Preliminary Material -- What is Proof? -- History of Proof -- Usages of “Proof” and “Proving” -- Researcher Perspectives -- Important Research Foci, Past and Present -- Empirical Results -- The Role of Proof -- Types of Reasoning -- Classifying Proofs and Arguments -- Argumentation -- Teaching Experiments -- Processes of Reasoning and Argumentation -- Argumentation Structures -- Patterns of Reasoning -- Conclusions -- Implications for Teaching -- Directions for Research -- References -- Author Index -- Subject Index.

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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