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Advanced Mathematical Thinking : Mathematics Education Library, Vol.11 - David Tall

Advanced Mathematical Thinking

Mathematics Education Library, Vol.11

By: David Tall (Editor)

Hardcover

Published: 30th November 1991
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edited by David Tall Science Education Dept., University of Warwick, Coventry, UK Series: MATHEMATICS EDUCATION LIBRARY volume: 11. 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. Its three main parts focus on the nature of advanced mathematical thinking, the theory of its cognitive development, and reviews of cognitive research. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. The reviews of recent research concentrate on cognitive development and conceptual difficulties with the notions of functions, limits, infinity, analysis, proof, and the use of the computer. They provide a wide overview and an introduction to current thinking which is highly appropriate for the college professor in mathematics or the general mathematics educator. Kluwer Academic Publishers, Dordrecht. October 1991. 308 pp. Hardbound. Dfl.180.00. BrP.72.25. July 1994. 312 pp. Paperback. ISBN 0-7923-2812-4. Dfl.65.00. BrP.26.00.

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: 9780792314561
ISBN-10: 0792314565
Series: Mathematics Education Library, Vol.11
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 292
Published: 30th November 1991
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.77 x 16.51  x 2.54
Weight (kg): 0.66