This article sets out the components of a theoretical framework that served in a study of the teaching of elementary geometry - in particular, in the context of pre-service teacher education. The notions of geometrical paradigms and geometrical working space are discussed in detail. For one, elementary geometry is presented as being split among three different geometrical paradigms, according to a perspective that carries forward with the Douady’s notion of geometrical framework. Parallels are drawn between these paradigms and Van Hiele levels. The notion of working space provides a basis for examining the specific characteristics attaching to the activity performed by geometers - be they expert or novice. A possible interrelationship with Duval’s notion of cognitive approach is entertained.