Details

Advances in Mathematics Education Research on Proof and Proving


Advances in Mathematics Education Research on Proof and Proving

An International Perspective
ICME-13 Monographs

von: Andreas J. Stylianides, Guershon Harel

Fr. 99.00

Verlag: Springer
Format: PDF
Veröffentl.: 10.01.2018
ISBN/EAN: 9783319709963
Sprache: englisch

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Beschreibungen

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.
Preface Andreas J. Stylianides*; Guershon Harel as899@cam.ac.uk   THEME 1: EPISTEMOLOGICAL ISSUES RELATED TO PROOF AND PROVING   Chapter 1. Reflections on proof as explanation Gila Hanna - gila.hanna@utoronto.ca   Chapter 2. Working on proofs as contributing to conceptualization - The case of IR completeness Viviane Durand-Guerrier*; Denis Tanguay viviane.durand-guerrier@umontpellier.fr   Chapter 3. Types of epistemological justifications, with particular reference to complex numbers Guershon Harel harel@math.ucsd.edu   Chapter 4. Mathematical argumentation in elementary teacher education: The key role of the cultural analysis of the content Paolo Boero*; Giuseppina Fenaroli; Elda Guala boero@dima.unige.it   Chapter 5. Toward an evolving theory of mathematical practice informing pedagogy: What standards for this research paradigm should we adopt? Keith Weber*; Paul Dawkins keith.weber@gse.rutgers.edu     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 mariotti21@unisi.it   Chapter 7. Addressing key and persistent problems of students’ learning: The case of proof Andreas J. Stylianides*; Gabriel J. Stylianides as899@cam.ac.uk   Chapter 8. How can a teacher support students in constructing a proof? Bettina Pedemonte bettina.pedemonte@sjsu.edu   Chapter 9. Proof validation and modification by example generation: A classroom-based intervention in secondary school geometry Kotaro Komatsu*; Tomoyuki Ishikawa; Akito Narazaki kkomatsu@shinshu-u.ac.jp   Chapter 10. Classroom-based issues related to proofs and proving Ruhama Even ruhama.even@weizmann.ac.il   THEME 3: COGNITIVE AND CURRICULAR ISSUES RELATED TO PROOF AND PROVING   Chapter 11. Mathematical argumentation in pupils’ written dialogues Gjert-Anders Askevold; Silke Lekaus* slek@hib.no   Chapter 12. The need for “linearity” of deductive logic: An examination of expert and novice proving processes Shiv Smith Karunakaran karunak3@msu.edu   Chapter 13. Reasoning-and-proving in algebra in school mathematics textbooks in Hong Kong Kwong-Cheong Wong*; Rosamund Sutherland wongkwongcheong@gmail.com   Chapter 14. Irish teachers' perceptions of reasoning-and-proving amidst a national educational reform Jon D. Davis jon.davis@wmich.edu   Chapter 15. About the teaching and learning of proof and proving: Cognitive issues, curricular issues and beyond Lianghuo Fan*; Keith Jones l.fan@southampton.ac.uk   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 kempen@khdm.de   Chapter 17. When is a generic argument a proof? David Reid*; Estela Vallejo Vargas dreid@math.uni-bremen.de   Chapter 18. Systematic exploration of examples as proof: Analysis with four theoretical frameworks Orly Buchbinder orly.buchbinder@unh.edu   Chapter 19. Using examples of unsuccessful arguments to facilitate students’ reflection on their processes of proving Yosuke Tsujiyama*; Koki Yui tsujiyama@chiba-u.jp   Chapter 20. Genericity, conviction, and conventions: Examples that prove and examples that don’t prove Orit Zaslavsky orit.zaslavsky@nyu.edu
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.
Presents an extensive survey of international perspectives on proof and proving students’ mathematics progress Serves as a comprehensive volume addressing a wide range of issues related to proof and proving in mathematics education research Offers important insights into the difficulties faced by students and teachers in this area
Presents an extensive survey of international perspectives on proof and proving students’ mathematics progressServes as a comprehensive volume addressing a wide range of issues related to proof and proving in mathematics education researchOffers important insights into the difficulties faced by students and teachers in this area

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