Proof and proving in mathematics education. The 19th ICMI study.

*(English)*Zbl 1234.00015
New ICMI Study Series 15. Berlin: Springer (ISBN 978-94-007-2128-9/hbk; 978-94-007-2129-6/ebook). xii, 475 p. (2012).

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The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades.

The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving.

The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.

TABLE OF CONTENTS

1. Aspects of proof in mathematics education: Gila Hanna and Michael de Villiers.

Part I: Proof and cognition.- 2. Cognitive development of proof: David Tall, Oleksiy Yevdokimov, Boris Koichu, Walter Whiteley, Margo Kondratieva, and Ying-Hao Cheng .- 3. Theorems as constructive visions: Giuseppe Longo.

Part II: Experimentation: Challenges and opportunities.- 4. Exploratory experimentation: Digitally-assisted discovery and proof: Jonathan M. Borwein.- 5. Experimental approaches to theoretical thinking: Artefacts and proofs.- Ferdinando Arzarello, Maria Giuseppina Bartolini Bussi, Allen Leung, Maria Alessandra Mariotti, and Ian Stevenson (With response by J. Borwein and J. Osborn).

Part III: Historical and educational perspectives of proof.- 6. Why proof? A historian’s perspective: Judith V. Grabiner.- 7. Conceptions of proof – in research and in teaching: Richard Cabassut, AnnaMarie Conner, Filyet Asli Ersoz, Fulvia Furinghetti, Hans Niels Jahnke, and Francesca Morselli.- 8. Forms of proof and proving in the classroom: Tommy Dreyfus, Elena Nardi, and Roza Leikin.- 9. The need for proof and proving: mathematical and pedagogical perspectives: Orit Zaslavsky, Susan D. Nickerson, Andreas Stylianides, Ivy Kidron, and Greisy Winicki.- 10. Contemporary proofs for mathematics education: Frank Quinn.

Part IV: Proof in the school curriculum.- 11. Proof, Proving, and teacher-student interaction: Theories and contexts: Keith Jones and Patricio Herbst.- 12. From exploration to proof production: Feng-Jui Hsieh, Wang-Shian Horng, and Haw-Yaw Shy.- 13. Principles of task design for conjecturing and proving: Fou-Lai Lin, Kyeong-Hwa Lee, Kai-Lin Yang, Michal Tabach, and Gabriel Stylianides.- 14. Teachers’ professional learning of teaching proof and proving: Fou-Lai Lin, Kai-Lin Yang, Jane-Jane Lo, Pessia Tsamir, Dina Tirosh, and Gabriel Stylianides.

Part V: Argumentation and transition to tertiary level.- 15. Argumentation and proof in the mathematics classroom: Viviane Durand-Guerrier, Paolo Boero, Nadia Douek, Susanna Epp, and Denis Tanguay.- 16. Examining the role of logic in teaching proof: Viviane Durand-Guerrier, Paolo Boero, Nadia Douek, Susanna Epp, and Denis Tanguay.- 17. Transitions and proof and proving at tertiary level: Annie Selden.

Part VI: Lessons from the Eastern cultural traditions.- 18. Using documents from ancient China to teach mathematical proof: Karine Chemla .- 19. Proof in the Western and Eastern traditions: Implications for mathematics education: Man Keung Siu.

Acknowledgements.- Appendix 1: Discussion Document.- Appendix 2: Conference Proceedings: Table of contents.- Author Index.- Subject Index.

The articles of this volume will be reviewed individually in MathEduc.

Indexed articles:

Tall, David; Yevdokimov, Oleksiy; Koichu, Boris; Whiteley, Walter; Kondratieva, Margo; Cheng, Ying-Hao, Cognitive development of proof, 13-49 [Zbl 1247.97020]

Longo, Giuseppe, Theorems as constructive visions, 51-66 [Zbl 1247.97002]

Borwein, Jonathan Michael, Exploratory experimentation: digitally-assisted discovery and proof, 69-96 [Zbl 1259.97011]

Arzarello, Ferdinando; Bartolini Bussi, Maria Giuseppina; Leung, Allen Yuk Lun; Mariotti, Maria Alessandra; Stevenson, Ian, Experimental approaches to theoretical thinking: artefacts and proofs. With a response by Jonathan M. Borwein and Judy-anne Osborn, 97-143 [Zbl 1247.97006]

Grabiner, Judith V., Why proof? A historian’s perspective, 147-167 [Zbl 1247.97012]

Cabassut, Richard; Conner, AnnaMarie; İşçimen, Filyet Aslı; Furinghetti, Fulvia; Jahnke, Hans Niels; Morselli, Francesca, Conceptions of proof – in research and teaching, 169-190 [Zbl 1247.97007]

Dreyfus, Tommy; Nardi, Elena; Leikin, Roza, Forms of proof and proving in the classroom, 191-213 [Zbl 1247.97009]

Zaslavsky, Orit; Nickerson, Susan D.; Stylianides, Andreas J.; Kidron, Ivy; Winicki-Landman, Greisy, The need for proof and proving: mathematical and pedagogical perspectives, 215-229 [Zbl 1247.97021]

Quinn, Frank, Contemporary proofs for mathematics education, 231-257 [Zbl 1247.97017]

Jones, Keith; Herbst, Patricio, Proof, proving, and teacher-student interaction: theories and contexts, 261-277 [Zbl 1247.97014]

Hsieh, Feng-Jui; Horng, Wang-Shian; Shy, Haw-Yaw, From exploration to proof production, 279-303 [Zbl 1247.97013]

Lin, Fou-Lai; Yang, Kai-Lin; Lee, Kyeong-Hwa; Tabach, Michal; Stylianides, Gabriel, Principles of task design for conjecturing and proving, 305-325 [Zbl 1247.97015]

Lin, Fou-Lai; Yang, Kai-Lin; Lo, Jane-Jane; Tsamir, Pessia; Tirosh, Dina; Stylianides, Gabriel, Teachers’ professional learning of teaching proof and proving, 327-346 [Zbl 1247.97016]

Durand-Guerrier, Viviane; Boero, Paolo; Douek, Nadia; Epp, Susanna S.; Tanguay, Denis, Argumentation and proof in the mathematics classroom, 349-367 [Zbl 1247.97010]

Durand-Guerrier, Viviane; Boero, Paolo; Douek, Nadia; Epp, Susanna S.; Tanguay, Denis, Examining the role of logic in teaching proof, 369-389 [Zbl 1247.97011]

Selden, Annie, Transitions and proof and proving at tertiary level, 391-420 [Zbl 1247.97018]

Chemla, Karine, Using documents from ancient China to teach mathematical proof, 423-429 [Zbl 1247.97008]

Siu, Man Keung, Proof in the Western and Eastern traditions: implications for mathematics education, 431-440 [Zbl 1247.97019]

##### MSC:

00B15 | Collections of articles of miscellaneous specific interest |

00A35 | Methodology of mathematics |

97-06 | Proceedings, conferences, collections, etc. pertaining to mathematics education |

97E50 | Reasoning and proving in the mathematics classroom |

97D40 | Mathematics teaching methods and classroom techniques |