Drawing on my own experience, I will describe some approaches to teaching mathematics to non-specialists. Often the students in such a course are resistant to conventional methods of teaching so "creative pedagogy" can be needed. Although the examples I will give are from a mathematics course for prospective elementary school teachers, the issues raised are quite general. Furthermore, I will try to persuade the audience that the lessons you learn by trying to teach such a course successfully will have a positive impact on your teaching overall and can even change departmental culture.