Mathematical Argumentation: A Key Step on the Path to Learning Proof

This book is about research on the teaching and learning of proof in mathematics over the last fifty years. The second part details a classical case study of students’ dynamics of proof and refutation, resulting in a typology of proofs that sheds light on the links between proving and knowing. This book is about research on the teaching and learning of proof in mathematics over the last fifty years. The book comprises nine chapters, divided into three parts. The first part presents the theoretical framework for the research and situates it within the state of the art from a multidisciplinary perspective. The second part details a classical case study of students’ dynamics of proof and refutation, resulting in a typology of proofs that sheds light on the links between proving and knowing. Finally, the third part proposes entering the classroom with an experimental approach, in support of a reflection on the challenges of implementing and managing situations for the teaching and learning of proof in mathematics at the compulsory school level. The book balances theoretical discussions of interest to researchers and mathematics educators. The detailed case studies should serve as discussion generators for teachers involved in teaching proof and proving.