Teaching Reader Engagement as an Aspect of Proof

For the past decade, philosophers of mathematical practice have examined the nature and function of proofs in mathematical practice, most often in mathematical research practice. More recently they have examined how mathematicians assess and get to know a proof not just by reading it, but through active engagement with the proof. For example, mathematicians traverse gaps in the proof by filling in details. This paper examines the relevance of this literature to the teaching of mathematics. In particular, it examines how reader engagement can be taught as an aspect of proofs in the context of upper-secondary mathematics education, and the argument is illustrated by teaching material on Hero’s formula, which was developed for and tested in Danish upper-secondary mathematics teaching.