Contradictions in the initial mathematics teacher education: A study on the learning of Euclidean constructions with GeoGebra

Abstract

This research deals with dialectical contradictions and their relationship with the learning of geometric knowledge in the initial mathematics teacher education. Specifically, we analyze how a pre-service teacher and the teacher educator handle such a contradiction while collectively solving a construction problem using GeoGebra, and we offer an explanation of how this contributes to the learning of geometry mobilized in the activity. To do so, we adopted a historical-cultural educational perspective to analyze an episode in which a pre-service teacher and the teacher educator engage in a dialogue regarding the solution to the problem of constructing an isosceles triangle with GeoGebra. This analysis was carried out in two stages to capture the movement from the abstract to the concrete in the object of study. The results include the description of three formative actions that provide information on how a conceptual contradiction emerged and was confronted, as well as an explanation of how this contributed to the learning of the mobilized knowledge. We conclude that the way in which the contradiction was addressed by the participants facilitated awareness of the knowledge and allowed for the break from the practical-utilitarian relationship that the pre-service teacher maintained with the task.

Keywords
Mathematics teacher education; Theory of objectification; Contradictions; Geometric constructions