## Harel, Guershon

# Advances in Mathematics Education Research on Proof and Proving

**Table of contents**

**Part I. Epistemological Issues Related to Proof and Proving**

1. Reflections on Proof as Explanation*Gila Hanna*

2. Working on Proofs as Contributing to Conceptualization—The Case of IR Completeness*Viviane Durand-Guerrier, Denis Tanguay*

3. Types of Epistemological Justifications, with Particular Reference to Complex Numbers*Guershon Harel*

4. Mathematical Argumentation in Elementary Teacher Education: The Key Role of the Cultural Analysis of the Content*Paolo Boero, Giuseppina Fenaroli, Elda Guala*

5. Toward an Evolving Theory of Mathematical Practice Informing Pedagogy: What Standards for this Research Paradigm Should We Adopt?*Keith Weber, Paul Christian Dawkins*

**Part II. Classroom-Based Issues Related to Proof and Proving**

6. Constructing and Validating the Solution to a Mathematical Problem: The Teacher’s Prompt*Maria Alessandra Mariotti, Manuel Goizueta*

7. Addressing Key and Persistent Problems of Students’ Learning: The Case of Proof*Andreas J. Stylianides, Gabriel J. Stylianides*

8. How Can a Teacher Support Students in Constructing a Proof?*Bettina Pedemonte*

9. Proof Validation and Modification by Example Generation: A Classroom-Based Intervention in Secondary School Geometry*Kotaro Komatsu, Tomoyuki Ishikawa, Akito Narazaki*

10. Classroom-Based Issues Related to Proofs and Proving*Ruhama Even*

**Part III. Cognitive and Curricular Issues Related to Proof and Proving**

11. Mathematical Argumentation in Pupils’ Written Dialogues*Gjert-Anders Askevold, Silke Lekaus*

12. The Need for “Linearity” of Deductive Logic: An Examination of Expert and Novice Proving Processes*Shiv Smith Karunakaran*

13. Reasoning-and-Proving in Algebra in School Mathematics Textbooks in Hong Kong*Kwong-Cheong Wong, Rosamund Sutherland*

14. Irish Teachers’ Perceptions of Reasoning-and-Proving Amidst a National Educational Reform*Jon D. Davis*

15. About the Teaching and Learning of Proof and Proving: Cognitive Issues, Curricular Issues and Beyond*Lianghuo Fan, Keith Jones*

**Part IV. Issues Related to the Use of Examples in Proof and Proving**

16. How Do Pre-service Teachers Rate the Conviction, Verification and Explanatory Power of Different Kinds of Proofs?*Leander Kempen*

17. When Is a Generic Argument a Proof?*David Reid, Estela Vallejo Vargas*

18. Systematic Exploration of Examples as Proof: Analysis with Four Theoretical Frameworks*Orly Buchbinder*

19. Using Examples of Unsuccessful Arguments to Facilitate Students’ Reflection on Their Processes of Proving*Yosuke Tsujiyama, Koki Yui*

20. Genericity, Conviction, and Conventions: Examples that Prove and Examples that Don’t Prove*Orit Zaslavsky*

**Keywords:** Education, Mathematics Education, Teaching and Teacher Education, Learning & Instruction, Study and Learning Skills, International and Comparative Education

- Editor
- Harel, Guershon
- Stylianides, Andreas J.
- Publisher
- Springer
- Publication year
- 2018
- Language
- en
- Edition
- 1
- Series
- ICME-13 Monographs
- Page amount
- 11 pages
- Category
- Upbringing, Education
- Format
- Ebook
- eISBN (PDF)
- 9783319709963
- Printed ISBN
- 978-3-319-70995-6