Personal geometrical work of pre-service teachers: a case study based on the theory of Mathematical Working Spaces

Overview & Synopsis

In this contribution, we intend to revisit the interplay between geometrical paradigms GI and GII in the context of the current French curriculum, which gives an important place to modelling activities in mathematics learning. We asked master students to perform a geometric modelling task on the estimation of the area of a field. The resolution of the task requires an articulation between GI and GII by considering measurement and approximation. From this first study, it results that the vast majority of students have developed a geometric work in the GI paradigm by mobilizing a low use of the classical property-based proof discourse. These results question teacher training and, more broadly, the today's mathematics teaching in France.