Explanation and Proof in Mathematics

1. Introduction
Gila Hanna, Hans Niels Jahnke, Helmut Pulte

2. The Conjoint Origin of Proof and Theoretical Physics
Hans Niels Jahnke

3. Lakatos, Lakoff and Núñez: Towards a Satisfactory Definition of Continuity
Teun Koetsier

4. Preaxiomatic Mathematical Reasoning: An Algebraic Approach
Mary Leng

5. Completions, Constructions, and Corollaries
Thomas Mormann

6. Authoritarian Versus Authoritative Teaching: Polya and Lakatos
Brendan Larvor

7. Proofs as Bearers of Mathematical Knowledge
Gila Hanna, Ed Barbeau

8. Mathematicians’ Individual Criteria for Accepting Theorems and Proofs: An Empirical Approach
Aiso Heinze

9. Bridging Knowing and Proving in Mathematics: A Didactical Perspective
Nicolas Balacheff

10. The Long-Term Cognitive Development of Reasoning and Proof
David Tall, Juan Pablo Mejia-Ramos

11. Historical Artefacts, Semiotic Mediation and Teaching Proof
Maria G. Bartolini Bussi

12. Proofs, Semiotics and Artefacts of Information Technologies
Maria Alessandra Mariotti

13. Proof as Experiment in Wittgenstein
Alfred Nordmann

14. Experimentation and Proof in Mathematics
Michael Villiers

15. Proof, Mathematical Problem-Solving, and Explanation in Mathematics Teaching
Kazuhiko Nunokawa

16. Evolving Geometric Proofs in the Seventeenth Century: From Icons to Symbols
Evelyne Barbin

17. Proof in the Wording: Two Modalities from Ancient Chinese Algorithms
Karine Chemla

Nyckelord: Education, Mathematics Education, Educational Philosophy