Example Construction Tasks and Mathematical Generality

Abstract

Generality is at the heart of mathematics. When executing a mathematical procedure, what do students learn … the procedure or the generality present in the procedure? In this paper I report on a study which engages learners in an activity that not only reveals dimensions and depth of learners’ awareness but also acts to promote and enrich their appreciation of mathematical topics. Twenty five students studying A-level and undergraduate engineering, pure mathematics and education were invited to construct relevant mathematical objects meeting specified constraints. Having constructed these objects, learners displayed a range of awareness of the effect of the construction tasks on their understanding of the concepts involved.