The thirteen Year 6 teachers of the study were selected from national participants of the second year of the two-year SM intervention. The study adopted a multiple-case study approach with augmenting teacher episodes situated in the English primary school setting. The aims of the research were to trace the evolution of teachers’ mathematical knowledge, as they taught SM microworlds designed for exploration and reasoning about place value, variable and angle through computer programming. SM is a two-year mathematics and computing curriculum designed for pupils aged nine to eleven years old. This thesis is based on research to explore the role of primary school teachers’ mathematical and pedagogical knowledge in their engagement with computer-based microworlds that formed part of ScratchMaths (SM). Finally, the author reflects on the relationships between theoretical and applied research on teacher behavior, and the relevant research methods.
It is hoped that the final scheme provided will be of some value, both on theoretical and pragmatic grounds.
It provides details of some of the failed attempts along the way, in order to document the complexities of constructing such schemes. This essay characterizes and reflects on the evolution of the observational scheme. It turns out, however, that, although the theoretical and practical enterprise are in many ways overlapping, the theoretical underpinnings for the observation scheme are sufficiently different (narrower in some ways and broader in others) and the constraints of almost real-time implementation so strong that the resulting analytic scheme is in many ways radically different from the theoretical framing that gave rise to it.
One would think that a comprehensive theory of decision-making would provide the bases for a classroom observation scheme. This essay explores the dialectic between theorizing teachers’ decision-making and producing a workable, theoretically grounded scheme for classroom observations.
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