Theorising theorising: About mathematics teachers' and mathematics teacher educators' energetic learning

What is learning? How is learning done? There is a developing literature within mathematics education that explores these questions through an enactivist perspective. This literature covers children doing mathematics in classrooms, teachers learning about teaching mathematics to children and mathematics teacher educators’ learning. In previous articles and chapters, we have discussed ideas of reflecting and developing expertise that come from an enactivist worldview in which knowing and doing are equivalent. What seems to be implicit in much of this writing is how making a new connection related to action, in a way that we call theorising, brings with it energy, what we call energetic learning. In this chapter, we explore energetic learning, including, as mathematics teacher educators, our own theorising on how to support mathematics teachers’ theorising on how to teach mathematics. We illustrate our own theorising through extracts from our professional discussions after sessions whilst working together on the one-year teacher education course for prospective teachers at the University of Bristol, School of Education. Petitmengin’s second-person interviewing strategies can be used as teaching strategies to support energetic learning at all levels of the system.