Research on understanding of proof in Mathematics education: Linking key distinctions in a common framework

Proofs are of central importance in mathematics, and therefore proofs are part of mathematics instruction. Thus, learners are confronted with mathematical proofs as part of their mathematical education. In particular, learners are expected to develop an understanding of proof over the course of their mathematics instruction. However, it remains unclear what exactly constitutes an individual’s understanding of proof, given that prior studies have conceptualised it in diverse ways and adopted different approaches. Moreover, the lack of a common theoretical framework makes it difficult both to compare existing findings and to investigate and describe an understanding of proof in the course of mathematics instruction. Although several frameworks exist within the field of proof, they differ substantially in terms of their objectives, approaches, and, if applicable, operationalisations. To address this, we propose a conceptual framework for understanding of proof, bringing together approaches of previous research. Moreover, we illustrate how investigations of individual’s understanding of proof can be designed using the framework. Finally, we discuss how the framework can be used to support systematic future research on the development of learners’ understanding of proof.