The Need for Proof and Proving: Mathematical and Pedagogical Perspectives

Abstract

This chapter first examines why mathematics educators need to teach proof, as reflected in the needs that propelled proof to develop historically. We analyse the interconnections between the functions of proof within the discipline of mathematics and the needs for proof. We then take a learner’s perspective and discuss learners’ difficulties in understanding and appreciating proof, as well as a number of intellectual needs that may drive learners to prove (for certitude, for causality, for quantification, for communication, and for structure and connection). We conclude by examining pedagogical issues involved in teachers’ attempts to foster necessity-based learning that motivates the need to prove, in particular the use of tasks and activities that elicit uncertainty, cognitive conflict and inquiry-based learning. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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