Developing mathematical proficiency

It has long been recognised that successful mathematical learning comprises much more than just knowledge of skills and procedures. For example, Skemp (1976) identified the advantages of teaching mathematics for what he referred to as “relational” rather than “Instrumental” understanding. More recently, Kilpatrick, Swafford and Findell (2001) proposed five “intertwining strands” of mathematical proficiency, namely Conceptual Understanding, Procedural Fluency, Strategic Competence, Adaptive Reasoning, and Productive Disposition. In Australia, the new Australian Curriculum: Mathematics (F–10), which will be implemented from 2013, has adapted and adopted the first four of these proficiency strands to emphasise the breadth of mathematical capabilities that students need to acquire through their study of the various content strands. This paper addresses the question of what types of classroom practice can provide opportunities for the development of these capabilities in elementary schools. It draws on data from a number of projects, as well as the literature, to provide illustrative examples. Finally, the paper argues that developing the full set of capabilities requires complex changes in teachers’ pedagogy.