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How Humans Learn To Think Mathematically

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How Humans Learn To Think Mathematically

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Author : David Tall
language : en
Publisher: Cambridge University Press
Release Date : 2013-09-02

How Humans Learn To Think Mathematically written by David Tall and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-02 with Psychology categories.

How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.

How Humans Learn To Think Mathematically

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Author : David Tall
language : en
Publisher: Cambridge University Press
Release Date : 2013-09-02

Understanding Emotions In Mathematical Thinking And Learning

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Author : Ulises Xolocotzin
language : en
Publisher: Academic Press
Release Date : 2017-05-12

Understanding Emotions In Mathematical Thinking And Learning written by Ulises Xolocotzin and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-12 with Psychology categories.

Emotions play a critical role in mathematical cognition and learning. Understanding Emotions in Mathematical Thinking and Learning offers a multidisciplinary approach to the role of emotions in numerical cognition, mathematics education, learning sciences, and affective sciences. It addresses ways in which emotions relate to cognitive processes involved in learning and doing mathematics, including processing of numerical and physical magnitudes (e.g. time and space), performance in arithmetic and algebra, problem solving and reasoning attitudes, learning technologies, and mathematics achievement. Additionally, it covers social and affective issues such as identity and attitudes toward mathematics. - Covers methodologies in studying emotion in mathematical knowledge - Reflects the diverse and innovative nature of the methodological approaches and theoretical frameworks proposed by current investigations of emotions and mathematical cognition - Includes perspectives from cognitive experimental psychology, neuroscience, and from sociocultural, semiotic, and discursive approaches - Explores the role of anxiety in mathematical learning - Synthesizes unifies the work of multiple sub-disciplines in one place

Humanizing Mathematics And Its Philosophy

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Author : Bharath Sriraman
language : en
Publisher: Birkhäuser
Release Date : 2017-11-07

Humanizing Mathematics And Its Philosophy written by Bharath Sriraman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-07 with Mathematics categories.

This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.

How To Think About Analysis

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Author : Lara Alcock
language : en
Publisher: OUP Oxford
Release Date : 2014-09-25

How To Think About Analysis written by Lara Alcock and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-25 with Mathematics categories.

Analysis (sometimes called Real Analysis or Advanced Calculus) is a core subject in most undergraduate mathematics degrees. It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the student's existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.

Lesson Study Challenges In Mathematics Education

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Author : Maitree Inprasitha
language : en
Publisher: World Scientific
Release Date : 2015-03-25

Lesson Study Challenges In Mathematics Education written by Maitree Inprasitha and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-25 with Mathematics categories.

Classroom Innovations through Lesson Study is an APEC EDNET (Asia-Pacific Economic Cooperation Education Network) project that aims to improve the quality of education in the area of mathematics. This book includes challenges of lesson study implementation from members of the APEC economies.Lesson study is one of the best ways to improve the quality of teaching. It is a model approach for improvement of teacher education across the globe. This book focuses on mathematics education, teacher education, and curriculum implementation and reforms.

Mathematics Rebooted

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Author : Lara Alcock
language : en
Publisher: Oxford University Press
Release Date : 2017-10-06

Mathematics Rebooted written by Lara Alcock and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-06 with Mathematics categories.

Would you like to understand more mathematics? Many people would. Perhaps at school you liked mathematics for a while but were then put off because you missed a key idea and kept getting stuck. Perhaps you always liked mathematics but gave it up because your main interest was music or languages or science or philosophy. Or perhaps you studied mathematics to advanced levels, but have now forgotten most of what you once knew. Whichever is the case, this book is for you. It aims to build on what you know, revisiting basic ideas with a focus on meaning. Each chapter starts with an idea from school mathematics - often primary school mathematics - and gradually builds up a network of links to more advanced material. It explores fundamental ideas in depth, using insights from research in mathematics education and psychology to explain why people often get confused, and how to overcome that confusion. For nervous readers, it will build confidence by clarifying basic ideas. For more experienced readers, it will highlight new connections to more advanced material. Throughout, the book explains how mathematicians think, and how ordinary people can understand and enjoy mathematical ideas and arguments. If you would like to be better informed about the intrinsic elegance of mathematics, this engaging guide is the place to start.

Learning To Teach Mathematics In The Secondary School

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Author : Sue Johnston-Wilder
language : en
Publisher: Taylor & Francis
Release Date : 2016-09-13

Learning To Teach Mathematics In The Secondary School written by Sue Johnston-Wilder and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-13 with Education categories.

Learning to Teach Mathematics in the Secondary School combines theory and practice to present a broad introduction to the opportunities and challenges of teaching mathematics in the secondary school classroom. This fourth edition has been fully updated to reflect the latest changes to the curriculum and research in the field, taking into account key developments in teacher training and education, including examinations and assessment. Written specifically with the new and student teacher in mind, the book covers a wide range of issues related to the teaching of mathematics, such as: why we teach mathematics the place of mathematics in the National Curriculum planning, teaching and assessing for mathematics learning how to communicate mathematically using digital technology to advance mathematical learning working with students with special educational needs post-16 teaching the importance of professional development the affective dimension when learning mathematics, including motivation, confidence and resilience Already a major text for many university teaching courses, this revised edition features a glossary of useful terms and carefully designed tasks to prompt critical reflection and support thinking and writing up to Masters Level. Issues of professional development are also examined, as well as a range of teaching approaches and styles from whole-class strategies to personalised learning, helping you to make the most of school experience, during your training and beyond. Designed for use as a core textbook, Learning to Teach Mathematics in the Secondary School provides essential guidance and advice for all those who aspire to be effective mathematics teachers.

Teaching And Learning Discrete Mathematics Worldwide Curriculum And Research

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Author : Eric W. Hart
language : en
Publisher: Springer
Release Date : 2017-12-09

Teaching And Learning Discrete Mathematics Worldwide Curriculum And Research written by Eric W. Hart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-09 with Education categories.

This book discusses examples of discrete mathematics in school curricula, including in the areas of graph theory, recursion and discrete dynamical systems, combinatorics, logic, game theory, and the mathematics of fairness. In addition, it describes current discrete mathematics curriculum initiatives in several countries, and presents ongoing research, especially in the areas of combinatorial reasoning and the affective dimension of learning discrete mathematics. Discrete mathematics is the math of our time.' So declared the immediate past president of the National Council of Teachers of Mathematics, John Dossey, in 1991. Nearly 30 years later that statement is still true, although the news has not yet fully reached school mathematics curricula. Nevertheless, much valuable work has been done, and continues to be done. This volume reports on some of that work. It provides a glimpse of the state of the art in learning and teaching discrete mathematics around the world, and it makes the case once again that discrete mathematics is indeed mathematics for our time, even more so today in our digital age, and it should be included in the core curricula of all countries for all students.

And The Rest Is Just Algebra

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Author : Sepideh Stewart
language : en
Publisher: Springer
Release Date : 2016-10-20

And The Rest Is Just Algebra written by Sepideh Stewart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-20 with Education categories.

This book addresses college students' weak foundation in algebra, its causes, and potential solutions to improve their long-term success and understanding in mathematics as a whole. The authors, who are experts in a wide variety of fields, emphasize that these difficulties are more complex than just forgotten rules, and offer strategic approaches from a number of angles that will increase the chances of student understanding. Instructors who are frustrated with their students’ lack of skills and knowledge at college level will find this volume helpful, as the authors confront the deeper reasons why students have difficulties with Algebra and reveal how to remedy the issue.

How Humans Learn To Think Mathematically

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