Learning to teach mathematics: The lesson de-briefing conversation

In the UK it is typical for prospective teachers to teach lesson which are observed by a school-based mentor and a university tutor, following which there is a de-brief between those three, about the lesson. In this chapter, we will explore the significance of these de-briefing conversations, between a mentor and university tutor and a prospective mathematics teacher, within the broader process of becoming a teacher of mathematics. There has been limited attention given to ways of running the lesson de-brief within the mathematics education literature, but there are many characterisations of mentoring relationships, which have implications for such discussions, within, for example, writing on nursing. We draw on the work of Heron, to set out six forms of mentoring relationship, to which we have added a seventh that is specific to learning to teach mathematics. Using this framework, we analyse the practice that has developed at the University of Bristol, making use of fictionalised accounts, based on our experiences. Our particular de-briefing practice appears to be highly effective in allowing prospective teachers to identify and become committed to next steps in their development as teachers. We put forward some tentative reasons for why what we do is effective, linked to our overall enactivist perspective on the process of becoming a teacher of mathematics.