目次

Preface Andreas J. Stylianides*; Guershon Harel as899@cam.ac.uk THEME 1: EPISTEMOLOGICAL ISSUES RELATED TO PROOF AND PROVING Chapter 1. Reflections on proof as explanation Gila Hanna - gila.hanna@utoronto.ca Chapter 2. Working on proofs as contributing to conceptualization - The case of IR completeness Viviane Durand-Guerrier*; Denis Tanguay viviane.durand-guerrier@umontpellier.fr Chapter 3. Types of epistemological justifications, with particular reference to complex numbers Guershon Harel harel@math.ucsd.edu Chapter 4. Mathematical argumentation in elementary teacher education: The key role of the cultural analysis of the content Paolo Boero*; Giuseppina Fenaroli; Elda Guala boero@dima.unige.it Chapter 5. Toward an evolving theory of mathematical practice informing pedagogy: What standards for this research paradigm should we adopt? Keith Weber*; Paul Dawkins keith.weber@gse.rutgers.edu THEME 2: CLASSROOM-BASED ISSUES RELATED TO PROOF AND PROVING Chapter 6. Constructing and validating the solution to a mathematical problem: The teacher?fs prompt Maria Alessandra Mariotti*; Manuel Goizueta mariotti21@unisi.it Chapter 7. Addressing key and persistent problems of students?f learning: The case of proof Andreas J. Stylianides*; Gabriel J. Stylianides as899@cam.ac.uk Chapter 8. How can a teacher support students in constructing a proof? Bettina Pedemonte bettina.pedemonte@sjsu.edu Chapter 9. Proof validation and modification by example generation: A classroom-based intervention in secondary school geometry Kotaro Komatsu*; Tomoyuki Ishikawa; Akito Narazaki kkomatsu@shinshu-u.ac.jp Chapter 10. Classroom-based issues related to proofs and proving Ruhama Even ruhama.even@weizmann.ac.il THEME 3: COGNITIVE AND CURRICULAR ISSUES RELATED TO PROOF AND PROVING Chapter 11. Mathematical argumentation in pupils?f written dialogues Gjert-Anders Askevold; Silke Lekaus* slek@hib.no Chapter 12. The need for ?glinearity?h of deductive logic: An examination of expert and novice proving processes Shiv Smith Karunakaran karunak3@msu.edu Chapter 13. Reasoning-and-proving in algebra in school mathematics textbooks in Hong Kong Kwong-Cheong Wong*; Rosamund Sutherland wongkwongcheong@gmail.com Chapter 14. Irish teachers' perceptions of reasoning-and-proving amidst a national educational reform Jon D. Davis jon.davis@wmich.edu Chapter 15. About the teaching and learning of proof and proving: Cognitive issues, curricular issues and beyond Lianghuo Fan*; Keith Jones l.fan@southampton.ac.uk THEME 4: ISSUES RELATED TO THE USE OF EXAMPLES IN PROOF AND PROVING Chapter 16. How do pre-service teachers rate the conviction, verification and explanatory power of different kinds of proofs? Leander Kempen kempen@khdm.de Chapter 17. When is a generic argument a proof? David Reid*; Estela Vallejo Vargas dreid@math.uni-bremen.de Chapter 18. Systematic exploration of examples as proof: Analysis with four theoretical frameworks Orly Buchbinder orly.buchbinder@unh.edu Chapter 19. Using examples of unsuccessful arguments to facilitate students?f reflection on their processes of proving Yosuke Tsujiyama*; Koki Yui tsujiyama@chiba-u.jp Chapter 20. Genericity, conviction, and conventions: Examples that prove and examples that don?ft prove Orit Zaslavsky orit.zaslavsky@nyu.edu