Mathematical walks in search of symmetries: from visualization to conceptualization

This work refers to a research project named ‘Math walks’, whose aim is to investigate a few students’ common conceptions and difficulties related to symmetries as well as to guide the student in the transition from visualization to conceptualization. As far as this issue is concerned, we designed a learning activity (LA) according to Dina van Hiele-Geldof and Pierre van Hiele’s theory of the development of geometric thought and we have experimented LA with sixthgrade students. Data show that LA seems to be effective in revealing students’ difficulties about symmetries, on the one hand, and in providing students scaffolding to overcome them, on the other. From the data collected in the experimentation, new research questions arise.