Proof and Proving in Mathematics Education: The 19th ICMI Study - Softcover

Inhaltsangabe

1. Aspects of proof in mathematics education: Gila Hanna and Michael de Villiers.- Part I: Proof and cognition.- 2. Cognitive development of proof: David Tall, Oleksiy Yevdokimov, Boris Koichu, Walter Whiteley, Margo Kondratieva, and Ying-Hao Cheng .- 3. Theorems as constructive visions: Giuseppe Longo.- Part II: Experimentation: Challenges and opportunities.- 4. Exploratory experimentation: Digitally-assisted discovery and proof: Jonathan M. Borwein.- 5. Experimental approaches to theoretical thinking: Artefacts and proofs.- Ferdinando Arzarello, Maria Giuseppina Bartolini Bussi, Allen Leung, Maria Alessandra Mariotti, and Ian Stevenson (With response by J. Borwein and J. Osborn).- Part III: Historical and educational perspectives of proof.- 6. Why proof? A historian's perspective: Judith V. Grabiner.- 7. Conceptions of proof - in research and in teaching: Richard Cabassut, AnnaMarie Conner, Filyet Asli Ersoz, Fulvia Furinghetti, Hans Niels Jahnke, and Francesca Morselli.- 8. Forms of proof and proving in the classroom: Tommy Dreyfus, Elena Nardi, and Roza Leikin.- 9. The need for proof and proving: mathematical and pedagogical perspectives: Orit Zaslavsky, Susan D. Nickerson, Andreas Stylianides, Ivy Kidron, and Greisy Winicki.- 10. Contemporary proofs for mathematics education: Frank Quinn.- Part IV: Proof in the school curriculum.- 11. Proof, Proving, and teacher-student interaction: Theories and contexts: Keith Jones and Patricio Herbst.- 12. From exploration to proof production: Feng-Jui Hsieh, Wang-Shian Horng, and Haw-Yaw Shy.- 13. Principles of task design for conjecturing and proving: Fou-Lai Lin, Kyeong-Hwa Lee, Kai-Lin Yang, Michal Tabach, and Gabriel Stylianides.- 14. Teachers' professional learning of teaching proof and proving: Fou-Lai Lin, Kai-Lin Yang, Jane-Jane Lo, Pessia Tsamir, Dina Tirosh, and Gabriel Stylianides.- Part V: Argumentation and transition to tertiary level.- 15. Argumentation and proof in the mathematics classroom: Viviane Durand-Guerrier, Paolo Boero, Nadia Douek, Susanna Epp, and Denis Tanguay.- 16. Examining the role of logic in teaching proof: Viviane Durand-Guerrier, Paolo Boero, Nadia Douek, Susanna Epp, and Denis Tanguay.- 17. Transitions and proof and proving at tertiary level: Annie Selden.- Part VI: Lessons from the Eastern cultural traditions.- 18. Using documents from ancient China to teach mathematical proof: Karine Chemla .- 19. Proof in the Western and Eastern traditions: Implications for mathematics education: Man Keung Siu.- Acknowledgements.- Appendix 1: Discussion Document.- Appendix 2: Conference Proceedings: Table of contents.- Author Index.- Subject Index.

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