mathematics that need to be modified. For example, the use of four-square-and-a-diamond graphic organizer that infuses model drawing skill; and Polya’s problem solving principles, to solve Mathematical word problems may be some of the strategies that can help in improving students’ word problem solving skills. This study, through quantitative analysis found that the use of graphic organizer improved students’ performance in terms of Mathematical knowledge, Mathematical strategy and Mathematical explanation in solving word problems. Further qualitative analysis revealed that the use of graphic organizer boosted students’ confidence level and positive attitudes towards solving word problems.Keywords: Word Problems, Graphic Organizer, Algebra, Action Research, Secondary School Mathematics DOI: http://dx.doi.org/10.22342/jme.7.2.3546.83-90

Accounting for primitive terms in mathematics

Directory of Open Access Journals (Sweden)

D.F.M. Strauss

2005-07-01

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

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

OpenAIRE

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

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

DEVELOPING EVALUATION INSTRUMENT FOR MATHEMATICS EDUCATIONAL SOFTWARE

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Wahyu Setyaningrum

2012-02-01

Full Text Available The rapid increase and availability of mathematics software, either for classroom or individual learning activities, presents a challenge for teachers. It has been argued that many products are limited in quality. Some of the more commonly used software products have been criticized for poor content, activities which fail to address some learning issues, poor graphics presentation, inadequate documentation, and other technical problems. The challenge for schools is to ensure that the educational software used in classrooms is appropriate and effective in supporting intended outcomes and goals. This paper aimed to develop instrument for evaluating mathematics educational software in order to help teachers in selecting the appropriate software. The instrument considers the notion of educational including content, teaching and learning skill, interaction, and feedback and error correction; and technical aspects of educational software including design, clarity, assessment and documentation, cost and hardware and software interdependence. The instrument use a checklist approach, the easier and effective methods in assessing the quality of educational software, thus the user needs to put tick in each criteria. The criteria in this instrument are adapted and extended from standard evaluation instrument in several references.   Keywords: mathematics educational software, educational aspect, technical aspect.

Enhancing Formative Assessment Practice and Encouraging Middle School Mathematics Engagement and Persistence

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Beesley, Andrea D.; Clark, Tedra F.; Dempsey, Kathleen; Tweed, Anne

2018-01-01

In the transition to middle school, and during the middle school years, students' motivation for mathematics tends to decline from what it was during elementary school. Formative assessment strategies in mathematics can help support motivation by building confidence for challenging tasks. In this study, the authors developed and piloted a…

The SAMPLE experience: The development of a rich media online mathematics learning environment

OpenAIRE

Chang, Jen

2006-01-01

This report documents the development of Sample Architecture for Mathematically Productive Learning Experiences (SAMPLE), a rich media, online, mathematics learning environment created to meet the needs of middle school educators. It explores some of the current pedagogical challenges in mathematics education, and their amplified impacts when coupled with under-prepared teachers, a decidedly wide-spread phenomenon. The SAMPLE publishing experience is discussed in terms of its instructional de...

Exploring a Structure for Mathematics Lessons That Foster Problem Solving and Reasoning

Science.gov (United States)

Sullivan, Peter; Walker, Nadia; Borcek, Chris; Rennie, Mick

2015-01-01

While there is widespread agreement on the importance of incorporating problem solving and reasoning into mathematics classrooms, there is limited specific advice on how this can best happen. This is a report of an aspect of a project that is examining the opportunities and constraints in initiating learning by posing challenging mathematics tasks…

Student-Perceived Mothers' and Fathers' Beliefs, Mathematics and English Motivations, and Career Choices.

Science.gov (United States)

Lazarides, Rebecca; Watt, Helen M G

2017-12-01

According to Eccles and Jacobs' (1986) parent socialization model, parents' gendered ability and value beliefs influence girls' and boys' interpretations of those beliefs, and hence students' domain-specific valuing of tasks and competence beliefs and subsequent career plans. Studies have rarely analyzed how both student-perceived mothers' and fathers' beliefs affect girls' and boys' task values, success expectancies, and career plans across domains. This study analyzed survey data of 459 students (262 boys) assessed through Grades 9, 10, and 11 from three coeducational secondary schools in Sydney, Australia. Longitudinal structural equation models revealed gendered value transmission pathways for girls in mathematics. Although mathematics test scores did not vary statistically significantly, girls reported statistically significantly lower mothers' ability beliefs for them in mathematics than boys at Time 1, which led to their statistically significantly lower mathematics intrinsic value at Time 2 and mathematics-related career plans at Time 3. Such gendered pathways did not occur in English. Matched same-gender effects and gendered pathways in parent socialization processes were evident; perceived mothers' value beliefs were more strongly related to girls' than boys' importance values in English. Student-perceived fathers' ability beliefs positively predicted boys', not girls', importance value in mathematics. Implications for educational practice emphasize the need to target girls' and boys' interest when aiming to enhance their mathematical career motivations. © 2017 The Authors. Journal of Research on Adolescence © 2017 Society for Research on Adolescence.

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

Science.gov (United States)

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

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

Mathematics Curriculum in Ireland: The Influence of PISA on the Development of Project Maths

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Liz KIRWAN

2015-12-01

Full Text Available This article interrogates the extent to which the Organization for Economic Cooperation and Development (OECD through its Programme for International Student Assessment (PISA influenced the development of Project Maths, a new second-level mathematics education policy in Ireland. It argues that the Irish government, in its revision of mathematics education policy, was strongly influenced by PISA and that concern with the country’s ‘average’ placement in the international assessment was instrumental in defining the direction of the revision. It traces the genetic imprint of PISA on the development of curriculum policy, the new mathematics syllabus, its content and assessment. It argues that Project Maths sets out to follow closely the PISA conceptual framework. However, the analysis finds that Project Maths is not a mini-PISA but that the programme is comprised of two distinct approaches, on the one hand retaining the abstract, symbolic mathematics of sections of the pre-existing curriculum, while on the other emphasizing a PISA-like approach to pedagogy and to real-life problem solving.

Educating Teachers of Mathematics: some important challenges and promising directions Formação de Professores de Matemática: desafios e direções

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Edward Silver

2008-02-01

Full Text Available Despite considerable variation in the processes and practices of initial preparation of teachers of mathematics and the extent and nature of support available for their continuing education and development, many fundamental challenges are shared across geographic boundaries. In this paper I draw on work that my colleagues and I are doing in the U.S to identify and discuss two foci of our work that may help others address problems and issues that appear to be endemic in mathematics teacher education around the world. The first is a focus on instructional practice as the lever for professional education of mathematics teachers; the second is a focus on the work of those who educate teachers of mathematics and on developing opportunities for them to improve their own practice. Keywords: Mathematics Education, Mathematics Teaching, Teacher Education, Teacher Professional DevelopmentApesar de consideráveis variações nos processos e práticas de preparação inicial de professores de matemática e na extensão e natureza do apoio que é dado à capacitação e à formação continuada dos mesmos, vários desafios fundamentais são comuns a muitos países. No presente artigo, apresento o trabalho que eu e meus colegas estamos desenvolvendo nos EUA para identificar e discutir dois focos de nossa pesquisa que podem auxiliar outros interessados a abordar problemas e questões de formação de professores de matemática que se manifestam em todo o mundo. O primeiro foco é o emprego da prática pedagógica como alavanca para o desenvolvimento profissional dos professores de matemática; o segundo é o trabalho daqueles que formam professores de matemática e a criação de oportunidades para que eles aperfeiçoem sua própria prática. Palavras-chave: Educação Matemática, Ensino de Matemática, Formação de Professores, Desenvolvimento Profissional.

The Mathematics Syllabus and Adult Learners in Community Colleges: Integrating Technique with Content.

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Baker, Robert N.

2001-01-01

Presents a brief discussion of the challenges presented to mathematics education by changes in social dependence on mathematics, in professional response to the needs of students, in institutional expectations of students and teachers, and in student demographics and expectations. Provides an extended outline for a syllabus used to clearly…

The Mathematics of Skateboarding: A Relevant Application of the 5Es of Constructivism

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Robertson, William H.; Meyer, Rachelle D.; Wilkerson, Trena L.

2012-01-01

Getting high school students to enjoy mathematics and to connect concepts to their daily lives is a challenge for many educators. The Mathematics of Skateboarding demonstrated innovative and creative ways to engage students in content and skills mapped to state requirements for high school students in Algebra and Geometry.

Effects of Mathematics Integration in a Teaching Methods Course on Self-Efficacy of Preservice Agricultural Education Teachers

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Stripling, Christopher T.; Roberts, T. Grady

2013-01-01

Teachers who are efficacious persevere through challenges in the learning environment and put forth more effort in designing learning activities. The purpose of this study was to determine the effects of mathematics teaching and integration strategies (MTIS) on preservice agricultural teachers' personal mathematics efficacy, mathematics teaching…

Mathematics related anxiety: Mathematics bogeyman or not?

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Videnović Marina

2011-01-01

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

Approaches to teaching primary level mathematics

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Caroline Long

2014-12-01

Full Text Available In this article we explore approaches to curriculum in the primary school in order to map and manage the omissions implicit in the current unfolding of the Curriculum and Assessment Policy Statement for mathematics. The focus of school-based research has been on curriculum coverage and cognitive depth. To address the challenges of teaching mathematics from the perspective of the learner, we ask whether the learners engage with the subject in such a way that they build foundations for more advanced mathematics. We firstly discuss three approaches that inform the teaching of mathematics in the primary school and which may be taken singly or in conjunction into organising the curriculum: the topics approach, the process approach, and the conceptual fields approach. Each of the approaches is described and evaluated by presenting both their advantages and disadvantages. We then expand on the conceptual fields approach by means of an illustrative example. The planning of an instructional design integrates both a topics and a process approach into a conceptual fields approach. To address conceptual depth within this approach, we draw on five dimensions required for understanding a mathematical concept. In conclusion, we reflect on an approach to curriculum development that draws on the integrated theory of conceptual fields to support teachers and learners in the quest for improved teaching and learning.

