Proof and Proving in Mathematics Education

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

Gila Hanna is Professor Emeritus at the University of Toronto. She taught graduate courses in mathematics education and in measurement and evaluation; she also led a large number of research projects and supervised several Ph.D. and M.A. theses in mathematics education. Her primary research interests are the role of proof and truth in mathematics and mathematics education, and gender issues in mathematics teaching and learning. She has been Convenor of the International Organisation of Women and Mathematics Education (1988-1992), Vice-Chair of the Canadian Mathematics Education Study Group (1986-1990), and has served on several Social Sciences and Humanities Research Council of Canada (SSHRC) adjudication committees and on the scientific program committees of a number of international conferences on mathematics education. From 1989 to 2000 she was Co-Editor of the international journal Educational Studies in Mathematics and is now one of its Advisory Editors. From 2000 to 2007 she was Co-Founder and Co-Editor of the Canadian Journal of Science, Mathematics and Technology Education. She served as Co-Chair of ICMI Study 19 on proof and proving in mathematics education. She has published extensively on proof and other aspects of mathematics education, and has delivered lectures at several universities as well as at numerous international conferences on mathematics education. In 2003 she was appointed "Fields Institute Fellow", a lifetime appointment conferred on certain individuals who have made outstanding contributions to the Fields Institute for Research in Mathematical Sciences, its programs, and to the Canadian mathematical community.

After teaching mathematics and science at high school for a few years, Michael de Villiers, received the Science Teacher of the Year award in South Africa in 1983. Later that same year he was appointed as a researcher at the Research Unit for Mathematics Education of the University of