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Advanced Mathematical Thinking : Mathematics Education Library - David Tall

Advanced Mathematical Thinking

Mathematics Education Library

By: David Tall (Editor)

Paperback Published: 31st May 1994
ISBN: 9780792328124
Number Of Pages: 292

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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.

This book can help mathematics educators place their research within a broader perspective of the development of mathematical reasoning, and it can help mathematicians see the deep connections between mathematics education research and their own teaching.
(Patrick W. Thompson in Journal for Research in Mathematics Education)
It promises to be the standard reference work for many years to come, and a source of both information and inspiration ... The book is a most welcome distillation and resource for further development in our collective sense of what constitutes advanced mathematical thinking, and how we can make it accessible to more people.
(John Mason in Zentralblatt fur Didaktik der Mathematik)

Preface
Introduction
The Psychology of Advanced Mathematical Thinking
The Nature of Advanced Mathematical Thinking
Advanced Mathematical Thinking Processes
Mathematical Creativity
Mathematical Proof
Cognitive Theory of Advanced Mathematical Thinking
The Role of Definitions in the Teaching and Learning of Mathematics
The Role of Conceptual Entities and their Symbols in Building Advanced Mathematical Concepts
Reflective Abstraction in Advanced Mathematical Thinking
Research into the Teaching and Learning of Advanced Mathematical Thinking
Research in Teaching and Learning Mathematics at an Advanced Level
Functions and Associated Learning Difficulties
Limits
Analysis
The Role of Students' Intuitions of Infinity in Teaching the Cantorial Theory
Research on Mathematical Proof
Advanced Mathematical Thinking and the Computer
Appendix to 14 ISETL: A Computer Language for Advanced Mathematical Thinking
Epilogue
Reflections
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792328124
ISBN-10: 0792328124
Series: Mathematics Education Library
Audience: General
Format: Paperback
Language: English
Number Of Pages: 292
Published: 31st May 1994
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.37 x 16.05  x 1.83
Weight (kg): 0.45