Artifact Based Geometric Constructions

Abstract

This study examines the integration of an artifact in teaching Euclidean geometry at upper secondary school, as a way of enabling students to enter the theoretical world of a geometrical proof. The key assumption underlying this research was that the deliberate use of artifacts in mathematics instruction may render detectable learning processes. In particular, we worked with students who had never worked with geometric tools before, apart from pair of compasses and rulers, observing and analyzing their geometric reasoning, while they performed geometric constructions using the artifact. Results demonstrate that the physical, and functional characteristics of the artifact, and the type of mathematics it incorporates, allows students to reach geometric conclusions by induction, based on the mathematics of the artifact, and devise ways, based on the mathematics of the artifact, to prove their initial reasoning.