Similarity of triangles in a historical perspective in the light of the mathematical working space in geometry

Abstract

The present study concerns research conducted with 21 students of the third grade of high school during the academic year 2020-2021 in the teaching unit “Similar Triangles”. The design of the teaching intervention was carried out under the prism of the Mathematical Working Space for Geometry (MWSG). Seven worksheets with sources and problems from the History of Mathematics and a final cognitive test were used. Additionally, the students worked in groups, constructed the historical tool of Errard, and used it to measure an inaccessible distance. The aim was to study how the integration of the History of Mathematics, within the framework of the MWSG, affects the degree of understanding of the concept of similar triangles by the students. After the qualitative analysis of the students’ responses, it was found that the integration of historical problems in teaching helped activate them, resulting in the creation of a positive climate towards the course requirements. Furthermore, the enrichment of the students’ personal working space gave them the opportunity to cultivate a reflective dimension in problem-solving, something not supported by the activities of the school textbook.