- 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
- Antal komponenter
- 1 Paperback / softback
- 445 g
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Advances in Mathematics Education Research on Proof and Proving
An International Perspective1059Skickas inom 10-15 vardagar.
Fri frakt inom Sverige för privatpersoner.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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Fler böcker av författarna
Seven papers by mathematicians and educators reflect current research concerning the understanding, teaching, and learning of mathematics at the post-secondary level. Focusing on the ways students think about and learn mathematics, rather than on ...
Andreas J Stylianides
Although proving is core to mathematics as a sense-making activity, it currently has a marginal place in elementary classrooms internationally. Blending research with practical perspectives, this book addresses what it would take to elevate the pl...
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"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 email@example.com THEME 1: EPISTEMOLOGICAL ISSUES RELATED TO PROOF AND PROVING Chapter 1. Reflections on proof as explanation Gila Hanna - firstname.lastname@example.org Chapter 2. Working on proofs as contributing to conceptualization - The case of IR completeness Viviane Durand-Guerrier*; Denis Tanguay email@example.com Chapter 3. Types of epistemological justifications, with particular reference to complex numbers Guershon Harel firstname.lastname@example.org Chapter 4. Mathematical argumentation in elementary teacher education: The key role of the cultural analysis of the content Paolo Boero*; Giuseppina Fenaroli; Elda Guala email@example.com Chapter 5. Toward an evolving theory of mathematical practice informing pedagogy: What standards for this research paradigm should we adopt? Keith Weber*; Paul Dawkins firstname.lastname@example.org 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 email@example.com Chapter 7. Addressing key and persistent problems of students' learning: The case of proof Andreas J. Stylianides*; Gabriel J. Stylianides firstname.lastname@example.org Chapter 8. How can a teacher support students in constructing a proof? Bettina Pedemonte email@example.com Chapter 9. Proof validation and modification by example generation: A classroom-based intervention in secondary school geometry Kotaro Komatsu*; Tomoyuki Ishikawa; Akito Narazaki firstname.lastname@example.org Chapter 10. Classroom-based issues related to proofs and proving Ruhama Even email@example.com THEME 3: COGNITIVE AND CURRICULAR ISSUES RELATED TO PROOF AND PROVING Chapter 11. Mathematical argumentation in pupils' written dialogues Gjert-Anders Askevold; Silke Lekaus* firstname.lastname@example.org Chapter 12. The need for "linearity" of deductive logic: An examination of expert and novice proving processes Shiv Smith Karunakaran email@example.com Chapter 13. Reasoning-and-proving in algebra in school mathematics textbooks in Hong Kong Kwong-Cheong Wong*; Rosamund Sutherland firstname.lastname@example.org Chapter 14. Irish teachers' perceptions of reasoning-and-proving amidst a national educational reform Jon D. Davis email@example.com Chapter 15. About the teaching and learning of proof and proving: Cognitive issues, curricular issues and beyond Lianghuo Fan*; Keith Jones firstname.lastname@example.org 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 email@example.com Chapter 17. When is a generic argument a proof? David Reid*; Estela Vallejo Vargas firstname.lastname@example.org Chapter 18. Systematic exploration of examples as proof: Analysis with four theoretical frameworks Orly Buchbinder email@example.com Chapter 19. Using examples of unsuccessful arguments to facilitate students' reflection on their processes of proving Yosuke Tsujiyama*; Koki Yui firstname.lastname@example.org Chapter 20. Genericity, conviction, and conventions: Examples that prove and examples that don't prove Orit Zaslavsky email@example.com