Deepening the geometric work of future teachers in technological environments and pencil and paper

This article presents the results of a case study on the geometric work developed by prospective mathematics teachers. We first propose a geometrical task in a pencil-and-paper environment, and then its adaptation for a digital environment. The analyses are based on the framework of the Mathematical Work Space (MWS), which allows to focus on cognitive processes and epistemological aspects developed in the work. The findings show differences between the intended and the personal MWS of prospective mathematics teachers and the specific phases that they prioritize within the mathematical work. This research contributes to the enrichment of knowledge on geometric work thanks to a theoretical and methodological framework that allows an in-depth analysis of the mathematical work of individuals performing specific geometric tasks.

Keywords:
Geometry; Prospective mathematics teachers; Artifacts; Visualization; Mathematical Work Space