Proof in Mathematics Education

Research, Learning and Teaching

Research on teaching and learning proof and proving has expanded in recent decades. This reflects the growth of mathematics education research in general, but also an increased emphasis on proof in mathematics education. This development is a welcome one for those interested in the topic, but also poses a challenge, especially to teachers and new scholars. It has become more and more difficult to get an overview of the field and to identify the key concepts used in research on proof and proving.

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Preliminary Material
Pages: i–xiv
History of Proof
Pages: 3–24
Researcher Perspectives
Pages: 35–55
Empirical Results
Pages: 59–72
The Role of Proof
Pages: 73–82
Types of Reasoning
Pages: 83–128
Argumentation
Pages: 153–164
Teaching Experiments
Pages: 165–176
Argumentation Structures
Pages: 179–192
Patterns of Reasoning
Pages: 193–208
Conclusions
Pages: 209
Implications for Teaching
Pages: 211–220
Directions for Research
Pages: 221–226
References
Pages: 227–239
Author Index
Pages: 241–244
Subject Index
Pages: 245–251
This book is intended to help teachers, researchers and graduate students to overcome the difficulty of getting an overview of research on proof and proving. It reviews the key findings and concepts in research on proof and proving, and embeds them in a contextual frame that allows the reader to make sense of the sometimes contradictory statements found in the literature. It also provides examples from current research that explore how larger patterns in reasoning and argumentation provide insight into teaching and learning.
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