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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