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The Nature of Mathematical Thinking

Author : Robert J. Sternberg
Publisher : Routledge
Release Date : 2012-10-12
ISBN : 1136487506
Pages : 352 pages
Rating : 4.6/5 (487 Download)

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Download Free The Nature of Mathematical Thinking PDF by Robert J. Sternberg Full Book and published by Routledge. This book was released on 2012-10-12 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why do some children seem to learn mathematics easily and others slave away at it, learning it only with great effort and apparent pain? Why are some people good at algebra but terrible at geometry? How can people who successfully run a business as adults have been failures at math in school? How come some professional mathematicians suffer terribly when trying to balance a checkbook? And why do school children in the United States perform so dismally in international comparisons? These are the kinds of real questions the editors set out to answer, or at least address, in editing this book on mathematical thinking. Their goal was to seek a diversity of contributors representing multiple viewpoints whose expertise might converge on the answers to these and other pressing and interesting questions regarding this subject. The chapter authors were asked to focus on their own approach to mathematical thinking, but also to address a common core of issues such as the nature of mathematical thinking, how it is similar to and different from other kinds of thinking, what makes some people or some groups better than others in this subject area, and how mathematical thinking can be assessed and taught. Their work is directed to a diverse audience -- psychologists interested in the nature of mathematical thinking and abilities, computer scientists who want to simulate mathematical thinking, educators involved in teaching and testing mathematical thinking, philosophers who need to understand the qualitative aspects of logical thinking, anthropologists and others interested in how and why mathematical thinking seems to differ in quality across cultures, and laypeople and others who have to think mathematically and want to understand how they are going to accomplish that feat.

Nature of Mathematical Thinking

Author : Jagat Narain Kapur
Publisher :
Release Date : 1975
ISBN :
Pages : 98 pages
Rating : 4.2/5 (14 Download)

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Download Free Nature of Mathematical Thinking PDF by Jagat Narain Kapur Full Book and published by . This book was released on 1975 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Nature of Mathematical Thinking

Author : Frank Wyndham Mitchell
Publisher :
Release Date : 1938
ISBN :
Pages : 130 pages
Rating : 4.4/5 ( Download)

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Download Free The Nature of Mathematical Thinking PDF by Frank Wyndham Mitchell Full Book and published by . This book was released on 1938 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advanced Mathematical Thinking

Author : Annie Selden
Publisher : Routledge
Release Date : 2013-10-15
ISBN : 1135478384
Pages : 80 pages
Rating : 4.5/5 (478 Download)

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Download Free Advanced Mathematical Thinking PDF by Annie Selden Full Book and published by Routledge. This book was released on 2013-10-15 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

The Math Gene

Author : Keith Devlin
Publisher : Hachette UK
Release Date : 2001-05-17
ISBN : 0786725087
Pages : 352 pages
Rating : 4.6/5 (725 Download)

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Download Free The Math Gene PDF by Keith Devlin Full Book and published by Hachette UK. This book was released on 2001-05-17 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: If people are endowed with a "number instinct" similar to the "language instinct" -- as recent research suggests -- then why can't everyone do math? In The Math Gene, mathematician and popular writer Keith Devlin attacks both sides of this question. Devlin offers a breathtakingly new theory of language development that describes how language evolved in two stages and how its main purpose was not communication. Devlin goes on to show that the ability to think mathematically arose out of the same symbol-manipulating ability that was so crucial to the very first emergence of true language. Why, then, can't we do math as well as we speak? The answer, says Devlin, is that we can and do -- we just don't recognize when we're using mathematical reasoning.

Advanced Mathematical Thinking

Author : David Tall
Publisher : Springer Science & Business Media
Release Date : 2006-04-11
ISBN : 0306472031
Pages : 298 pages
Rating : 4.6/5 (472 Download)

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Download Free Advanced Mathematical Thinking PDF by David Tall Full Book and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Thinking and Writing

Author : Randall Maddox
Publisher : Academic Press
Release Date : 2002
ISBN : 0124649769
Pages : 324 pages
Rating : 4.4/5 (649 Download)

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Download Free Mathematical Thinking and Writing PDF by Randall Maddox Full Book and published by Academic Press. This book was released on 2002 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ability to construct proofs is one of the most challenging aspects of the world of mathematics. It is, essentially, the defining moment for those testing the waters in a mathematical career. Instead of being submerged to the point of drowning, readers of Mathematical Thinking and Writing are given guidance and support while learning the language of proof construction and critical analysis. Randall Maddox guides the reader with a warm, conversational style, through the task of gaining a thorough understanding of the proof process, and encourages inexperienced mathematicians to step up and learn how to think like a mathematician. A student's skills in critical analysis will develop and become more polished than previously conceived. Most significantly, Dr. Maddox has the unique approach of using analogy within his book to clarify abstract ideas and clearly demonstrate methods of mathematical precision.