Teachers' Mathematics as Mathematics-at-Work

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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…

Methods of mathematical modelling continuous systems and differential equations

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Witelski, Thomas

2015-01-01

This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

Teaching Mathematics to Secondary Students with Emotional and Behavioral Disorders: Challenges and Practical Suggestions for Teachers

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Mulcahy, Candace A.; Krezmien, Michael; Maccini, Paula

2014-01-01

While the Common Core State Standards and state learning standards guide teachers in what mathematical content knowledge should be addressed as well as the processes and proficiencies necessary for developing mathematical competence, several student- and teacher-related factors may hinder student access to the general education curriculum for…

Accessing and assessing young learner’s mathematical dispositions

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mellony Graven

2012-07-01

Full Text Available It is argued in this paper that there is an absence of literature relating to research on learner mathematical dispositions, particularly with young learners. Drawing on Kilpatrick, Swafford and Findell’s (2001 five interrelated strands of mathematical proficiency, which include: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition, it is argued that there has been little engagement with productive disposition in the field of mathematics education and how we might access and assess this strand. Despite competence in all strands being essential for mathematical proficiency, literature and assessments that seek to establish learner levels of mathematical proficiency have tended to focus on the first four and have neglected the last; productive disposition. Finding ways in which to access student mathematical learning dispositions can be challenging, especially with young learners who struggle to articulate their views. An instrument is shared that the author has designed with doctoral fellow, Debbie Stott, in order to access and assess the productive disposition of learners participating in maths clubs run within the South African Numeracy Chair. The findings that emerge in one Grade 3 club with six learners is shared. These findings are related to the data collected through instruments that assess the other four strands of mathematical proficiency. This enables a holistic picture of learner’s mathematical proficiency as intended in the conceptualisation of the interrelated five strands of proficiency.

Examining Individual and Collective Level Mathematical Progress

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Rasmussen, Chris; Wawro, Megan; Zandieh, Michelle

2015-01-01

A challenge in mathematics education research is to coordinate different analyses to develop a more comprehensive account of teaching and learning. We contribute to these efforts by expanding the constructs in Cobb and Yackel's (Educational Psychologist 31:175-190, 1996) interpretive framework that allow for coordinating social and individual…

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

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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…

Student Performance in Mathematics: Should We Be Concerned? Evidence from a Retail Course

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Enderson, Mary C.; Mann, Manveer

2018-01-01

This article describes how for many college students the transition to college-level mathematics courses presents new challenges beyond those that were part of the high school experience. In this interdisciplinary study forty-four non-mathematics and non-science majors, enrolled in a retail-buying course, were studied to examine student confidence…

A Modular Approach to Teaching Mathematical Modeling in Biotechnology in the Undergraduate Curriculum

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Larripa, Kamila R.; Mazzag, Borbala

2016-01-01

Our paper describes a solution we found to a still existing need to develop mathematical modeling courses for undergraduate biology majors. Some challenges of such courses are: (i) relatively limited exposure of biology students to higher-level mathematical and computational concepts; (ii) availability of texts that can give a flavor of how…

Mathematics curriculum in Ireland: The ınfluence of PISA on the development of project maths

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Liz Kirwan

2015-12-01

Full Text Available This article interrogates the extent to which the Organization for Economic Cooperation and Development (OECD through its Programme for International Student Assessment (PISA influenced the development of Project Maths, a new second-level mathematics education policy in Ireland. It argues that the Irish government, in its revision of mathematics education policy, was strongly influenced by PISA and that concern with the country’s ‘average’ placement in the international assessment was instrumental in defining the direction of the revision. It traces the genetic imprint of PISA on the development of curriculum policy, the new mathematics syllabus, its content and assessment. It argues that Project Maths sets out to follow closely the PISA conceptual framework. However, the analysis finds that Project Maths is not a mini-PISA but that the programme is comprised of two distinct approaches, on the one hand retaining the abstract, symbolic mathematics of sections of the pre-existing curriculum, while on the other emphasizing a PISA-like approach to pedagogy and to real-life problem solving.

Teaching Mathematical Modeling in Mathematics Education

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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…

Mathematical Modeling and Pure Mathematics

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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…

Main challenges of residential areas

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Oana Luca

2017-06-01

Full Text Available The present article is a position paper aiming to initiate a professional debate related to the aspects related to the urban dysfunctions leading to the wear of the residential areas. The paper proposes a definition of the wear process, identify the main causes leading to its occurrence and propose a number of solutions to neutralise the dysfunctions. The three wearing phases of residential areas components are emphasized, exploring their lifecycle. In order to perform the study of urban wear, the status of the residential areas components can be established and monitored, and also the variables of the function that can mathematically model the specific wear process may be considered. The paper is considered a first step for the model adjustment, to be tested and validated in the following steps. Based on the mathematical method and model, there can be created, in a potential future research, the possibility of determining the precarity degree for residential areas/neighbourhoods and cities, by minimising the subjective component of the analyses preceding the decision for renovation or regeneration.

Using a Before-During-After (BDA) Model to Plan Effective Secondary Mathematics Lessons

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Wilburne, Jane Murphy; Peterson, Winnie

2007-01-01

Creating effective mathematics lessons can be a challenge for any teacher. One approach to design an effective lesson is using a before-during-after (BDA) format. This article describes what a BDA format is and provides two examples of how it is implemented in high school mathematics classes. (Contains 2 tables and 5 figures.)

Should mathematics be a creative subject? How is this realized in practice in Denmark?

DEFF Research Database (Denmark)

Ejersbo, Lisser Rye

as a creative subject. How do they understand creativity and how do they realize it in practice? And what makes mathematics a creative subject? Is it the task, the way it is performed or the relationship between teacher and students? The crucial difference between different classrooms seems to be the ways......The ministerial objectives for mathematics education in the Danish Folkeskole (grades K-ten) state that students will learn that mathematics is both a tool for problem-solving and a creative subject. In this article, I explore how teachers in Denmark meet the challenge of teaching mathematics....... The discussion will focus on how to make mathematics a creative subject....

MATHEMATICS COURSES AND NEW EMERGING DESIGN TOOL AN OVERVIEW OF ARCHITECTURAL EDUCATION IN INDONESIA

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Aswin Indraprastha

2008-01-01

Full Text Available Since the beginning, mathematics courses are inherent within architecture education. In Indonesia, the legacy from Dutch education system has influenced most of the architectural schools and this courses stand as one of basic engineering courses for architecture education system. This situation has been remaining well adopted until recently, some of architectural schools are tailoring mathematics to shape with contemporary challenges particularly regards to the digital tools. This paper aims to present brief information about mathematics courses in architectural schools in Indonesia, the importance of mathematics in learning digital design tools and propose thoughts to upgrade mathematics content in architectural education towards new emerging design tools.

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

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

2011-01-01

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

Mathematics, curriculum and assessment: The role of taxonomies in the quest for coherence

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Caroline Long

2014-12-01

Full Text Available A challenge encountered when monitoring mathematics teaching and learning at high school is that taxonomies such as Bloom’s, and variations of this work, are not entirely adequate for providing meaningful feedback to teachers beyond very general cognitive categories that are difficult to interpret. Challenges of this nature are also encountered in the setting of examinations, where the requirement is to cover a range of skills and cognitive domains. The contestation as to the cognitive level is inevitable as it is necessary to analyse the relationship between the problem and the learners’ background experience. The challenge in the project described in this article was to find descriptive terms that would be meaningful to teachers. The first attempt at providing explicit feedback was to apply the assessment frameworks that include a content component and a cognitive component, namely knowledge, routine procedures, complex procedures and problem solving, currently used in the South African curriculum documents. The second attempt investigated various taxonomies, including those used in international assessments and in mathematics education research, for constructs that teachers of mathematics might find meaningful. The final outcome of this investigation was to apply the dimensions required to understand a mathematical concept proposed by Usiskin (2012: the skills-algorithm, property-proof, use-application and representation-metaphor dimension. A feature of these dimensions is that they are not hierarchical; rather, within each of the dimensions, the mathematical task may demand recall but may also demand the highest level of creativity. For our purpose, we developed a two-way matrix using Usiskin’s dimensions on one axis and a variation of Bloom’s revised taxonomy on the second axis. Our findings are that this two-way matrix provides an alternative to current taxonomies, is more directly applicable to mathematics and provides the

Emphasizing Language and Visualization in Teaching Linear Algebra

Science.gov (United States)

Hannah, John; Stewart, Sepideh; Thomas, Mike

2013-01-01

Linear algebra with its rich theoretical nature is a first step towards advanced mathematical thinking for many undergraduate students. In this paper, we consider the teaching approach of an experienced mathematician as he attempts to engage his students with the key ideas embedded in a second-year course in linear algebra. We describe his…

AI and Mathematical Education

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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.

The Challenge of Teaching Quantitative Skills to Students with Limited Mathematical Background.

Science.gov (United States)

Anosike, Nnamdi

There is a myth in the African American community that only a few students are bright enough to effectively learn quantitative skills, and many African American students attend college with the assumption that they are not good at mathematics and as a result cannot choose majors that require the mastery of quantitative skills. African American…

Experience of three-dimensional vision in the era of digital interaction new devices : opportunity and challenges for applied mathematics and visual design

CERN Document Server

Brunetti, Federico Alberto

2014-01-01

It will be soon presented to the public a new version of stereoscopic viewers designed for observing files and video projected images through a system of transparent optical prisms which allow the simultaneous perception of the surrounding environment. The real challenge for applied mathematics and visual design will be to prefigure how to use them and their applications, since these new devices can actually enable a deeper visual experience. A specific case study concerns the visualizations of the collisions at the LHC at CERN, selected to verify the traces of the boson theorized by Francois Englert and Peter Higgs, with Robert Brout, who recently (2013) received the Nobel Prize for their research.

