Juxtaposing Mathematical Extensions with Cognitvely Loaded Questions in the Mathematics Classrom

Abstract

Providing mathematical extensions (i.e. bonus questions) intended to evoke deep mathematical thinking after students complete assigned tasks is challenging for teachers. In this paper, we use the Variation Theory of Learning to challenge a common misconception that mathematical extensions should include many interrelated elements and impose a high cognitive load to promote deeper thinking. We present an analysis of observed extensions and provide alternative routes. Pedagogical implications for the design of mathematical extensions are presented.