Advances in Mathematics Education Research on Proof and Proving (häftad)
Häftad (Paperback / softback)
Antal sidor
Softcover reprint of the original 1st ed. 2018
Springer International Publishing AG
Harel, Guershon
48 Illustrations, black and white; XI, 301 p. 48 illus.
234 x 156 x 17 mm
445 g
Antal komponenter
1 Paperback / softback
Advances in Mathematics Education Research on Proof and Proving (häftad)

Advances in Mathematics Education Research on Proof and Proving

An International Perspective

Häftad Engelska, 2019-06-04
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This book explores new trends and developments in mathematics education research related to proof and proving, the implications of these trends and developments for theory and practice, and directions for future research. With contributions from researchers working in twelve different countries, the book brings also an international perspective to the discussion and debate of the state of the art in this important area. The book is organized around the following four themes, which reflect the breadth of issues addressed in the book: * Theme 1: Epistemological issues related to proof and proving; * Theme 2: Classroom-based issues related to proof and proving; * Theme 3: Cognitive and curricular issues related to proof and proving; and * Theme 4: Issues related to the use of examples in proof and proving. Under each theme there are four main chapters and a concluding chapter offering a commentary on the theme overall.
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Recensioner i media

"The contents cover new trends and developments in mathematics education on proof and proving. ... will give readers an idea of what can be found in this volume." (Annie Selden, MAA Reviews, March 29, 2019)


Preface Andreas J. Stylianides*; Guershon Harel THEME 1: EPISTEMOLOGICAL ISSUES RELATED TO PROOF AND PROVING Chapter 1. Reflections on proof as explanation Gila Hanna - Chapter 2. Working on proofs as contributing to conceptualization - The case of IR completeness Viviane Durand-Guerrier*; Denis Tanguay Chapter 3. Types of epistemological justifications, with particular reference to complex numbers Guershon Harel Chapter 4. Mathematical argumentation in elementary teacher education: The key role of the cultural analysis of the content Paolo Boero*; Giuseppina Fenaroli; Elda Guala Chapter 5. Toward an evolving theory of mathematical practice informing pedagogy: What standards for this research paradigm should we adopt? Keith Weber*; Paul Dawkins 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 Maria Alessandra Mariotti*; Manuel Goizueta Chapter 7. Addressing key and persistent problems of students' learning: The case of proof Andreas J. Stylianides*; Gabriel J. Stylianides Chapter 8. How can a teacher support students in constructing a proof? Bettina Pedemonte Chapter 9. Proof validation and modification by example generation: A classroom-based intervention in secondary school geometry Kotaro Komatsu*; Tomoyuki Ishikawa; Akito Narazaki Chapter 10. Classroom-based issues related to proofs and proving Ruhama Even THEME 3: COGNITIVE AND CURRICULAR ISSUES RELATED TO PROOF AND PROVING Chapter 11. Mathematical argumentation in pupils' written dialogues Gjert-Anders Askevold; Silke Lekaus* Chapter 12. The need for "linearity" of deductive logic: An examination of expert and novice proving processes Shiv Smith Karunakaran Chapter 13. Reasoning-and-proving in algebra in school mathematics textbooks in Hong Kong Kwong-Cheong Wong*; Rosamund Sutherland Chapter 14. Irish teachers' perceptions of reasoning-and-proving amidst a national educational reform Jon D. Davis Chapter 15. About the teaching and learning of proof and proving: Cognitive issues, curricular issues and beyond Lianghuo Fan*; Keith Jones 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 Chapter 17. When is a generic argument a proof? David Reid*; Estela Vallejo Vargas Chapter 18. Systematic exploration of examples as proof: Analysis with four theoretical frameworks Orly Buchbinder Chapter 19. Using examples of unsuccessful arguments to facilitate students' reflection on their processes of proving Yosuke Tsujiyama*; Koki Yui Chapter 20. Genericity, conviction, and conventions: Examples that prove and examples that don't prove Orit Zaslavsky