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.