CHARTING KEY ELEMENTS OF CHILDREN’S MATHEMATICAL ARGUMENT IN DISCUSSION: A TEACHING TOOL

We investigate how children reveal and develop their understanding of mathematics through collaborative argument in group discussion. Working with eleven-year-old children who had different responses to diagnostic test items, we describe how those children developed argument across conceptual locales. The analyses of the discussions led to a chart of the key elements of argument that arose, as well as general strategies for managing such discussions productively. Such devices and strategies are presented as planning tools for classroom teachers in the next stage of our study. DISCUSSION AS A TEACHING STRATEGY It has long been ‘known ’ that children’s errors and misconceptions can be the starting point for effective diagnostically-designed mathematics teaching. The seminal mathematical work on this in the UK was done in the 1980s by the ESRC Diagnostic Teaching Project (Bell et al, 1985), in which cognitive conflict was seen as the route to developing understanding. Argument in discussion is seen as one important source of such conflict. The TIMS