Educational Designer

Every classroom has a ‘contract’, usually implicit, between the teacher and the students as to what each will do, what roles they will fulfill. In most mathematics classrooms, the teacher plays directive roles (manager, explainer, task setter, answer provider) while the students play passive imitative roles, listening to the teacher's explanations (not always attentively!) and imitating in a series of repetitive exercises the procedures that the teacher has just demonstrated in working through an example. Students soon learn that the worked example is the key for what they have to do. (Indeed there is much to be said for delaying the explanation until after the examples.) Teaching and learning mathematics this way does not develop students' ability to ‘do mathematics’ themselves.

For that they need to develop autonomy in developing chains of reasoning and solving problems. The teacher needs to ‘get out of the way’ to make room for the students to make the mathematics they do their own – and to and encourage and support this ‘from the side’. This implies a shift of roles with teachers shifting from the directive roles to more facilitative ones, sometimes described (Phillips 1988) as counsellor, fellow student, and resource – providing information only on demand. Students in turn become explainers and play a role in task-setting – an important part of an inquiry-based approach. Teacher interventions are mainly in the form of non-directive questions. (See Common issues tables)

TRU provides a broader framework on this issue. It identifies five dimensions that characterise classrooms that develop mathematically powerful students. Such classrooms provide positive answers to these questions: