Advanced Mathematical Thinking

Editors:

ISBN: 978-0-7923-1456-1 (Print) 978-0-306-47203-9 (Online)

Table of contents (15 chapters)

  1. Front Matter

    Pages i-xvii

  2. Introduction

    1. No Access

      Book Chapter

      Pages 3-21

      The Psychology of Advanced Mathematical Thinking

  3. The Nature of Advanced Mathematical Thingking

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      Book Chapter

      Pages 25-41

      Advanced Mathematical Thinking Processes

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      Book Chapter

      Pages 42-53

      Mathematical Creativity

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      Book Chapter

      Pages 54-61

      Mathematical Proof

  4. Cognitive Theory of Advanced Mathematical Thinking

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      Book Chapter

      Pages 65-81

      The Role of Definitions in the Teaching and Learning of Mathematics

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      Book Chapter

      Pages 82-94

      The Role of Conceptual Entities and Their Symbols in Building Advanced Mathematical Concepts

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      Book Chapter

      Pages 95-126

      Reflective Abstraction in Advanced Mathematical Thinking

  5. Research into the Teaching and Learning of Advanced Mathematical Thinking

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      Book Chapter

      Pages 127-139

      Research in Teaching and Learning Mathematics at an Advanced Level

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      Book Chapter

      Pages 140-152

      Functions and Associated Learning Difficulties

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      Book Chapter

      Pages 153-166

      Limits

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      Book Chapter

      Pages 167-198

      Analysis

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      Book Chapter

      Pages 199-214

      The Role of Studients’ Intuitions of Infinity in Teaching the Cantorian Theory

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      Book Chapter

      Pages 215-230

      Research on Mathematical Proof

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      Book Chapter

      Pages 231-248

      Advanced Mathematical Thinking and the Computer

  6. Epilogue

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      Book Chapter

      Pages 251-259

      Reflections

  7. Back Matter

    Pages 261-290