Abstract
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.
Highlights
This paper considers the place of mathematical activity in Initial Teacher Education (ITE) for elementary school preservice teachers
In our work the “event” or “action” is preservice teachers’ own mathematical activity, and we examine the awarenesses that emerge from their deliberate retro-spection of this activity, and how it connects with pro-spection of their own teaching
We have explored the kinds of expressed awarenesses that emerge when preservice teachers are encouraged to engage in mathematical activity for themselves, and in deliberate retrospective analysis of their own learning and pro-spection of their teaching
Summary
This paper considers the place of mathematical activity in Initial Teacher Education (ITE) for elementary school preservice teachers. We view Mason’s (2010) notion of spection as being closely linked to the enactivist notion of deliberate analysis (Varela 1999), defined as the way that expert teachers are able to act spontaneously and to analyse their actions retrospectively, as they reflect upon the reasons for their actions Both notions underscore the importance of retrospective thought about an action or event for the awakening of awareness that can inform future action in teaching and in learning. Terry explained the importance that he attached to children being allowed time in the lesson to try different approaches and discuss these with others His view is based on what he found helpful when working on the patterns himself.
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