Explanation and proof in mathematics : philosophical and educational perspectives
Gila Hanna, Hans Niels Jahnke, Helmut Pulte, editors.
New York : Springer, ©2010.
viii, 294 págs. : ilustraciones ; 24 cm.
ISBN: 9781441905758 (hbk.), 1441905758 (hbk.), 1441905766 (ebk.), 9781441905765 (ebk.)
Versiones extendidas de los trabajos presentados en la conferencia realizada en Essen en noviembre de 2006.
Incluye referencias bibliográficas e índice.
Reseña: Zbl, 1196.00025
Contenido
- 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 and 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 and 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 de 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.
