Geometric constructions in GeoGebra from different representation systems: A study with prospective primary education teachers

Abstract

In this work, we study the implementation using GeoGebra of three construction processes as described in two different editions of Euclid's Elements: the classical and the less known one by Oliver Byrne. These editions use dramatically different representation systems to present the same mathematical content. We analyze the influence between the representation systems, the correctness of the constructions and the adjustment to the given instructions shown in the answers of 18 pairs of third year students of the Degree of Primary Education. We observe no influence of the representation systems over the adjustment while in the case of correctness this influence is associated to the particular task. In addition, we identify and analyze four different phenomena related to mathematical, instrumentation and instrumentalization aspects.