Using Mathematics Literature with Prospective Secondary Mathematics Teachers

Science.gov (United States)

Jett, Christopher C.

2014-01-01

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

Good Questions: Great Ways to Differentiate Mathematics Instruction

Science.gov (United States)

Small, Marian

2009-01-01

Using differentiated instruction in the classroom can be a challenge, especially when teaching mathematics. This book cuts through the difficulties with two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks. Specific strategies and examples for grades Kindergarten - 8 are organized…

TEACHING MATHEMATICS USING LECTURE CAPTURE TECHNOLOGY

OpenAIRE

Audi, Diana

2017-01-01

Technology in highereducation is dramatically changing and continuously giving a challenging timefor educators and institutions to provide the same level of innovativecontents, environment and interaction to a digital native generation which iswell powered with technology. It has been well observed and recognized thatvideo lectures technology can have positive impacts on student learning andsatisfaction however research on Mathematics intensive subjects have yet to befully explored. This expl...

Bernhard Riemann 1826-1866 Turning Points in the Conception of Mathematics

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Laugwitz, Detlef

2008-01-01

The name of Bernard Riemann is well known to mathematicians and physicists around the world. College students encounter the Riemann integral early in their studies. Real and complex function theories are founded on Riemann’s work. Einstein’s theory of gravitation would be unthinkable without Riemannian geometry. In number theory, Riemann’s famous conjecture stands as one of the classic challenges to the best mathematical minds and continues to stimulate deep mathematical research. The name is indelibly stamped on the literature of mathematics and physics. This book, originally written in German and presented here in an English-language translation, examines Riemann’s scientific work from a single unifying perspective. Laugwitz describes Riemann’s development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hi...

About the Effectiveness of the Training Technology Model of Trigonometry Teaching for the Mathematical Profile Students

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N. I. Popov

2013-01-01

Full Text Available The paper is devoted to trigonometry teaching in higher school as a part of the elementary mathematics course with a complex hierarchical structure. Due to the complicated content of the given discipline,each of its modules can be divided into separate themes; though, the teacher should emphasize their interrelations, as well as the links with the coordinate method, geometry and mathematical analysis.The recommended training technology model allows the teacher to build up and control the training process, and achieve good results in accordance with the assigned tasks. In the course of the model approbation, theauthor developed the e-learning resource and identification method for selecting the key mathematical examples and exercises for each theme and module. The analysis of students’ tests and questionnaires conducted for several years proves the effectiveness of the designed model for the senior university students of mathematical profile. Based on the research findings, the author developed the educational methodology complex for the Basics of Trigonometry course.

The Affordances of Using a Flipped Classroom Approach in the Teaching of Mathematics: A Case Study of a Grade 10 Mathematics Class

Science.gov (United States)

Muir, Tracey; Geiger, Vince

2016-01-01

Teaching secondary mathematics has a number of challenges, including the expectations that teachers cover the prescribed curriculum, help students learn difficult concepts, prepare students for future studies, and, increasingly, that they do so incorporating digital technologies. This study investigates a teacher's, and his students', perceptions…

Doing Mathematics with Purpose: Mathematical Text Types

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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'…

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

Science.gov (United States)

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

2016-01-01

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

A mathematical model of insulin resistance in Parkinson's disease.

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Braatz, Elise M; Coleman, Randolph A

2015-06-01

This paper introduces a mathematical model representing the biochemical interactions between insulin signaling and Parkinson's disease. The model can be used to examine the changes that occur over the course of the disease as well as identify which processes would be the most effective targets for treatment. The model is mathematized using biochemical systems theory (BST). It incorporates a treatment strategy that includes several experimental drugs along with current treatments. In the past, BST models of neurodegeneration have used power law analysis and simulation (PLAS) to model the system. This paper recommends the use of MATLAB instead. MATLAB allows for more flexibility in both the model itself and in data analysis. Previous BST analyses of neurodegeneration began treatment at disease onset. As shown in this model, the outcomes of delayed, realistic treatment and full treatment at disease onset are significantly different. The delayed treatment strategy is an important development in BST modeling of neurodegeneration. It emphasizes the importance of early diagnosis, and allows for a more accurate representation of disease and treatment interactions. Copyright © 2015 Elsevier Ltd. All rights reserved.

Understanding Immunology via Engineering Design: The Role of Mathematical Prototyping

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Klinke, David J.; Wang, Qing

2012-01-01

A major challenge in immunology is how to translate data into knowledge given the inherent complexity and dynamics of human physiology. Both the physiology and engineering communities have rich histories in applying computational approaches to translate data obtained from complex systems into knowledge of system behavior. However, there are some differences in how disciplines approach problems. By referring to mathematical models as mathematical prototypes, we aim to highlight aspects related to the process (i.e., prototyping) rather than the product (i.e., the model). The objective of this paper is to review how two related engineering concepts, specifically prototyping and “fitness for use,” can be applied to overcome the pressing challenge in translating data into improved knowledge of basic immunology that can be used to improve therapies for disease. These concepts are illustrated using two immunology-related examples. The prototypes presented focus on the beta cell mass at the onset of 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. PMID:22973412

A mathematical medley fifty easy pieces on mathematics

CERN Document Server

Szpiro, George G

2010-01-01

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

Preparing and Supporting Black Students to Enroll and Achieve in Advanced Mathematics Classes in Middle School: A Case Study

OpenAIRE

Cobbs, Joyce Bernice

2015-01-01

The literature on minority student achievement indicates that Black students are underrepresented in advanced mathematics courses. Advanced mathematics courses offer students the opportunity to engage with challenging curricula, experience rigorous instruction, and interact with quality teachers. The middle school years are particularly significant for mathematics education since the courses students pursue during those years affect later access to rigorous mathematics coursework at the high ...

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

OpenAIRE

Hadley, Kristin M.; Dorward, Jim

2011-01-01

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

Family Mathematics Nights: An Opportunity to Improve Preservice Teachers' Understanding of Parents' Roles and Expectations

Science.gov (United States)

Bofferding, Laura; Kastberg, Signe; Hoffman, Andrew

2016-01-01

Providing preservice teachers with opportunities to engage with parents and begin to see them as collaborators in their children's education is a persistent challenge in mathematics methods courses and teacher preparation programs more broadly. We describe the use of family mathematics nights as a model for engaging parents and preservice…

Acknowledging Spanish and English resources during mathematical reasoning

Science.gov (United States)

LópezLeiva, Carlos A.; Torres, Zayoni; Khisty, Lena L.

2013-12-01

As English-only efforts continue in the US schooling system, dual-language programs have served as attempts to preserve students' home language. An after-school, dual-language, Spanish-English, mathematics program, Los Rayos was developed in a predominantly Mexican/Mexican-American neighborhood in Chicago. As participant observers with a sociocultural perspective, we explored the linguistic and personal resources used by participating 4th grade bilingual Latina/o students. We found that students used imaginative, playful, and hybrid linguistic resources to make sense of and solve probability tasks when engaged within a zone of mathematical practice. Results challenge narrow perspectives on bilingual students' linguistic resources. Language implications are discussed.

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.

Mathematical phantoms for use in reassessment of radiation doses to Japanese atomic-bomb survivors

International Nuclear Information System (INIS)

Cristy, M.

1985-07-01

In 1972 committees of the United Nations and the US National Academy of Sciencs emphasized the need for organ dose estimates on the Japanese atomic-bomb survivors. These estimates were then supplied by workers in Japan and the US, and they were used with the so-called T65D estimates of a survivor's radiation exposure to assess risk from radiation. Recently the T65D estimates have been questioned, and programs for reassessment of atomic-bomb radiation dosimetry have been started in Japan and the US. As a part of this new effort a mathematical analogue of the human body (or ''mathematical phantom''), to be used in estimating organ doses in adult survivors, is presented here. Recommendations on organ dosimetry for juvenile survivors are also presented and discussed. 57 refs., 10 figs., 6 tabs

Mathematical modeling for novel cancer drug discovery and development.

Science.gov (United States)

Zhang, Ping; Brusic, Vladimir

2014-10-01

Mathematical modeling enables: the in silico classification of cancers, the prediction of disease outcomes, optimization of therapy, identification of promising drug targets and prediction of resistance to anticancer drugs. In silico pre-screened drug targets can be validated by a small number of carefully selected experiments. This review discusses the basics of mathematical modeling in cancer drug discovery and development. The topics include in silico discovery of novel molecular drug targets, optimization of immunotherapies, personalized medicine and guiding preclinical and clinical trials. Breast cancer has been used to demonstrate the applications of mathematical modeling in cancer diagnostics, the identification of high-risk population, cancer screening strategies, prediction of tumor growth and guiding cancer treatment. Mathematical models are the key components of the toolkit used in the fight against cancer. The combinatorial complexity of new drugs discovery is enormous, making systematic drug discovery, by experimentation, alone difficult if not impossible. The biggest challenges include seamless integration of growing data, information and knowledge, and making them available for a multiplicity of analyses. Mathematical models are essential for bringing cancer drug discovery into the era of Omics, Big Data and personalized medicine.