Mathematical Reasoning

Author : Raymond Nickerson
Publisher : Taylor & Francis
Release Date : 2011-02-25
ISBN : 1136945393
Pages : 597 pages
Rating : 4.6/5 (945 Download)

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Download Free Mathematical Reasoning PDF by Raymond Nickerson Full Book and published by Taylor & Francis. This book was released on 2011-02-25 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction. This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.

Play from Birth to Twelve and Beyond

Author : Doris Pronin Fromberg
Publisher : Psychology Press
Release Date : 1998
ISBN : 9780815317456
Pages : 608 pages
Rating : 4.7/5 (45 Download)

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Download Free Play from Birth to Twelve and Beyond PDF by Doris Pronin Fromberg Full Book and published by Psychology Press. This book was released on 1998 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Encyclopedia presents 62 essays by 78 distinguished experts who draw on their expertise in pedagogy, anthropology, ethology, history, philosophy, and psychology to examine play and its variety, complexity, and usefulness. Here you'll find out why play is vital in developing mathematical thinking and promoting social skills, how properly constructed play enhances classroom instruction, which games foster which skills, how playing stimulates creativity, and much more.

Understanding Emotions in Mathematical Thinking and Learning

Author : Ulises Xolocotzin
Publisher : Academic Press
Release Date : 2017-05-12
ISBN : 0128024895
Pages : 474 pages
Rating : 4.8/5 (24 Download)

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Download Free Understanding Emotions in Mathematical Thinking and Learning PDF by Ulises Xolocotzin Full Book and published by Academic Press. This book was released on 2017-05-12 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

The Nature and Development of Mathematics

Author : John Adams
Publisher : Taylor & Francis
Release Date : 2017-04-21
ISBN : 131730019X
Pages : 244 pages
Rating : 4.7/5 (3 Download)

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Download Free The Nature and Development of Mathematics PDF by John Adams Full Book and published by Taylor & Francis. This book was released on 2017-04-21 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: From an infant’s first grasp of quantity to Einstein’s theory of relativity, the human experience of number has intrigued researchers for centuries. Numeracy and mathematics have played fundamental roles in the development of societies and civilisations, and yet there is an essential mystery to these concepts, evidenced by the fear many people still feel when confronted by apparently simple sums. Including perspectives from anthropology, education and psychology, The Nature and Development of Mathematics addresses three core questions: Is maths natural? What is the impact of our culture and environment on mathematical thinking? And how can we improve our mathematical ability? Examining the cognitive processes that we use, the origins of these skills and their cultural context, and how learning and teaching can be supported in the classroom, the book contextualises each issue within the wider field, arguing that only by taking a cross-disciplinary perspective can we fully understand what it means to be numerate, as well as how we become numerate in our modern world. This is a unique collection including contributions from a range of renowned international researchers. It will be of interest to students and researchers across cognitive psychology, cultural anthropology and educational research.

Mathematical Thinking and Problem Solving

Author : Alan H. Schoenfeld
Publisher : Routledge
Release Date : 2016-05-06
ISBN : 1135440867
Pages : 360 pages
Rating : 4.5/5 (44 Download)

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Download Free Mathematical Thinking and Problem Solving PDF by Alan H. Schoenfeld Full Book and published by Routledge. This book was released on 2016-05-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the early 1980s there was virtually no serious communication among the various groups that contribute to mathematics education -- mathematicians, mathematics educators, classroom teachers, and cognitive scientists. Members of these groups came from different traditions, had different perspectives, and rarely gathered in the same place to discuss issues of common interest. Part of the problem was that there was no common ground for the discussions -- given the disparate traditions and perspectives. As one way of addressing this problem, the Sloan Foundation funded two conferences in the mid-1980s, bringing together members of the different communities in a ground clearing effort, designed to establish a base for communication. In those conferences, interdisciplinary teams reviewed major topic areas and put together distillations of what was known about them.* A more recent conference -- upon which this volume is based -- offered a forum in which various people involved in education reform would present their work, and members of the broad communities gathered would comment on it. The focus was primarily on college mathematics, informed by developments in K-12 mathematics. The main issues of the conference were mathematical thinking and problem solving.

How Mathematicians Think

Author : William Byers
Publisher : Princeton University Press
Release Date : 2010-05-02
ISBN : 0691145997
Pages : 424 pages
Rating : 4.1/5 (145 Download)

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Download Free How Mathematicians Think PDF by William Byers Full Book and published by Princeton University Press. This book was released on 2010-05-02 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.

