ABSTRACT
What contributions can Ernst von Glasersfeld’s epistemology make to the teaching of geometry and, in particular, to formalization in geometry? I have found a number of striking ideas described by Glasersfeld and, among them, a basic idea that is shared by radical constructivism and didactic realism, which was developed in The Netherlands. Both of these frameworks stress the ‘students’ constructions’. This chapter is a report of a didactic phenomenological investigation into spherical geometry in mathematics education for 16 year olds. The research demonstrates that the students’ intuitive constructions and viewpoints, which were inspired by various types of geometry (spherical geometry, plane geometry, solid geometry) contributed to the process of formalization. Without the students’ intuitive ideas no genuine formalization in geometry is possible.
