Advanced Mathematical Thinking


ISBN: 978-0-7923-1456-1 (Print) 978-0-306-47203-9 (Online)
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Table of contents (15 chapters)

  1. Introduction

    1. Book Chapter

      Pages 3-21

      The Psychology of Advanced Mathematical Thinking

  2. The Nature of Advanced Mathematical Thingking

    1. Book Chapter

      Pages 25-41

      Advanced Mathematical Thinking Processes

    2. Book Chapter

      Pages 42-53

      Mathematical Creativity

    3. Book Chapter

      Pages 54-61

      Mathematical Proof

  3. Cognitive Theory of Advanced Mathematical Thinking

    1. Book Chapter

      Pages 65-81

      The Role of Definitions in the Teaching and Learning of Mathematics

    2. Book Chapter

      Pages 82-94

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

    3. Book Chapter

      Pages 95-126

      Reflective Abstraction in Advanced Mathematical Thinking

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

    1. Book Chapter

      Pages 127-139

      Research in Teaching and Learning Mathematics at an Advanced Level

    2. Book Chapter

      Pages 140-152

      Functions and Associated Learning Difficulties

    3. Book Chapter

      Pages 153-166


    4. Book Chapter

      Pages 167-198


    5. Book Chapter

      Pages 199-214

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

    6. Book Chapter

      Pages 215-230

      Research on Mathematical Proof

    7. Book Chapter

      Pages 231-248

      Advanced Mathematical Thinking and the Computer

  5. Epilogue

    1. Book Chapter

      Pages 251-259