Scaffolding Instrumental Genesis: how conversions between semiotic registers fostered geometric reasoning in a dynamic environment

This study investigates how a learning sequence, moving from tangible artifacts to a Dynamic Geometry Environment, supports the transition from visuo-spatial perception to formal geometric reasoning. We combine Duval's theory of semiotic registers with the Instrumental Approach, to analyse students’ challenges in producing robust geometric constructions. Undergraduate mathematics students engaged in a task sequence on the Pythagorean Theorem: they first manipulated a physical tangram, then created a static diagram with written instructions, and finally built a robust construction in GeoGebra. Findings show that the intermediate task compels students to make geometric properties explicit. Success in the final GeoGebra task, however, depends on translating these properties into robust schemes of use. A collective reflection was essential for completing the instrumental genesis for struggling students.