A Conversation-Gesture Approach to Recognising Mathematical Understanding in Group Problem Solving (Teaching from the Sidelines)

Teaching from the sidelines is the practice of allowing students to work in small group settings while actively, but not intrusively, monitoring their progress. This requires that the teacher is looking for and listening to actions that unfold through group talk. By viewing understanding as ‘an ability to go on conversationally’ this research puts forward a method by which teaching from the sidelines can be a productive activity. The idea of knowledge as a basis for action and understanding as a dynamic activity that develops from this knowledge builds on the work of Wittgenstein, Sfard, and Davis. Techniques of conversation and gesture analysis are employed to examine examples of classroom talk to support and develop these ideas. In being more aware of the conversational organization of group talk, teachers can be more attuned to how mathematical understanding is developing. Variations in student gesturing are examined to illustrate how students who are more confident in their knowledge generally use larger gestures, particularly when presenting their ideas. The research also finds that groups of students tend to mimic (echo) each other’s gestures and posture when they are working together to develop a shared understanding.