Inhaltsangabe
Part I. Reflections on the Nature and Teaching of Proof Chapter 1. The Conjoint Origin of Proof and Theoretical Physics Hans Niels Jahnke Chapter 2. Lakatos, Lakoff and Núñez: Towards a Satisfactory Definition of Continuity. Teun Koetsier Chapter 3. Pre-Axiomatic Mathematical Reasoning: An Algebraic Approach Mary Catherine Leng Chapter 4. Completions, Constructions and Corrollaries Thomas Mormann Chapter 5. Authoritarian vs. Authoritative Teaching: Polya and Lakatos Brendan Larvor Chapter 6. Proofs as Bearers of Mathematical Knowledge Gila Hanna & Ed Barbeau Chapter 7. Mathematicians' Individual Criteria for Accepting Theorems and Proofs: An Empirical Approach Aiso Heinze Part II. Proof and Cognitive Development Chapter 8. Bridging Knowing and Proving in Mathematics: A Didactical Perspective Nicolas Balacheff Chapter 9. The Long-term Cognitive Development of Reasoning and Proof David Tall & Juan Pablo Mejia-Ramos Chapter 10. Historical Artefacts, Semiotic Mediation and Teaching Proof Mariolina Bartolini-Bussi Chapter 11. Proofs, Semiotics and Artefacts of Information Technologies Alessandra Mariotti Part III. Experiments, Diagrams and Proofs Chapter 12. Proof as Experiment in Wittgenstein Alfred Nordmann Chapter 13. Experimentation and Proof in Mathematics Michael D. de Villiers Chapter 14. Proof, Mathematical Problem-Solving, and Explanation in Mathematics Teaching Kazuhiko Nunokawa Chapter 15. Evolving Geometric Proofs in the 17th Century: From Icons toSymbols Evelyne Barbin Chapter 16. Proof in the Wording: Two modalities from Ancient Chinese Algorithms Karine Chemla
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