Explanation and Proof in Mathematics

Philosophical and Educational Perspectives


ISBN: 978-1-4419-0575-8 (Print) 978-1-4419-0576-5 (Online)
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Table of contents (17 chapters)

  1. Front Matter

    Pages i-viii

  2. Reflections on the Nature and Teaching of Proof

    1. Front Matter

      Pages 16-16

    2. Book Chapter

      Pages 1-13


    3. Book Chapter

      Pages 17-32

      The Conjoint Origin of Proof and Theoretical Physics

    4. Book Chapter

      Pages 33-46

      Lakatos, Lakoff and Núñez: Towards a Satisfactory Definition of Continuity

    5. Book Chapter

      Pages 47-57

      Preaxiomatic Mathematical Reasoning: An Algebraic Approach

    6. Book Chapter

      Pages 59-70

      Completions, Constructions, and Corollaries

    7. Book Chapter

      Pages 71-83

      Authoritarian Versus Authoritative Teaching: Polya and Lakatos

    8. Book Chapter

      Pages 85-100

      Proofs as Bearers of Mathematical Knowledge

    9. Book Chapter

      Pages 101-111

      Mathematicians’ Individual Criteria for Accepting Theorems and Proofs: An Empirical Approach

  3. Proof and Cognitive Development

    1. Front Matter

      Pages 114-114

    2. Book Chapter

      Pages 115-135

      Bridging Knowing and Proving in Mathematics: A Didactical Perspective

    3. Book Chapter

      Pages 137-149

      The Long-Term Cognitive Development of Reasoning and Proof

    4. Book Chapter

      Pages 151-167

      Historical Artefacts, Semiotic Mediation and Teaching Proof

    5. Book Chapter

      Pages 169-188

      Proofs, Semiotics and Artefacts of Information Technologies

  4. Experiments, Diagrams and Proofs

    1. Front Matter

      Pages 190-190

    2. Book Chapter

      Pages 191-204

      Proof as Experiment in Wittgenstein

    3. Book Chapter

      Pages 205-221

      Experimentation and Proof in Mathematics

    4. Book Chapter

      Pages 223-236

      Proof, Mathematical Problem-Solving, and Explanation in Mathematics Teaching

    5. Book Chapter

      Pages 237-251

      Evolving Geometric Proofs in the Seventeenth Century: From Icons to Symbols

    6. Book Chapter

      Pages 253-285

      Proof in the Wording: Two Modalities from Ancient Chinese Algorithms

  5. Back Matter

    Pages 287-294