This paper presents results from a study of 19 teacher education students' knowledge of mathematics and discusses an analytic framework for examing and appraising teachers' and prospective teachers' subject matter knowledge. Participants in the study were 10 elementary education majors and 9 mathematics majors or minors who were preparing to teach high school. Results discussed in this paper focus on the concept of division, examined across three mathematical contexts: division with fractions, division by zero, and division with algebra. Although many of the teacher candidates could produce correct answers, several could not, and few were able to give mathematical explanations for the underlying principles and meanings. Their knowledge was also fragmented. The results challenge assumptions about the subject matter preparation of prospective elementary and secondary mathematics teachers. (Author)