Abstract
In this paper, we identify various forms of geometric work carried out by student teachers who were asked to perform a geometric task for the estimation of a land area. The theory of Mathematical Working Spaces is used to analyze and characterize the work produced. This study provides evidence that students developed forms of geometric work that are compliant with at least two distinct geometric paradigms, one characterized by the utilization of measuring and drawing tools and the other by a property-based discourse on proof. Significantly, a sizable number of students also developed work forms that do not correspond to any geometrical paradigm. A broader purpose of this paper is to highlight three criteria born by the theory and shown to be useful for the description and evaluation of geometric work: compliance, completeness, and correctness.
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Kuzniak, A., Nechache, A. On forms of geometric work: a study with pre-service teachers based on the theory of Mathematical Working Spaces. Educ Stud Math 106, 271–289 (2021). https://doi.org/10.1007/s10649-020-10011-2
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DOI: https://doi.org/10.1007/s10649-020-10011-2