Articulating ‘understanding’: Deploying mathematical cognition

Abstract

Scotland's Curriculum for Excellence (CfE), constitutes the demands that teachers are supposed to meet. Its intentions for the mathematics curriculum are similar to those in many countries: that learners be sufficiently mathematically literate to use mathematics in the personal, professional and societal dimensions of their lives. But like many attempts to reform mathematical curricula elsewhere, CfE does not address the fundamental issue of mathematical understanding. Of course, learner understanding transcends the mathematical curriculum per se, but the significance of mathematical understanding for competent functioning exemplifies the imperative of teaching for understanding or 'deep learning'. The article begins with some conceptual 'ground clearing' to establish mathematical understanding as a neglected issue. It then considers what mathematical understanding is, why it is important, the increasingly important role of metacognition, and the very necessary role of teachers. At each of these points, implications for pedagogical practice are raised.