Pedagogical maps provide a graphic depiction of the way in which teachers exploit the presence of Computer Algebra Systems (CAS) in their classrooms. They can show differences, and can also show growth, as well as personal preferences and reactions to particular teaching assignments. They might also be used for teachers to reflect on their own practice of teaching with technology and to set goals for expanding their pedagogical repertoires. Highlighting the different pedagogical uses made by the teachers on the pedagogical map gives a visual representation of differences between teaching practices. In this article, the authors describe the practice of three different teachers using CAS in quite different ways. These differences may result from their beliefs about mathematics and the culture they prefer to foster in their classroom. On the other hand it may be a result of their experience or inexperience in teaching with technology, in general, and with CAS, in particular. Just as students need to learn to work effectively with CAS so do teachers need to learn to teach effectively with CAS and avail themselves, and their students, of the opportunities for improved ways of both doing and learning mathematics which CAS may afford. (Contains 4 figures.)