19th European Conference on Mathematics for Industry

CERN Document Server

Barral, Patricia; Gómez, Dolores; Pena, Francisco; Rodríguez, Jerónimo; Salgado, Pilar; Vázquez-Méndez, Miguel; ECMI 2016; Progress in industrial mathematics

2017-01-01

This book addresses mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. Using the classification system defined in the EU Framework Programme for Research and Innovation H2020, several of the topics covered belong to the challenge climate action, environment, resource efficiency and raw materials; and some to health, demographic change and wellbeing; while others belong to Europe in a changing world – inclusive, innovative and reflective societies. The 19th European Conference on Mathematics for Industry, ECMI2016, was held in Santiago de Compostela, Spain in June 2016. The proceedings of this conference include the plenary lectures, ECMI awards and special lectures, mini-symposia (including the description of each mini-symposium) and contributed talks. The ECMI conferences are organized by the European Consortium for Mathematics in Industry with the aim of promoting interaction between academy and industry, leading...

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…

Mathematics Underground

Science.gov (United States)

Luther, Kenneth H.

2012-01-01

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

In accordance with a "more majestic order". The new math and the nature of mathematics at midcentury.

Science.gov (United States)

Phillips, Christopher J

2014-09-01

The "new math" curriculum, one version of which was developed in the 1950s and 1960s by the School Mathematics Study Group under the auspices of the National Science Foundation, occasioned a great deal of controversy among mathematicians. Well before its rejection by parents and teachers, some mathematicians were vocal critics, decrying the new curriculum because of the way it described the practice and history of the discipline. The nature of mathematics, despite the field's triumphs in helping to win World War II and its midcentury promotion as the key to a modern technological society, was surprisingly contested in this period. Supporters of the School Mathematics Study Group, like its director, Edward Begle, emphasized the importance of portraying mathematics as a system of abstract structures, while opponents like Morris Kline argued that math was essentially a tool for understanding the natural world. The debate about the curriculum--and the role of mathematicians in its design--was also a debate about the underlying identity of the subject itself.

NATO Advanced Research Workshop on Exploiting Mental Imagery with Computers in Mathematics Education

CERN Document Server

Mason, John

1995-01-01

The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.

Exploring mathematics anxiety and attitude: Mathematics students' experiences

Science.gov (United States)

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

2017-11-01

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

A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers

Science.gov (United States)

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

2012-01-01

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

Challenges of Critical Colleagueship: Examining and Reflecting on Mathematics Teacher Study Group Interactions

Science.gov (United States)

Males, Lorraine M.; Otten, Samuel; Herbel-Eisenmann, Beth A.

2010-01-01

This article examines mathematics teacher collegiality by focusing on both the ways in which teachers interacted as critical colleagues in a long-term professional development project and the evolving role of the teacher-educator-researcher as the facilitator of this project. The professional development collaboration comprised two phases: one…

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…

Theoretical Mathematics

Science.gov (United States)

Stöltzner, Michael

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

Exploring Differential Effects of Mathematics Courses on Mathematics Achievement

Science.gov (United States)

Ma, Xin; McIntyre, Laureen J.

2005-01-01

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

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 ...

On the non-uniqueness of the nodal mathematical adjoint

International Nuclear Information System (INIS)

Müller, Erwin

2014-01-01

Highlights: • We evaluate three CMFD schemes for computing the nodal mathematical adjoint. • The nodal mathematical adjoint is not unique and can be non-positive (nonphysical). • Adjoint and forward eigenmodes are compatible if produced by the same CMFD method. • In nodal applications the excited eigenmodes are purely mathematical entities. - Abstract: Computation of the neutron adjoint flux within the framework of modern nodal diffusion methods is often facilitated by reducing the nodal equation system for the forward flux into a simpler coarse-mesh finite-difference form and then transposing the resultant matrix equations. The solution to the transposed problem is known as the nodal mathematical adjoint. Since the coarse-mesh finite-difference reduction of a given nodal formulation can be obtained in a number of ways, different nodal mathematical adjoint solutions can be computed. This non-uniqueness of the nodal mathematical adjoint challenges the credibility of the reduction strategy and demands a verdict as to its suitability in practical applications. This is the matter under consideration in this paper. A selected number of coarse-mesh finite-difference reduction schemes are described and compared. Numerical calculations are utilised to illustrate the differences in the adjoint solutions as well as to appraise the impact on such common applications as the computation of core point kinetics parameters. Recommendations are made for the proper application of the coarse-mesh finite-difference reduction approach to the nodal mathematical adjoint problem

"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…

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)

Mathematical Intelligence and Mathematical Creativity: A Causal Relationship

Science.gov (United States)

Tyagi, Tarun Kumar

2017-01-01

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

Teachers Perspective of Using English as a Medium of Instruction in Mathematics and Science Subjects

Science.gov (United States)

Mansor, Norudin; Badarudin, Mohamed Ishak; Mat, Azman Che

2011-01-01

The policy of changing the medium of instruction in the teaching of mathematics and science from Bahasa Melayu to English is an important innovation affecting teachers of mathematics and science. It poses special challenges not only for teachers who have been trained in the Malay medium but also for those trained in English. This investigation…

Mathematics make microbes beautiful, beneficial, and bountiful.

Science.gov (United States)

Jungck, John R

2012-01-01

biodiversity by using game theory, of epidemics with algebraic models, bacterial motion by using motion picture analysis and fluid mechanics of motility in multiple dimensions through the physics of "Life at Low Reynolds Numbers," and pattern formation of quorum sensing bacterial populations. Through a developmental model for preprofessional education that emphasizes the beauty, utility, and diversity of microbiological systems, we hope to foster creativity as well as mathematically rigorous reasoning. Copyright © 2012 Elsevier Inc. All rights reserved.

Coaching in Early Mathematics.

Science.gov (United States)

Germeroth, Carrie; Sarama, Julie

2017-01-01

Falling scores in math have prompted a renewed interest in math instruction at early ages. By their own admission, early childhood educators are generally underprepared and not always comfortable teaching math. Professional development (PD) in early mathematics is widely considered a main way to increase teachers' skills and efficacy (e.g., Guskey, 2000; Hyson & Woods, 2014; Munby, Russell, & Martin, 2001; Piasta, Logan, Pelatti, Capps, & Petrill, 2015; Richardson & Placier, 2001; Sarama, Clements, Wolfe, & Spitler, 2016; Sarama & DiBiase, 2004; Zaslow, 2014). However, it has been documented that stand-alone PD is not as effective in changing practice (e.g., Biancarosa & Bryk, 2011; Garet et al., 2008; Guskey, 2000; Hyson & Woods, 2014; Institute of Medicine and National Research Council, 2015; Joyce & Showers, 2002; Zaslow, 2014). Site-embedded ongoing support in the form of coaching or mentoring has been shown to be critical for successful implementation (Neuman & Cunningham, 2009; Powell, Diamond, Burchinal, & Koehler, 2010). In this chapter, we describe coaching models and abstract characteristics of effective coaching from the research. With this background, we provide an in-depth view of the coaching aspect of two large empirical studies in early mathematics. We introduce the theoretical framework from which the coaching models for these projects were developed and describe the research on which they were based. We then summarize how the planned models were instantiated and challenges to their implementation within each project. In the final section, we summarize what we have learned and described implications and challenges for the field. © 2017 Elsevier Inc. All rights reserved.

The (Mathematical) Modeling Process in Biosciences.

Science.gov (United States)

Torres, Nestor V; Santos, Guido

2015-01-01

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

The Relationship between 8th Grade Students’ Opinions about Problem Solving, Beliefs about Mathematics, Learned Hopelessness and Academics Success

OpenAIRE

Agaç, Gülay; MASAL, Ercan

2017-01-01

Related literature emphasizes that affective factors are impactful on cognitive factors. For this reason, this study aims at revealing the relationship between problem solving,  which is one of metacognitive characteristics, beliefs about mathematics and learned hopelessness, which are two affective characteristics. Therefore, addressing emotional aspects together with cognitive abilities will give rise to understanding of the students’ current situation and predicting ab...

Learning biology through connecting mathematics to scientific mechanisms: Student outcomes and teacher supports

Science.gov (United States)

Schuchardt, Anita

Integrating mathematics into science classrooms has been part of the conversation in science education for a long time. However, studies on student learning after incorporating mathematics in to the science classroom have shown mixed results. Understanding the mixed effects of including mathematics in science has been hindered by a historical focus on characteristics of integration tangential to student learning (e.g., shared elements, extent of integration). A new framework is presented emphasizing the epistemic role of mathematics in science. An epistemic role of mathematics missing from the current literature is identified: use of mathematics to represent scientific mechanisms, Mechanism Connected Mathematics (MCM). Building on prior theoretical work, it is proposed that having students develop mathematical equations that represent scientific mechanisms could elevate their conceptual understanding and quantitative problem solving. Following design and implementation of an MCM unit in inheritance, a large-scale quantitative analysis of pre and post implementation test results showed MCM students, compared to traditionally instructed students) had significantly greater gains in conceptual understanding of mathematically modeled scientific mechanisms, and their ability to solve complex quantitative problems. To gain insight into the mechanism behind the gain in quantitative problem solving, a small-scale qualitative study was conducted of two contrasting groups: 1) within-MCM instruction: competent versus struggling problem solvers, and 2) within-competent problem solvers: MCM instructed versus traditionally instructed. Competent MCM students tended to connect their mathematical inscriptions to the scientific phenomenon and to switch between mathematical and scientifically productive approaches during problem solving in potentially productive ways. The other two groups did not. To address concerns about teacher capacity presenting barriers to scalability of MCM

Experiences Teaching a Software Aided Mathematics Course for a General University Audience.

Science.gov (United States)

McGivney, Raymond J., Jr.

