NON-EUCLIDEAN GEOMETRIES IN MATHEMATICS TEACHER EDUCATION: REFLECTIONS FROM EXPERIENCED TEACHER EDUCATORS IN GEOMETRY TEACHING

Abstract

This article aims to discuss focal points of the reflections expressed by experienced teachers in the teaching of geometry regarding Non-Euclidean Geometries (NEG) in the education of Math Teachers (MaT). This qualitative research with an interpretive approach involved requesting participants to produce written narratives on this topic. The analytical process identified three focal points: justifications for incorporating NEG in MaT education; challenges inherent in including NEG in MaT training; and suggestions for methodologies, approaches, and teaching resources. These focal points address aspects deemed relevant by the teachers for inclusion in training programs. The conclusion is that the debate on these aspects may contribute to broadening conceptual horizons, allowing for a comprehensive understanding of space and geometric properties; foster critical thinking about mathematics; prepare for educational challenges by considering different approaches and resources; and encourage curiosity and exploration.