Advanced mathematical thinking

著者

書誌事項

Advanced mathematical thinking

edited by David Tall

Kluwer Academic Publishers, c1991

  • : pbk

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注記

Includes bibliographical references (p. 261-274) and index

オンデマンド版(ディスク無し)により<BA13871963>とは別書誌

Originally published in series: Mathematics education library ; v. 11

"Printed by Books on Demand, Germany"--P. [296]

内容説明・目次

内容説明

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.

目次

  • Preface. Introduction. 1. The Psychology of Advanced Mathematical Thinking
  • D. Tall. I: The Nature of Advanced Mathematical Thinking. 2. Advanced Mathematical Thinking Processes
  • T. Dreyfus. 3. Mathematical Creativity
  • G. Ervynck. 4. Mathematical Proof
  • G. Hanna. II: Cognitive Theory of Advanced Mathematical Thinking. 5. The Role of Definitions in the Teaching and Learning of Mathematics
  • S. Vinner. 6. The Role of Conceptual Entities and their Symbols in Building Advanced Mathematical Concepts
  • G. Harel, J. Kaput. 7. Reflective Abstraction in Advanced Mathematical Thinking
  • E. Dubinsky. III: Research into the Teaching and Learning of Advanced Mathematical Thinking. 8. Research in Teaching and Learning Mathematics at an Advanced Level
  • A. Robert, R. Schwarzenberger. 9. Functions and Associated Learning Difficulties
  • T. Eisenberg. 10. Limits
  • B. Cornu. 11. Analysis
  • M. Artigue. 12. The Role of Students' Intuitions of Infinity in Teaching the Cantorial Theory
  • D. Tirosh. 13. Research on Mathematical Proof
  • D. Alibert, M. Thomas. 14. Advanced Mathematical Thinking and the Computer
  • E. Dubinsky, D. Tall. Appendix to 14. ISETL: A Computer Language for Advanced Mathematical Thinking. Epilogue. 15. Reflections
  • D. Tall. Bibliography. Index.

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