1990-01-01

Described is a nonmajor mathematics course taught using computers and lab experiments. Included are the challenge, solution, description of the first class, problems, successes, the syllabus, student comments, and the conclusion. (KR)

Quantitative Literacy and the Common Core State Standards in Mathematics

Directory of Open Access Journals (Sweden)

Bernard L. Madison

2015-01-01

Full Text Available How supportive of quantitative literacy (QL are the Common Core State Standards in Mathematics (CCSSM? The answer is tentative and conditional. There are some QL-supportive features including a strong probability and statistics strand in grade 6 through high school; a measurements and data strand in K-5; ratio and proportional reasoning standards in grades 6 and 7; and a comprehensive and coherent approach to algebraic reasoning and logical argument. However, the standards are weak in supporting reasoning and interpretation, and there are indications that the applications in CCSSM – mostly unspecified – will not include many QL contextual situations. Early indicators of assessment items follow a similar path. Except for statistics, most of the high school standards are aimed at development of algebra and precalculus topics, and there will likely be little room for more sophisticated applications of the QL-friendly mathematics of grades 6-8. The experience with CCSSM is limited at this point, leaving several crucial results uncertain, including assessments, emphases on statistics, and kinds of modeling and other applications.

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

Science.gov (United States)

Crisan, Cosette; Rodd, Melissa

2017-01-01

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

Pioneering space research in the USSR and mathematical modeling of large problems of radiation transfer

International Nuclear Information System (INIS)

Sushkevich, T.A.

2011-01-01

This review is to remind scientists of the older generation of some memorable historical pages and of many famous researchers, teachers and colleagues. For the younger researchers and foreign colleagues it will be useful to get to know about pioneer advancements of the Soviet scientists in the field of information and mathematical supply for cosmonautic problems on the eve of the space era. Main attention is paid to the scientific experiments conducted on the piloted space vehicles and the research teams who created the information and mathematical tools for the first space projects. The role of Mstislav Vsevolodovich Keldysh, the Major Theoretician of cosmonautics, is particularly emphasized. He determined for the most part the basic directions of development of space research and remote sensing of the Earth and planets that are shortly called remote sensing

Teaching mathematics to able children

CERN Document Server

Koshy, Valsa

2012-01-01

This book enables teachers to effectively meet the needs of their most able mathematicians. Using a tried and tested set of principles developed and used by The Able Children's Education Unit at Brunel University, the author demonstrates how to: identify high mathematical ability in a pupil, plan suitably challenging activities and teach them most effectively within the existing National Numeracy framework, make the most of the classroom resources available, including ICT and external agencies, implement strategies for differentiation, illustrated with real-life classroom examples. Ac

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

Science.gov (United States)

Sriraman, Bharath, Ed.

2012-01-01

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

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...

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

Science.gov (United States)

Battista, Michael T.

1986-01-01

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

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

Science.gov (United States)

Briley, Jason S.

2012-01-01

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

Using Challenging Tasks for Formative Assessment on Quadratic Functions with Senior Secondary Students

Science.gov (United States)

Wilkie, Karina J.

2016-01-01

Senior secondary mathematics students who develop conceptual understanding that moves them beyond "rules without reasons" to connections between related concepts are in a strong place to tackle the more difficult mathematics application problems. Current research is examining how the use of challenging tasks at different levels of…

Pyloric atresia: a challenge in an underdeveloped country | Sagna ...

African Journals Online (AJOL)

Pyloric atresia is a rare congenital malformation. We report a case in a 5-day newborn with pyloric atresia type C. Authors emphasize the diagnostic difficulties and therapeutic challenges in a resource-limited country. Keywords: Pyloric atresia, newborn, rare congenital malformation ...

Mathematics teachers’ reflective practice within the context of adapted lesson study

Directory of Open Access Journals (Sweden)

Barbara Posthuma

2012-11-01

Full Text Available There seems to be paucity of research in South Africa on mathematics teachers’ reflective practice. In order to study this phenomenon, the context of lesson study (in an adapted form was introduced to five mathematics teachers in a rural school in the Free State. The purpose was to investigate their reflective practice whilst they collaboratively planned mathematics lessons and reflected on the teaching of the lessons. Data were obtained through interviews, video-recorded lesson observations, field notes taken during the lesson study group meetings and document analyses (lesson plans and reflective writings. The adapted lesson study context provided a safe space for teachers to reflect on their teaching and they reported an increase in self-knowledge and finding new ways of teaching mathematics to learners. This finding has some potential value for planning professional learning programmes in which teachers are encouraged to talk about their classroom experiences, share their joys and challenges with one another and strive to build a community of reflective practitioners to enhance their learners’ understanding of mathematics.

Mathematical modelling

DEFF Research Database (Denmark)

Blomhøj, Morten

2004-01-01

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

Non-linear wave equations:Mathematical techniques

International Nuclear Information System (INIS)

1978-01-01

An account of certain well-established mathematical methods, which prove useful to deal with non-linear partial differential equations is presented. Within the strict framework of Functional Analysis, it describes Semigroup Techniques in Banach Spaces as well as variational approaches towards critical points. Detailed proofs are given of the existence of local and global solutions of the Cauchy problem and of the stability of stationary solutions. The formal approach based upon invariance under Lie transformations deserves attention due to its wide range of applicability, even if the explicit solutions thus obtained do not allow for a deep analysis of the equations. A compre ensive introduction to the inverse scattering approach and to the solution concept for certain non-linear equations of physical interest are also presented. A detailed discussion is made about certain convergence and stability problems which arise in importance need not be emphasized. (author) [es

Discrete Mathematics and the Secondary Mathematics Curriculum.

Science.gov (United States)

Dossey, John

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

Promoting Student Collaboration in a Detracked, Heterogeneous Secondary Mathematics Classroom

Science.gov (United States)

Staples, Megan E.

2008-01-01

Detracking and heterogeneous groupwork are two educational practices that have been shown to have promise for affording all students needed learning opportunities to develop mathematical proficiency. However, teachers face significant pedagogical challenges in organizing productive groupwork in these settings. This study offers an analysis of one…

Make your trappings count: The mathematics of pest insect monitoring. Comment on “Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks” by Petrovskii et al.

Science.gov (United States)

Blasius, Bernd

2014-09-01

Since the beginnings of agriculture the production of crops is characterized by an ongoing battle between farmers and pests [1]. Already during biblical times swarms of the desert locust, Schistocerca gregaria, were known as major pest that can devour a field of corn within an hour. Even today, harmful organisms have the potential to threaten food production worldwide. It is estimated that about 37% of all potential crops are destroyed by pests. Harmful insects alone destroy 13%, causing financial losses in the agricultural industry of millions of dollars each year [2-4]. These numbers emphasize the importance of pest insect monitoring as a crucial step of integrated pest management [1]. The main approach to gain information about infestation levels is based on trapping, which leads to the question of how to extrapolate the sparse population counts at singularly disposed traps to a spatial representation of the pest species distribution. In their review Petrovskii et al. provide a mathematical framework to tackle this problem [5]. Their analysis reveals that this seemingly inconspicuous problem gives rise to surprisingly deep mathematical challenges that touch several modern contemporary concepts of statistical physics and complex systems theory. The review does not aim for a collection of numerical recipes to support crop growers in the analysis of their trapping data. Instead the review identifies the relevant biological and physical processes that are involved in pest insect monitoring and it presents the mathematical techniques that are required to capture these processes.

A Classroom Research Skills Development Emphasizing Data Analysis and Result of SSRU Students by RBL

Science.gov (United States)

Waree, Chaiwat

2017-01-01

The purpose of the study is the learning using research as a base. To strengthen the skills of classroom research Emphasizing Data Analysis and Result and to study the development of research skills in the class Emphasizing Data Analysis and Result of SSRU' Students by learning using research base. The target group are students in the 2nd semester…

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....

Networking of theories as a research practice in mathematics education

CERN Document Server

Bikner-Ahsbahs, Angelika

2014-01-01

How can we deal with the diversity of theories in mathematics education This was the main question that led the authors of this book to found the Networking Theories Group. Starting from the shared assumption that the existence of different theories is a resource for mathematics education research, the authors have explored the possibilities of interactions between theories, such as contrasting, coordinating, and locally integrating them. The book explains and illustrates what it means to network theories; it presents networking as a challenging but fruitful research practice and shows how the Group dealt with this challenge considering five theoretical approaches, namely the approach of Action, Production, and Communication (APC), the Theory of Didactical Situations (TDS), the Anthropological Theory of the Didactic (ATD), the approach of Abstraction in Context (AiC), and the Theory of Interest-Dense Situations (IDS). A synthetic presentation of each theory and their connections shows how the activity of netw...

Integrating quantitative thinking into an introductory biology course improves students' mathematical reasoning in biological contexts.

Science.gov (United States)

Hester, Susan; Buxner, Sanlyn; Elfring, Lisa; Nagy, Lisa

2014-01-01

Recent calls for improving undergraduate biology education have emphasized the importance of students learning to apply quantitative skills to biological problems. Motivated by students' apparent inability to transfer their existing quantitative skills to biological contexts, we designed and taught an introductory molecular and cell biology course in which we integrated application of prerequisite mathematical skills with biology content and reasoning throughout all aspects of the course. In this paper, we describe the principles of our course design and present illustrative examples of course materials integrating mathematics and biology. We also designed an outcome assessment made up of items testing students' understanding of biology concepts and their ability to apply mathematical skills in biological contexts and administered it as a pre/postcourse test to students in the experimental section and other sections of the same course. Precourse results confirmed students' inability to spontaneously transfer their prerequisite mathematics skills to biological problems. Pre/postcourse outcome assessment comparisons showed that, compared with students in other sections, students in the experimental section made greater gains on integrated math/biology items. They also made comparable gains on biology items, indicating that integrating quantitative skills into an introductory biology course does not have a deleterious effect on students' biology learning.

