Preface.- Theme 1: Epistemological Issues Related to Proof and Proving.- Chapter 1. Reflections on proof as explanation.- Chapter 2. Working on proofs as contributing to conceptualization - The case of IR completeness.- Chapter 3. Types of epistemological justifications, with particular reference to complex numbers,- Chapter 4. Mathematical argumentation in elementary teacher education: The key role of the cultural analysis of the content.- Chapter 5. Toward an evolving theory of mathematical practice informing pedagogy: What standards for this research paradigm should we adopt?.- Theme 2: Classroom-Based Issues Related to Proof and Proving.- Chapter 6. Constructing and validating the solution to a mathematical problem: The teacher's prompt.- Chapter 7. Addressing key and persistent problems of students' learning: The case of proof.- Chapter 8. How can a teacher support students in constructing a proof?.- Chapter 9. Proof validation and modification by example generation: A classroom-based intervention in secondary school geometry.- Chapter 10. Classroom-based issues related to proofs and proving.- Theme 3: Cognitive and Curricular Issues Related to Proof and Proving.- Chapter 11. Mathematical argumentation in pupils' written dialogues.- Chapter 12. The need for "linearity" of deductive logic: An examination of expert and novice proving processes.- Chapter 13. Reasoning-and-proving in algebra in school mathematics textbooks in Hong Kong.- Chapter 14. Irish teachers' perceptions of reasoning-and-proving amidst a national educational reform.- Chapter 15. About the teaching and learning of proof and proving: Cognitive issues, curricular issues and beyond.- 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?.- Chapter 17. When is a generic argument a proof?.- Chapter 18. Systematic exploration of examples as proof: Analysis with four theoretical frameworks.- Chapter 19. Using examples of unsuccessful arguments to facilitate students' reflection on their processes of proving.- Chapter 20. Genericity, conviction, and conventions: Examples that prove and examples that don't prove.