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Explanation and Proof in Mathematics

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Cover of 'Explanation and Proof in Mathematics'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction
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    Chapter 2 The Conjoint Origin of Proof and Theoretical Physics
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    Chapter 3 Lakatos, Lakoff and Núñez: Towards a Satisfactory Definition of Continuity
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    Chapter 4 Preaxiomatic Mathematical Reasoning: An Algebraic Approach
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    Chapter 5 Completions, Constructions, and Corollaries
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    Chapter 6 Authoritarian Versus Authoritative Teaching: Polya and Lakatos
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    Chapter 7 Proofs as Bearers of Mathematical Knowledge
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    Chapter 8 Mathematicians’ Individual Criteria for Accepting Theorems and Proofs: An Empirical Approach
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    Chapter 9 Bridging Knowing and Proving in Mathematics: A Didactical Perspective
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    Chapter 10 The Long-Term Cognitive Development of Reasoning and Proof
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    Chapter 11 Historical Artefacts, Semiotic Mediation and Teaching Proof
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    Chapter 12 Proofs, Semiotics and Artefacts of Information Technologies
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    Chapter 13 Proof as Experiment in Wittgenstein
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    Chapter 14 Experimentation and Proof in Mathematics
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    Chapter 15 Proof, Mathematical Problem-Solving, and Explanation in Mathematics Teaching
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    Chapter 16 Evolving Geometric Proofs in the Seventeenth Century: From Icons to Symbols
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    Chapter 17 Proof in the Wording: Two Modalities from Ancient Chinese Algorithms
Attention for Chapter 3: Lakatos, Lakoff and Núñez: Towards a Satisfactory Definition of Continuity
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