Integrating Quantitative Thinking into an Introductory Biology Course Improves Students’ Mathematical Reasoning in Biological Contexts

Science.gov (United States)

Hester, Susan; Buxner, Sanlyn; Elfring, Lisa; Nagy, Lisa

2014-01-01

Recent calls for improving undergraduate biology education have emphasized the importance of students learning to apply quantitative skills to biological problems. Motivated by students’ apparent inability to transfer their existing quantitative skills to biological contexts, we designed and taught an introductory molecular and cell biology course in which we integrated application of prerequisite mathematical skills with biology content and reasoning throughout all aspects of the course. In this paper, we describe the principles of our course design and present illustrative examples of course materials integrating mathematics and biology. We also designed an outcome assessment made up of items testing students’ understanding of biology concepts and their ability to apply mathematical skills in biological contexts and administered it as a pre/postcourse test to students in the experimental section and other sections of the same course. Precourse results confirmed students’ inability to spontaneously transfer their prerequisite mathematics skills to biological problems. Pre/postcourse outcome assessment comparisons showed that, compared with students in other sections, students in the experimental section made greater gains on integrated math/biology items. They also made comparable gains on biology items, indicating that integrating quantitative skills into an introductory biology course does not have a deleterious effect on students’ biology learning. PMID:24591504

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

Science.gov (United States)

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

2017-01-01

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

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

Science.gov (United States)

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

2015-01-01

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

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

Science.gov (United States)

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

2015-10-01

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

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

Directory of Open Access Journals (Sweden)

Yinghui Lai

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

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

Science.gov (United States)

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

2015-01-01

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

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

Science.gov (United States)

Yang, Xinrong; Leung, Frederick K. S.

2015-01-01

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

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.

One-to-one iPad technology in the middle school mathematics and science classrooms

Science.gov (United States)

Bixler, Sharon G.

Science, technology, engineering, and mathematics (STEM) education has become an emphasized component of PreK-12 education in the United States. The US is struggling to produce enough science, mathematics, and technology experts to meet its national and global needs, and the mean scores of science and mathematics students are not meeting the expected levels desired by our leaders (Hossain & Robinson, 2011). In an effort to improve achievement scores in mathematics and science, school districts must consider many components that can contribute to the development of a classroom where students are engaged and growing academically. Computer technology (CT) for student use is a popular avenue for school districts to pursue in their goal to attain higher achievement. The purpose of this study is to examine the use of iPads in a one-to-one setting, where every student has his own device 24/7, to determine the effects, if any, on academic achievement in the areas of mathematics and science. This comparison study used hierarchical linear modeling (HLM) to examine three middle schools in a private school district. Two of the schools have implemented a one-to-one iPad program with their sixth through eighth grades and the third school uses computers on limited occasions in the classroom and in a computer lab setting. The questions addressed were what effect, if any, do the implementation of a one-to-one iPad program and a teacher's perception of his use of constructivist teaching strategies have on student academic achievement in the mathematics and science middle school classrooms. The research showed that although the program helped promote the use of constructivist activities through the use of technology, the one-to-one iPad initiative had no effect on academic achievement in the middle school mathematics and science classrooms.

The conceptual basis of mathematics in cardiology: (I) algebra, functions and graphs.

Science.gov (United States)

Bates, Jason H T; Sobel, Burton E

2003-02-01

This is the first in a series of four articles developed for the readers of. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease, abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and

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

Science.gov (United States)

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

2016-01-01

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

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

Science.gov (United States)

Areepattamannil, Shaljan; Kaur, Berinderjeet

2013-01-01

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

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

Directory of Open Access Journals (Sweden)

Fitria Habsah

2017-05-01

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

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

CERN Document Server

Schättler, Heinz

2015-01-01

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

Propaedeutics of Mathematical Language of Schemes and Structures in School Teaching of the Natural Sciences Profile

Directory of Open Access Journals (Sweden)

V. P. Kotchnev

2012-01-01

Full Text Available The paper looks at the teaching process at schools of the natural sciences profile. The subject of the research is devoted to the correlations between the students’ progress and the degree of their involvement in creative activities of problem solving in the natural sciences context. The research is aimed to demonstrate the reinforce- ment of students’ creative learning by teaching mathematical schemes and structures. The comparative characteristics of the task, problem and model approaches to mathematical problem solving are given; the experimental data on the efficiency of mathematical training based on the above approaches being discussed, as well as the specifics of modeling the tasks for problem solving. The author examines the ways for stimulating the students’ creative activity and motivating the knowledge acquisition, and search for the new mathematical conformities related to the natural science content. The significance of the Olympiad and other non-standard tasks, broadening the students’ horizons and stimulating creative thinking and abilities, is emphasized.The proposed method confirms the appropriateness of introducing the Olympiad and non-standard problem solving into the preparatory training curricula for the Unified State Examinations. 

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

Science.gov (United States)

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

2014-01-01

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

Preparing and Supporting Black Students to Enroll and Achieve in Advanced Mathematics Classes in Middle School: A Case Study

Science.gov (United States)

Cobbs, Joyce Bernice

2014-01-01

The literature on minority student achievement indicates that Black students are underrepresented in advanced mathematics courses. Advanced mathematics courses offer students the opportunity to engage with challenging curricula, experience rigorous instruction, and interact with quality teachers. The middle school years are particularly…

Teaching the pre-primary child reading and writing: a challenge for ...

African Journals Online (AJOL)

Teaching the pre-primary child reading and writing: a challenge for pre-primary school teachers in rivers state, Nigeria. ... Global Journal of Educational Research ... of the child's interactive learning and emphasizes specific teaching methods ...

Colloquy on Minority Males in Science, Technology, Engineering, and Mathematics

Science.gov (United States)

Didion, Catherine; Fortenberry, Norman L.; Cady, Elizabeth

2012-01-01

On August 8-12, 2010 the National Academy of Engineering (NAE), with funding from the National Science Foundation (NSF), convened the Colloquy on Minority Males in Science, Technology, Engineering, and Mathematics (STEM), following the release of several reports highlighting the educational challenges facing minority males. The NSF recognized the…

An Overview on Synergy between Mathematics and Biology

International Nuclear Information System (INIS)

He, Matthew

2013-01-01

Recent progress in the determination of genomic sequences has yielded many millions of gene sequences. But what do these sequences tell us and what are the generalities and rules that are governed by them? It seems that we understand very little about genetic contexts required to ''read'' them. There is more to life than the genomic blueprint of each organism. Life functions within the natural laws that we know and the ones we do not know. Mathematics can be used to understand life from the molecular to the biosphere level. This paper provides a brief overview of major historical events of molecular biology and genetics, current interface of emerging field of bioinformatics, and future challenges and perspectives between mathematics and biology

Teaching mathematics remotely: changed practices in distance education

Science.gov (United States)

Lowrie, Tom; Jorgensen, Robyn

2012-09-01

This investigation explored the challenges of creating meaningful mathematics practices for a community engaged in Distance Education (DE). Specifically, the study maps the influence of new technologies on the practices of a learning community where mathematics was taught remotely. The theoretical framework of this study utilised Bourdieu's work on practice to consider the changed nature of the field, in this case, remote education provision, over time. By using Bourdieu's notion of field, we are better able to understand the ways in which practices and discourses shape particular ways of working in rural education provision. The results of the study show that Field 1 was innovative and beyond the non-school world, while Field 2 lagged behind the technological resources of the non-school world.

Equity and spatial reasoning: reducing the mathematical achievement gap in gender and social disadvantage

Science.gov (United States)

Lowrie, Tom; Jorgensen, Robyn

2018-03-01

Since the early 70s, there has been recognition that there are specific differences in achievement based on variables, such as gender and socio-economic background, in terms of mathematics performance. However, these differences are not unilateral but rather quite specific and relate strongly to spatial reasoning. This early work has paved the way for thinking critically about who achieves in mathematics and why. This project innovatively combines the strengths of the two Chief Investigators—Lowrie's work in spatial reasoning and Jorgensen's work in equity. The assumptions, the approach and theoretical framing used in the study unite quite disparate areas of mathematics education into a cogent research program that seeks to challenge some of the long-held views in the field of mathematics education.

Collaborative innovations with rural and regional secondary teachers: enhancing student learning in mathematics

Science.gov (United States)

Pegg, John; Panizzon, Debra

2011-06-01

When questioned, secondary mathematics teachers in rural and regional schools in Australia refer to their limited opportunities to engage and share experiences with peers in other schools as an under-utilised and cost-effective mechanism to support their professional learning and enhance their students' learning. The paper reports on the creation and evaluation of a network of learning communities of rural secondary mathematics teachers around a common purpose—enhancement and increased engagement of student learning in mathematics. To achieve this goal, teams of teachers from six rural schools identified an issue hindering improved student learning of mathematics in their school. Working collaboratively with support from university personnel with expertise in curriculum, assessment and quality pedagogy, teachers developed and implemented strategies to address an identified issue in ways that were relevant to their teaching contexts. The research study identifies issues in mathematics of major concern to rural teachers of mathematics, the successes and challenges the teachers faced in working in learning communities on the issue they identified, and the efficacy of the professional learning model.

Making Recycled Paper: An Engineering Design Challenge

Science.gov (United States)

Song, Ting; Becker, Kurt

2013-01-01

Science, technology, engineering, and mathematics (STEM) educators are facing the challenge of attracting more students. The disparity between the need for engineers and the enrollment of engineering students is growing (Genalo, Bruning, & Adams, 2000), and career aspirations of high school students are inconsistent with the employment…

Incorporating Engineering Design Challenges into STEM Courses

Science.gov (United States)

Householder, Daniel L., Ed.; Hailey, Christine E., Ed.

2012-01-01

Successful strategies for incorporating engineering design challenges into science, technology, engineering, and mathematics (STEM) courses in American high schools are presented in this paper. The developers have taken the position that engineering design experiences should be an important component of the high school education of all American…

Confronting the Challenges Facing the Nigerian Nation State: Using ...

African Journals Online (AJOL)

This paper explains the concept of nation-state and sports. It critically examines some of the challenges characterizing Nigerian nation state such as ethnicity, corruption, politics of godfatherisms, tribalism, language differences, and religious crises among others. It emphasizes the use of sports for creating of friendship ...

