Preservice teachers’ expressed awarenesses: emerging threads of retro-spection of learning and pro-spection of teaching.

In this paper, we report an enquiry into elementary preservice teachers’ learning, as they engage in doing mathematics for themselves. As a group of researchers working in elementary initial teacher education in English universities, we co-planned and taught sessions on growing pattern generalisation. Following the sessions, interviews of fifteen preservice teachers at two universities focused on their expressed awareness of their approach to the mathematical activity. Preservice teachers’ prospective planning and post-teaching evaluations of similar activities in their classrooms were also examined. We draw on aspects of enactivism and the notion of reflective ‘spection' in the context of teacher learning, tracing threads between preservice teachers’ retro-spection of learning and pro-spection of teaching. Our analysis indicates that increasing sensitivity to their own embodied processes of generalisation offers opportunities for novice teachers to respond deliberately, rather than to react impulsively, to different pedagogical possibilities. The paper contributes a new dimension to the discussion about the focus of novice elementary school teachers’ retrospective reflection by examining how deliberate retrospective analysis of doing mathematics, and not only of teaching actions, can develop awarenesses that underlie the growth of expertise in mathematics teaching. We argue that engaging preservice teachers in mathematics to support deliberate retrospective analysis of their mathematics learning and prospective consideration of the implications for teaching, can enable more critical pedagogical choices.