Abstract

How can pupils be helped to construct mathematical insights in normal classroom conditions? In this presentation I report on a lesson (one in a series), based on the story of the young Gauss, that I taught at a primary school in Ireland. I trace the construction by pupils of new mathematical ideas and concepts using the RBC model developed by Hershkowitz, Schwartz, and Dreyfus (2001). I demonstrate how the fostering of a ‘conjecturing atmosphere’ (Mason, 1988) is the main factor that supports mathematically insightful behaviour. Conjecturing is evidenced by pupils’ use of pronouns and hedges (Rowland, 2000) and is facilitated by teacher follow-up moves (Brodie, 2008). In this context, I show how extended whole-class conversation can offer fertile ground for the growth of new mathematical understanding.