Advanced Mathematical Thinking
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Advanced Mathematical Thinking
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Author : David Tall
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Advanced Mathematical Thinking written by David Tall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Education categories.
Advanced Mathematical Thinking has played a central role in the development of human civilization for over two millennia. Yet in all that time the serious study of the nature of advanced mathematical thinking – what it is, how it functions in the minds of expert mathematicians, how it can be encouraged and improved in the developing minds of students – has been limited to the reflections of a few significant individuals scattered throughout the history of mathematics. In the twentieth century the theory of mathematical education during the compulsory years of schooling to age 16 has developed its own body of empirical research, theory and practice. But the extensions of such theories to more advanced levels have only occurred in the last few years. In 1976 The International Group for the Psychology of Mathematics (known as PME) was formed and has met annually at different venues round the world to share research ideas. In 1985 a Working Group of PME was formed to focus on Advanced Mathematical Thinking with a major aim of producing this volume. The text begins with an introductory chapter on the psychology of advanced mathema- cal thinking, with the remaining chapters grouped under three headings: • the nature of advanced mathematical thinking, • cognitive theory, and • reviews of the progress of cognitive research into different areas of advanced mathematics.
Advanced Mathematical Thinking
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Author : David Tall
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-11-30
Advanced Mathematical Thinking written by David Tall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-11-30 with Education categories.
This book is the first major study of advanced mathematical thinking as performed by mathematicians and taught to students in senior high school and university. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. It is highly appropriate for the college professor in mathematics or the general mathematics educator.
Advanced Mathematical Thinking
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Author : Annie Selden
language : en
Publisher: Routledge
Release Date : 2013-10-15
Advanced Mathematical Thinking written by Annie Selden and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-15 with Education categories.
This is Volume 7, Issue 1 2005, a Special Issue of 'Mathematical Thinking and Learning' which looks at Advanced Mathematical Thinking. Opening with a brief history of attempts to characterize advanced mathematical thinking, beginning with the deliberations of the Advanced Mathematical Thinking Working Group of the International Group for the Psychology of Mathematics Education. The articles follow the recurring themes: (a) the distinction between identifying kinds of thinking that might be regarded as advanced at any grade level and taking as advanced any thinking about mathematical topics considered advanced; (b) the utility of characterizing such thinking for integrating the entire curriculum; (c) general tests, or criteria, for identifying advanced mathematical thinking; and (d) an emphasis on advancing mathematical practices.
Advanced Mathematical Thinking
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Author : Annie Selden
language : en
Publisher: Routledge
Release Date : 2013-10-15
Advanced Mathematical Thinking written by Annie Selden and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-15 with Education categories.
This is Volume 7, Issue 1 2005, a Special Issue of 'Mathematical Thinking and Learning' which looks at Advanced Mathematical Thinking. Opening with a brief history of attempts to characterize advanced mathematical thinking, beginning with the deliberations of the Advanced Mathematical Thinking Working Group of the International Group for the Psychology of Mathematics Education. The articles follow the recurring themes: (a) the distinction between identifying kinds of thinking that might be regarded as advanced at any grade level and taking as advanced any thinking about mathematical topics considered advanced; (b) the utility of characterizing such thinking for integrating the entire curriculum; (c) general tests, or criteria, for identifying advanced mathematical thinking; and (d) an emphasis on advancing mathematical practices.
Advanced Mathematical Thinking
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Author : David Tall
language : en
Publisher:
Release Date : 2014-01-15
Advanced Mathematical Thinking written by David Tall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Introduction To Mathematical Thinking
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Author : Keith J. Devlin
language : en
Publisher:
Release Date : 2012
Introduction To Mathematical Thinking written by Keith J. Devlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
"Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.
Structural Understanding In Advanced Mathematical Thinking
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Author : Naďa Stehlíková
language : en
Publisher: Nada Stehlikova
Release Date : 2004
Structural Understanding In Advanced Mathematical Thinking written by Naďa Stehlíková and has been published by Nada Stehlikova this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
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 Education 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.
Mathematical Thinking How To Develop It In The Classroom
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Author : Shigeo Katagiri
language : en
Publisher: World Scientific
Release Date : 2012-01-27
Mathematical Thinking How To Develop It In The Classroom written by Shigeo Katagiri and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-27 with Mathematics categories.
Developing mathematical thinking is one of major aims of mathematics education. In mathematics education research, there are a number of researches which describe what it is and how we can observe in experimental research. However, teachers have difficulties to develope it in the classrooms. This book is the result of lesson studies over the past 50 years. It describes three perspectives of mathematical thinking: Mathematical Attitude (Minds set), Mathematical Methods in General and Mathematical Ideas with Content and explains how to develop them in the classroom with illuminating examples.
Mathematical Thinking
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Author : John P. D'Angelo
language : en
Publisher:
Release Date : 2018
Mathematical Thinking written by John P. D'Angelo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Business & Economics categories.
For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics-skills vital for success throughout the upperclass mathematics curriculum. The text offers both discrete and continuous mathematics, allowing instructors to emphasize one or to present the fundamentals of both. It begins by discussing mathematical language and proof techniques (including induction), applies them to easily-understood questions in elementary number theory and counting, and then develops additional techniques of proof via important topics in discrete and continuous mathematics. The stimulating exercises are acclaimed for their exceptional quality.