Invigorating self-regulated learning strategies of mathematics among higher education students

Science.gov (United States)

Chechi, Vijay Kumar; Bhalla, Jyoti

2017-07-01

The global market is transforming at its ever-increasing rate of knots. Consequently, the work skills challenges that current students will encounter throughout their lifetimes will be drastically different from those of present and past and proffering new-fangled opportunities and posing new challenges. However, in order to deal with tomorrow's opportunities and challenges students ought to equip with higher order cognitive skills which are substantially different from those needed in the past. In order to accomplish this intention, students must be academically self-regulated, as academic self-regulation is playing a vital role for academic success, particularly in higher education. Students must be prepared in such a way that they should take responsibility for their own learning. Self-regulation suggests activities and thinking processes that learners can engage in during his learning. Self-regulation is encompassing a number of inter-dependent aspect viz. affective beliefs, cognition and meta-cognitive skills [1]. It helps the learners to make sagacious use of their intellect and expertise [2]. As statistics has shown that the achievement of students in mathematics has persistently been poor. Along with it, mathematics is considered as one of the most important subject course in architecture, agriculture, medicine, pharmacy and especially in engineering. In spite of its importance, most of the students considered it as a dull and dry subject and their performance is remarkably low and alarming. Therefore, the present paper will highlight various factors affecting performance of higher education students in mathematics and will suggest different self-regulated learning strategies which will act as boon for higher education students.

Technological pedagogical content knowledge of junior high school mathematics teachers in teaching linear equation

Science.gov (United States)

Wati, S.; Fitriana, L.; Mardiyana

2018-04-01

Linear equation is one of the topics in mathematics that are considered difficult. Student difficulties of understanding linear equation can be caused by lack of understanding this concept and the way of teachers teach. TPACK is a way to understand the complex relationships between teaching and content taught through the use of specific teaching approaches and supported by the right technology tools. This study aims to identify TPACK of junior high school mathematics teachers in teaching linear equation. The method used in the study was descriptive. In the first phase, a survey using a questionnaire was carried out on 45 junior high school mathematics teachers in teaching linear equation. While in the second phase, the interview involved three teachers. The analysis of data used were quantitative and qualitative technique. The result PCK revealed teachers emphasized developing procedural and conceptual knowledge through reliance on traditional in teaching linear equation. The result of TPK revealed teachers’ lower capacity to deal with the general information and communications technologies goals across the curriculum in teaching linear equation. The result indicated that PowerPoint constitutes TCK modal technological capability in teaching linear equation. The result of TPACK seems to suggest a low standard in teachers’ technological skills across a variety of mathematics education goals in teaching linear equation. This means that the ability of teachers’ TPACK in teaching linear equation still needs to be improved.

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.

Genomic similarity and kernel methods I: advancements by building on mathematical and statistical foundations.

Science.gov (United States)

Schaid, Daniel J

2010-01-01

Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1]. Copyright © 2010 S. Karger AG, Basel.

Performance-based classrooms: A case study of two elementary teachers of mathematics and science

Science.gov (United States)

Jones, Kenneth W.

This case study depicts how two elementary teachers develop classrooms devoted to performance-based instruction in mathematics and science. The purpose is to develop empirical evidence of classroom practices that leads to a conceptual framework about the nature of performance-based instruction. Performance-based assessment and instruction are defined from the literature to entail involving students in tasks that are complex and engaging, requiring them to apply knowledge and skills in authentic contexts. In elementary mathematics and science, such an approach emphasizes problem solving, exploration, inquiry, and reasoning. The body of the work examines teacher beliefs, curricular orientations, instructional strategies, assessment approaches, management and organizational skills, and interpersonal relationships. The focus throughout is on those aspects that foster student performance in elementary mathematics and science. The resulting framework describes five characteristics that contribute to performance-based classrooms: a caring classroom community, a connectionist learning theory, a thinking and doing curriculum, diverse opportunities for learning, and ongoing assessment, feedback, and adjustment. The conclusion analyzes factors external to the classroom that support or constrain the development of performance-based classrooms and discusses the implications for educational policy and further research.

Meaningful Statistics in Professional Practices as a Bridge between Mathematics and Science: An Evaluation of a Design Research Project

Science.gov (United States)

Dierdorp, Adri; Bakker, Arthur; van Maanen, Jan A.; Eijkelhof, Harrie M. C.

2014-01-01

Background: Creating coherence between school subjects mathematics and science and making these school subjects meaningful are still topical challenges. This study investigates how students make meaningful connections between mathematics, statistics, science and applications when they engage in a specially developed unit that is based on…

Research in mathematics and computer science, March 1, 1991--September 30, 1992

Energy Technology Data Exchange (ETDEWEB)

Pieper, G.W.

1992-10-01

This report discusses the following topics in mathematics and computer science at Argonne National Laboratory: Harnessing the Power; Modeling Piezoelectric Crystals; A Two-Way Street; The Challenge Is On; A True Molecular Engineering Capability; CHAMMPions Attack Climate Issues; Studying Vortex Dynamics; Studying Vortex Structure; Providing Reliable and Fast Derivatives; Automating Reasoning for Scientific Problem Solving; Optimization and Mathematical Programming; Scalable Algorithms for Linear Algebra; Reliable Core Software; Computing Phylogenetic Trees; Managing Life-Critical Systems; Interacting with Data through Visualization; New Tools for New Technologies.

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

OpenAIRE

Habsah, Fitria

2017-01-01

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

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

Directory of Open Access Journals (Sweden)

Yu.I. Sinko

2012-03-01

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

Mathematics Connection

African Journals Online (AJOL)

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

Quickfire Challenges to Inspire Problem Solving

Science.gov (United States)

Harper, Suzanne R.; Cox, Dana C.

2017-01-01

In the authors' attempts to incorporate problem solving into their mathematics courses, they have found that student ambition and creativity are often hampered by feelings of risk, as many students are conditioned to value a produced solution over the actual process of building one. Eliminating risk is neither possible nor desired. The challenge,…

Improving the Graduate School Experience for Women in Mathematics: the Edge Program

Science.gov (United States)

Bozeman, Sylvia T.; Hughes, Rhonda J.

For over a decade, Spelman College and Bryn Mawr College have collaborated on initiatives designed to increase the presence of women, with a special focus on women of color, in the upper ranks of mathematical science. The most recent initiative is the EDGE Program (Enhancing Diversity in Graduate Education), which addresses this challenge by attempting to decrease the loss of talent from U.S. graduate programs. To this end, the program provides structures that help women make successful transitions from undergraduate into graduate mathematics programs, redirect or refocus their ambitions when programs are inappropriate or unsuitable, and, ultimately, enable them to "accumulate advantages" that will empower them and foster success in their careers. A broader goal of this program is to diversify the mathematics community by creating models for mathematics programs that allow people from all backgrounds and cultures to thrive, advance, and contribute to the profession.

Multiphysics simulations: Challenges and opportunities

KAUST Repository

Keyes, David E.; McInnes, Lois Curfman; Woodward, Carol S.; Gropp, William D.; Myra, Eric S.; Pernice, Michael; Bell, John B.; Brown, Jed; Clo, Alain M.; Connors, Jeffrey Mark; Constantinescu, Emil M.; Estep, Donald J.; Evans, Katherine J.; Farhat, Charbel H.; Hakim, Ammar H.; Hammond, Glenn E.; Hansen, Glen A.; Hill, Judith C.; Isaac, Tobin; Jiao, Xiangmin; Jordan, Kirk E.; Kaushik, Dinesh K.; Kaxiras, Efthimios; Koniges, Alice E.; Lee, Kihwan; Lott, Aaron; Lu, Qiming; Magerlein, John H.; Maxwell, Reed M.; McCourt, Michael J.; Mehl, Miriam; Pawlowski, Roger P.; Randles, Amanda Peters; Reynolds, Daniel R.; Riviè re, Bé atrice M.; Rü de, Ulrich; Scheibe, Timothy D.; Shadid, John N.; Sheehan, Brendan; Shephard, Mark S.; Siegel, Andrew R.; Smith, Barry F.; Tang, Xianzhu; Wilson, Cian R G; Wohlmuth, Barbara Ian

2013-01-01

We consider multiphysics applications from algorithmic and architectural perspectives, where "algorithmic" includes both mathematical analysis and computational complexity, and "architectural" includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities. © The Author(s) 2012.

Multiphysics simulations: Challenges and opportunities

KAUST Repository

Keyes, David E.

2013-02-01

We consider multiphysics applications from algorithmic and architectural perspectives, where "algorithmic" includes both mathematical analysis and computational complexity, and "architectural" includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities. © The Author(s) 2012.

Multiphysics simulations: challenges and opportunities.

Energy Technology Data Exchange (ETDEWEB)

Keyes, D.; McInnes, L. C.; Woodward, C.; Gropp, W.; Myra, E.; Pernice, M. (Mathematics and Computer Science); (KAUST and Columbia Univ.); (Lawrence Livermore National Laboratory); (Univ. of Illinois at Urbana-Champaign); (Univ. of Mich.); (Idaho National Lab.)

2012-11-29

This report is an outcome of the workshop Multiphysics Simulations: Challenges and Opportunities, sponsored by the Institute of Computing in Science (ICiS). Additional information about the workshop, including relevant reading and presentations on multiphysics issues in applications, algorithms, and software, is available via https://sites.google.com/site/icismultiphysics2011/. We consider multiphysics applications from algorithmic and architectural perspectives, where 'algorithmic' includes both mathematical analysis and computational complexity and 'architectural' includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities. We also initiate a modest suite of test problems encompassing features present in many applications.

HOW TO GENERATE AUTONOMOUS QUESTIONING IN SECONDARY MATHEMATICS TEACHING?

