Proof and Proving in Mathematics Education: The 19th ICMI Study

Description

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. Front Matter....Pages i-xii Aspects of Proof in Mathematics Education....Pages 1-10 Front Matter....Pages 11-11 Cognitive Development of Proof....Pages 13-49 Theorems as Constructive Visions....Pages 51-66 Front Matter....Pages 67-67 Exploratory Experimentation: Digitally-Assisted Discovery and Proof....Pages 69-96 Experimental Approaches to Theoretical Thinking: Artefacts and Proofs....Pages 97-143 Front Matter....Pages 145-145 Why Proof? A Historian’s Perspective....Pages 147-167 Conceptions of Proof – In Research and Teaching....Pages 169-190 Forms of Proof and Proving in the Classroom....Pages 191-213 The Need for Proof and Proving: Mathematical and Pedagogical Perspectives....Pages 215-229 Contemporary Proofs for Mathematics Education....Pages 231-257 Front Matter....Pages 259-259 Proof, Proving, and Teacher-Student Interaction: Theories and Contexts....Pages 261-277 From Exploration to Proof Production....Pages 279-303 Principles of Task Design for Conjecturing and Proving....Pages 305-325 Teachers’ Professional Learning of Teaching Proof and Proving....Pages 327-346 Front Matter....Pages 347-347 Argumentation and Proof in the Mathematics Classroom....Pages 349-367 Examining the Role of Logic in Teaching Proof....Pages 369-389 Transitions and Proof and Proving at Tertiary Level....Pages 391-420 Front Matter....Pages 421-421 Using Documents from Ancient China to Teach Mathematical Proof....Pages 423-429 Proof in the Western and Eastern Traditions: Implications for Mathematics Education....Pages 431-440 Back Matter....Pages 443-475