The University of New Mexico Bulletin

Author : C. V. Newsom
Publisher : Forgotten Books
Release Date : 2015-06-14
ISBN : 9781330296462
Pages : 43 pages
Rating : 4.6/5 (46 Download)

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Download Free The University of New Mexico Bulletin PDF by C. V. Newsom Full Book and published by Forgotten Books. This book was released on 2015-06-14 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The University of New Mexico Bulletin: An Introduction to Mathematics; A Study of the Nature of Mathematical Knowledge For several years the author has had the privilege of giving lectures upon the nature of mathematics to students in the University of New Mexico. One set of lectures has been given to certain classes of beginning students in college mathematics as it is the belief of many mathematicians that little actual mathematical thinking can be indulged in without some comprehension of the meaning of mathematics. An additional advanced course of lectures of the same fundamental nature has been made available to advanced students in mathematics with the hope that they would appreciate many of the problems which face the creative mathematician. As a result of this experience it would seem that a short monograph of popular appeal upon the nature of mathematics might be welcomed. Of course, there are a few excellent books available to the student who cares to work seriously in the field. However, these books contain difficult vocabularies or symbolic languages which hide difficult concepts. So it is the purpose of this short work to present a simple introduction to modern mathematical thought, omitting completely many of the important extensions which are occupying the attention of mathematicians. One must realize that the decision as to what is mathematics or what is not mathematics is, to a great extent, arbitrary. Hence not all mathematicians agree. Some mathematicians prefer to be called "pure mathematicians," and others prefer to be classified as "applied mathematicians." The purest of "pure mathematicians" refuses to soil his hands in the laboratory, and his meditations are the envy of modern philosophers to such an extent that philosophers are now studying mathematics. The extremist among the "applied mathematicians" goes to sleep while a theory is expounded; he wants a formula; and he wants to know when and how such a formula is used. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Handbook of Research on the Psychology of Mathematics Education

Author : Angel Gutiérrez
Publisher : Sense Publishers
Release Date : 2006
ISBN : 9077874194
Pages : 538 pages
Rating : 4.7/5 (874 Download)

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Download Free Handbook of Research on the Psychology of Mathematics Education PDF by Angel Gutiérrez Full Book and published by Sense Publishers. This book was released on 2006 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compilation of the research produced by the International Group for the Psychology of Mathematics Education (PME) since its creation in 1976. The first three sections summarize cognitively-oriented research on learning and teaching specific content areas, transversal areas, and based on technology-rich environments. The fourth section is devoted to the research on social, affective, cultural and cognitive aspects of mathematics education. The fifth section includes two chapters summarizing the PME research on teacher training and professional life of mathematics teachers.

Mathematical and Analogical Reasoning of Young Learners

Author : Lyn D. English
Publisher : Routledge
Release Date : 2004-07-19
ISBN : 1135638705
Pages : 237 pages
Rating : 4.5/5 (638 Download)

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Download Free Mathematical and Analogical Reasoning of Young Learners PDF by Lyn D. English Full Book and published by Routledge. This book was released on 2004-07-19 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and Analogical Reasoning of Young Learners provides foundational knowledge of the nature, development, and assessment of mathematical and analogical reasoning in young children. Reasoning is fundamental to understanding mathematics and is identified as one of the 10 key standards for school mathematics for the new millennium. The book draws on longitudinal and cross-cultural studies, conducted in the United States and Australia, of children's reasoning development as they progressed from preschool through the end of second grade. The multifaceted analysis of young children's development of mathematical and analogical reasoning focuses on individual learners, their learning environments, and the interaction between the two. The multidisciplinary team of authors present multiple perspectives and multiple methodologies, and provide valuable information on organizing and sustaining interdisciplinary and cross-cultural inquiry. Key issues addressed include: *the relationship between mathematical and analogical reasoning; *how changes in children's reasoning relate to the implicit instruction they receive in their classrooms; *analyses of the participating teachers' knowledge, beliefs, and practices with respect to mathematical and analogical reasoning of young learners; and *ways in which we might promote development of mathematical and analogical reasoning in young children. This volume is highly relevant for mathematics educators, researchers in mathematics education, educational psychologists, early childhood teachers, and others interested in mathematical development of young children, in particular, the development of their reasoning processes.

I, Mathematician

Author : Peter Casazza
Publisher : The Mathematical Association of America
Release Date : 2015-03-10
ISBN : 0883855852
Pages : 289 pages
Rating : 4.3/5 (855 Download)

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Download Free I, Mathematician PDF by Peter Casazza Full Book and published by The Mathematical Association of America. This book was released on 2015-03-10 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians have pondered the psychology of the members of our tribe probably since mathematics was invented, but for certain since Hadamard’s The Psychology of Invention in the Mathematical Field. The editors asked two dozen prominent mathematicians (and one spouse thereof) to ruminate on what makes us different. The answers they got are thoughtful, interesting and thought-provoking. Not all respondents addressed the question directly. Michael Atiyah reflects on the tension between truth and beauty in mathematics. T.W. Körner, Alan Schoenfeld and Hyman Bass chose to write, reflectively and thoughtfully, about teaching and learning. Others, including Ian Stewart and Jane Hawkins, write about the sociology of our community. Many of the contributions range into philosophy of mathematics and the nature of our thought processes. Any mathematician will find much of interest here.