About the Teaching and Learning of Proof and Proving: Cognitive Issues, Curricular Issues and Beyond

Abstract

In this commentary we provide an analytical look at the four studies reported within this theme of the volume and we discuss related issues and insights that we obtained from these studies. We offer a focused view of each study in the same order as presented in the four preceding chapters, and we conclude that these studies not only provide new insights into various cognitive and curricular issues in the teaching and learning of proof and proving , but also raise additional issues in relation to curriculum , textbooks and teacher education and professional development. Based on our analysis, we contend that mathematics education research in the area of proof and proving is still at an early stage, given that most studies are relatively small-scale and exploratory in nature. Further theoretical and methodological work, and more in-depth studies, especially larger-scale confirmatory and experimental studies, are needed to move research in this area forward.