DEFF Research Database (Denmark)

Jessen, Britta Eyrich

2017-01-01

In mathematics education it is still a major challenge to find ways to nurture students to pose and pursue their own questions in order to learn mathematics. During the last three decades problem posing has been explored through different approaches and in empirical studies. This paper presents...... the result of an empirical study, where teaching was designed and conducted based on The Anthropological Theory of the Didactic. It is shown how a changed didactic contract and open generating questions posed by the teacher can support students’ autonomous questioning of the taught knowledge. In the study......, students developed knowledge that went beyond curriculum requirements through autonomous activities, which were different from more traditional school and pedagogical culture....

Urban Big Data and Sustainable Development Goals: Challenges and Opportunities

OpenAIRE

Kharrazi, A.; Qin, H.; Zhang, Y.

2016-01-01

Cities are perhaps one of the most challenging and yet enabling arenas for sustainable development goals. The Sustainable Development Goals (SDGs) emphasize the need to monitor each goal through objective targets and indicators based on common denominators in the ability of countries to collect and maintain relevant standardized data. While this approach is aimed at harmonizing the SDGs at the national level, it presents unique challenges and opportunities for the development of innovative ur...

An Example Emphasizing Mass-Volume Relationships for Problem Solving in Soils

Science.gov (United States)

Heitman, J. L.; Vepraskas, M. J.

2009-01-01

Mass-volume relationships are a useful tool emphasized for problem solving in many geo-science and engineering applications. These relationships also have useful applications in soil science. Developing soils students' ability to utilize mass-volume relationships through schematic diagrams of soil phases (i.e., air, water, and solid) can help to…

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.

Mathematical modeling of physiological systems: an essential tool for discovery.

Science.gov (United States)

Glynn, Patric; Unudurthi, Sathya D; Hund, Thomas J

2014-08-28

Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?" Copyright © 2014 Elsevier Inc. All rights reserved.

The Magic of Mathematics Discovering the Spell of Mathematics

CERN Document Server

Pappas, Theoni

2011-01-01

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

Forensic Evaluation of Deaf Individuals: Challenges and Strategies.

Science.gov (United States)

Pollard, Robert Q; Berlinski, Brian T

2017-01-01

Forensic evaluation of deaf individuals presents unique challenges due to many examinees' fund of information deficits, potential for language deprivation, and examiners' frequent lack of creativity regarding communication methods. This article describes challenges most frequently encountered in competency to stand trial and criminal responsibility evaluations and offers strategies for overcoming them. The value of employing multiple communication methods, especially the use of illustrations, is emphasized. Suggestions also are offered regarding preparing evaluation reports and effectively communicating "key deaf fundamentals" to legal personnel. Encouragement is offered for qualified, sign-fluent professionals to engage in forensic work.

Quantitative Literacy for the Future Flourishing of our Students: A Guiding Aim for Mathematics Education

Directory of Open Access Journals (Sweden)

Samuel L. Tunstall

2017-01-01

Full Text Available In this essay, I examine the extent to which mathematics education and education for quantitative literacy support students’ present and future flourishing, a concept that entails realizing objective goods in a life lived from the inside. This perspective requires disentangling philosophical assumptions about the aims of mathematics education, which—in the context of flourishing—I take to be a hybrid of those that have informed curricular discussions over the past two centuries. In the process, I problematize ("make strange" many of the common reasons given for students learning mathematics, including: learning it for one’s career, for one’s logical reasoning skills, or for its own sake. My conclusion is that, through the end of compulsory schooling, all students should take coursework that fosters quantitative literacy, or the ability and disposition to use, interpret, and criticize numbers as they manifest in daily life. In addition, in the same environment, traditional mathematics should be included and compulsory up to grade eight, but afterward required only insofar as it is necessary for fulfilling one’s goals. I pursue this line of argument with full cognizance of sociopolitical elements of mathematics education and other challenges in implementation, noting that appealing to consequences—while fine as a justification for avoiding change in the short-term—is not a tenable justification for doing so in the long-term. I challenge readers to reflect on our ability to empower students for future flourishing, and to consider the role that mathematics has in doing so.

Interest in mathematics and science among students having high mathematics aptitude

Science.gov (United States)

Ely, Jane Alice

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

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

Directory of Open Access Journals (Sweden)

María F. Ayllón

2016-04-01

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

Mathematical thinking styles of undergraduate students and their achievement in mathematics

Science.gov (United States)

Risnanosanti

2017-08-01

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

Quotable Quotes in Mathematics

Science.gov (United States)

Lo, Bruce W. N.

1983-01-01

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

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…

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.

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.

Predicting Success in College Mathematics from High School Mathematics Preparation

OpenAIRE

Shepley, Richard A.

1983-01-01

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

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...

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

Science.gov (United States)

Haciomeroglu, Guney

2014-01-01

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

Mathematics across cultures the history of non-Western mathematics

CERN Document Server

2000-01-01

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

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

Science.gov (United States)

Bowyer, Jessica; Darlington, Ellie

2017-01-01

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

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

DEFF Research Database (Denmark)

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

2011-01-01

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

The Use of Questions within In-the-Moment Coaching in Initial Mathematics Teacher Education: Enhancing Participation, Reflection, and Co-Construction in Rehearsals of Practice

Science.gov (United States)

Averill, Robin; Drake, Michael; Anderson, Dayle; Anthony, Glenda

2016-01-01

Managing mathematical discussion is known to be challenging for novice teachers. Coaching within student teacher rehearsals of teaching has been shown to develop mathematics teaching practice, but can be time consuming. To examine how coaching using questions could assist novice teachers to promote mathematical thinking and discussions within…

The conceptual basis of mathematics in cardiology: (II). Calculus and differential equations.

Science.gov (United States)

Bates, Jason H T; Sobel, Burton E

2003-04-01

This is the second in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to

The conceptual basis of mathematics in cardiology IV: statistics and model fitting.

Science.gov (United States)

Bates, Jason H T; Sobel, Burton E

2003-06-01

This is the fourth in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to

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.

Mathematical marriages: intercourse between mathematics and Semiotic choice.

Science.gov (United States)

Wagner, Roy

2009-04-01

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

Official pedagogic identities from South African policy – some implications for mathematics teacher education practice

Directory of Open Access Journals (Sweden)

Diane Parker

2006-10-01

Full Text Available In South Africa the National Curriculum Statement for Grades 10 – 12 (General: Mathematics (DoE, 2003 together with the Norms and Standards for Educators (DoE, 2000a are key policy documents that provide the official basis for mathematics education reform and for the construction of new pedagogic identities. In this paper I use a framework based on the work of Bernstein (1996, 2000 to theorise the construction of pedagogic identities. I use this to build on Graven’s (2002 description of the new official pedagogic identity of the South African mathematics teacher, and on Adler et al. (2002 and others to raise questions related to teacher knowledge and the challenges  of developing specialist mathematics teacher identities through initial teacher education programmes.

Mathematical models for atmospheric pollutants. Final report

International Nuclear Information System (INIS)

Drake, R.L.; Barrager, S.M.

1979-08-01

The present and likely future roles of mathematical modeling in air quality decisions are described. The discussion emphasizes models and air pathway processes rather than the chemical and physical behavior of specific anthropogenic emissions. Summarized are the characteristics of various types of models used in the decision-making processes. Specific model subclasses are recommended for use in making air quality decisions that have site-specific, regional, national, or global impacts. The types of exposure and damage models that are currently used to predict the effects of air pollutants on humans, other animals, plants, ecosystems, property, and materials are described. The aesthetic effects of odor and visibility and the impact of pollutants on weather and climate are also addressed. Technical details of air pollution meteorology, chemical and physical properties of air pollutants, solution techniques, and air quality models are discussed in four appendices bound in separate volumes

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

Science.gov (United States)

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

2016-01-01

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

Factors Influencing Teacher Career Satisfaction, Teacher Collaboration and Everyday Challenges: An Exploratory Factor Analysis

Science.gov (United States)

Narayan, Nilesh Anish

2016-01-01

The main purpose of this study is to assess the construct validity of Australian eighth grade mathematics teachers' perceptions towards their career satisfaction, their teaching practice and the everyday challenges encountered in schools. The data were utilised from the Trends in International Mathematics and Science Study where a total of 802…

Mathematics

CERN Document Server

Eringen, A Cemal

2013-01-01

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

Teaching Mathematics by Comparison: Analog Visibility as a Double-Edged Sword

Science.gov (United States)

Begolli, Kreshnik Nasi; Richland, Lindsey Engle

2016-01-01

Comparing multiple solutions to a single problem is an important mode for developing flexible mathematical thinking, yet instructionally leading this activity is challenging (Stein, Engle, Smith, & Hughes, 2008). We test 1 decision teachers must make after having students solve a problem: whether to only verbally discuss students' solutions or…

The materiality of mathematics: presenting mathematics at the blackboard.

Science.gov (United States)

Greiffenhagen, Christian

2014-09-01

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

Rainforest Mathematics

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Kilpatrick, Jeremy

2014-01-01

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

Mathematical scandals

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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

Mathematical Model and Program for the Sizing of Counter-flow Natural Draft Wet Cooling Towers

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Victor-Eduard Cenușă

2017-08-01

Full Text Available Assuring the necessary temperature and mass flow rate of the cooling water to the condenser represents an essential condition for the efficient operation of a steam power plant. The paper presents equations which describe the physical phenomena and the mathematical model for the design of counter-flow natural draft wet cooling towers. Following is given the flow-chart of the associated computer program. A case study is made to show the results of the computer program and emphasize the interdependence between the main design parameters.

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

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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.

Financial mathematics

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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

Mathematics everywhere

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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

Engineering mathematics

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Stroud, K A

2013-01-01

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

Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

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

2014-01-01

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