Validating proofs in parallel mathematical and pedagogical tasks

Abstract

Educators often use tasks that situate teachers in pedagogical contexts, under the assumptions that such tasks activate knowledge authentic to teaching; and, furthermore, purely mathematical contexts may not activate such knowledge. These assumptions are based on analyses that contrast actual engagement with pedagogical context to hypothetical engagement without pedagogical context. We propose that it is important to conduct a direct comparison of responses, and we report on such a study using a set of tasks with and without pedagogical contexts – featuring the same underlying mathematics. The results revealed differences in how secondary teachers validated proof based on context. Context also influenced the importance participants placed on algebraic notation in validating a proof. This study has implications for how and when secondary teachers attend to validity and the role of algebraic notation, and the messages they may convey to their students about validity and notation.