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Advanced Mathematical Thinking David Tall

Advanced Mathematical Thinking By David Tall

Advanced Mathematical Thinking by David Tall

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Summary

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.

Advanced Mathematical Thinking Summary

Advanced Mathematical Thinking by David Tall

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 Reviews

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)

Table of Contents

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.

Additional information

NPB9780792314561
9780792314561
0792314565
Advanced Mathematical Thinking by David Tall
David Tall
Mathematics Education Library
New
Hardback
Springer
1991-11-30
292
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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Customer Reviews - Advanced Mathematical Thinking