Proof and Proving in Mathematics Education

The 19th ICMI Study

  • Gila Hanna
  • Michael de Villiers

Part of the New ICMI Study Series book series (NISS, volume 15)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Gila Hanna, Michael de Villiers
    Pages 1-10
  3. Proof and Cognition

    1. Front Matter
      Pages 11-11
    2. David Tall, Oleksiy Yevdokimov, Boris Koichu, Walter Whiteley, Margo Kondratieva, Ying-Hao Cheng
      Pages 13-49
    3. Giuseppe Longo
      Pages 51-66
  4. Experimentation: Challenges and Opportunities

    1. Front Matter
      Pages 67-67
    2. Ferdinando Arzarello, Maria Giuseppina Bartolini Bussi, Allen Yuk Lun Leung, Maria Alessandra Mariotti, Ian Stevenson
      Pages 97-143
  5. Historical and Educational Perspectives of Proof

    1. Front Matter
      Pages 145-145
    2. Judith V. Grabiner
      Pages 147-167
    3. Richard Cabassut, AnnaMarie Conner, Filyet Aslı İşçimen, Fulvia Furinghetti, Hans Niels Jahnke, Francesca Morselli
      Pages 169-190
    4. Tommy Dreyfus, Elena Nardi, Roza Leikin
      Pages 191-213
    5. Orit Zaslavsky, Susan D. Nickerson, Andreas J. Stylianides, Ivy Kidron, Greisy Winicki-Landman
      Pages 215-229
  6. Proof in the School Curriculum

    1. Front Matter
      Pages 259-259
    2. Feng-Jui Hsieh, Wang-Shian Horng, Haw-Yaw Shy
      Pages 279-303
    3. Fou-Lai Lin, Kai-Lin Yang, Kyeong-Hwa Lee, Michal Tabach, Gabriel Stylianides
      Pages 305-325
    4. Fou-Lai Lin, Kai-Lin Yang, Jane-Jane Lo, Pessia Tsamir, Dina Tirosh, Gabriel Stylianides
      Pages 327-346
  7. Argumentation and Transition to Tertiary Level

    1. Front Matter
      Pages 347-347
    2. Viviane Durand-Guerrier, Paolo Boero, Nadia Douek, Susanna S. Epp, Denis Tanguay
      Pages 349-367
    3. Viviane Durand-Guerrier, Paolo Boero, Nadia Douek, Susanna S. Epp, Denis Tanguay
      Pages 369-389
  8. Lessons from the Eastern Cultural Traditions

  9. Back Matter
    Pages 443-475

About this book


One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels.

Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification.

This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as:

  • 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.


ICMI 19 mathematical reasoning mathematics teaching proof proving

Editors and affiliations

  • Gila Hanna
    • 1
  • Michael de Villiers
    • 2
  1. 1.Ontario Institute for Studies in, Education (OISE)University of TorontoTorontoCanada
  2. 2.Faculty of EducationUniversity of KwaZulu-NatalAshwoodSouth Africa

Bibliographic information