Mathematical Teaching Practices at Tertiary Level: Working Group Report

Conclusion

This chapter represents an initial stumbling in the direction of collecting and sharing practices and principles, tasks and perspectives, which is the aim of the MEMEs project mentioned earlier. In order to make sense of the many stimulating contributions in the group it was helpful to me as summariser to organise what I heard in a three-fold structure of frameworks:

Preparing oneself to teach a topic, based on elaborating the notion of a concept image by interweaving cognition-awareness, affect-emotion and enaction-behaviour.

Preparing to teach a session or class, based on designing for activity by balancing resources-tasks with student and teacher current state and goals as well as mastering subject knowledge. It is useful to collect possible teaching acts or gambits, to imagine oneself using them in a particular situation and afterwards, to re-enter salient moments and re-affirm the use of specific gambits in the future.

Preparing to make effective choices in the flow of the event by developing awareness of your own mathematical thinking, so you can be sensitive to what your students are thinking. Becoming aware of the conditions and ethos which support mathematical thinking for you is likely to lead to working at developing a conjecturing mathematical atmosphere in your sessions, in which everything that is said is taken as a conjecture to be modified if necessary and those who are certain choose to listen to and support others, while those who are uncertain choose to try to express what they understand. Under these conditions, scientific debate and effective mathematical discussion become possible.

Despite different ways of articulating principles and practices, there was considerable agreement. The main difference lay in the degree of formality and explicitness of the underlying theories and principles that guide different teachers’ practices.