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.
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Voutsina Chronoula Alderton Julie Wilson Kirsty Ineson Gwen Donaldson Gina Rowland Tim 《Journal of Mathematics Teacher Education》2022,25(2):191-215
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Chronoula Voutsina 《Educational Studies in Mathematics》2012,79(2):193-214
This study analysed the different types of arithmetic knowledge that young children utilise when solving a multiple-step addition
task. The focus of the research was on the procedural and conceptual changes that occur as children develop their overall
problem solving approach. Combining qualitative case study with a micro-genetic approach, clinical interviews were conducted
with ten 5–6-year-old children. The aim was to document how children combine knowledge of addition facts, calculation procedures
and arithmetic concepts when solving a multiple-step task and how children’s application of different types of knowledge and
overall solving approach changes and develops when children engage with solving the task in a series of problem solving sessions.
The study documents children’s pathways towards developing a more effective and systematic approach to multiple-step tasks
through different phases of their problem solving behaviour. The analysis of changes in children’s overt behaviour reveals
a dynamic interplay between children’s developing representation of the task, their improved procedures and gradually their
more explicit grasp of the conceptual aspects of their strategy. The findings provide new evidence that supports aspects of
the “iterative model” hypothesis of the interaction between procedural and conceptual knowledge and highlight the need for
educational approaches and tasks that encourage and trigger the interplay of different types of knowledge in young children’s
arithmetic problem solving. 相似文献
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