Harel, Guershon

Advances in Mathematics Education Research on Proof and Proving

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ISBN: 9783319709963

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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

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

ICME-13 Monographs
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