Contradictions in the learning of Euclidean constructions with GeoGebra by pre-service mathematics teachers

This paper seeks to answer the question: How does the handling of the contradictions that emerge in activities of initial mathematics teacher education contribute to the learning of geometric knowledge when pre-service teachers and the teacher educator solve geometric construction problems with GeoGebra? A dialectical-materialist approach is used to analyze an episode in which pre-service teachers and the teacher educator discuss the solution to the task of drawing a line perpendicular to a segment given a point off that segment. The episode was video-recorded and transcribed in its totality. Evidence in this research comes directly from the transcription of the episode, and analysis was carried out in two stages. As a result, we identify three formative actions that show the manner in which the conceptual and emotional contradictions emerge and are handled and we offer an explanation of how the handling of these contradictions contributed to the learning of pre-service teachers. We conclude that the way of handling the conceptual contradiction favored the awareness of the mobilized knowledge and that the handling of this contradiction was not exempt from emotional tensions, the latter of which we interpret as the manifestation of a contradiction of the autonomy/dependence type.