Abstract
This inquiry presents two fine-grained case studies of students demonstrating different levels of cognitive functioning in relation to bilateral symmetry and reflection. The two students were asked to solve four sets of tasks and articulate their reasoning in task-based interviews. The first participant, Brittany, focused essentially on three criteria, namely (1) equidistance, (2) congruence of sides and (3) ‘exactly opposite’ as the intuitive counterpart of perpendicularity for performing reflection. On the other hand, the second participant, Sara, focused on perpendicularity and equidistance, as is the normative procedure. Brittany’s inadequate knowledge of reflection shaped her actions and served as a validation for her solutions. Intuitively, her visual strategies took over as a fallback measure to maintain congruence of sides in the absence of a formal notion of perpendicularity. In this paper, we address some of the well-known constraints that students encounter in dealing with bilateral symmetry and reflection, particularly situations involving inclined line of symmetry. Importantly, we make an attempt to show how visual and analytical strategies interact in the production of a reflected image. Our findings highlight the necessity to give more explicit attention to the notion of perpendicularity in bilateral symmetry and reflection tasks.
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A preliminary and shorter version of this paper was presented in: Oesterle, S., Liljedahl, P., Nicol, C., & Allan, D. (Eds.). Proceedings of the Joint Meeting of PME 38 and PME-NA 36, 2014, Vol. 3, pp. 313–320. Vancouver, Canada: PME.
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Ramful, A., Ho, S.Y. & Lowrie, T. Visual and analytical strategies in spatial visualisation: perspectives from bilateral symmetry and reflection. Math Ed Res J 27, 443–470 (2015). https://doi.org/10.1007/s13394-015-0144-0
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DOI: https://doi.org/10.1007/s13394-015-0144-0