Learning to teach mathematics is a complex undertaking, and in the last twenty years there has been a great deal of research looking at aspects of the process. There are many ways one might structure an analysis of research on learning to teach mathematics. It is clear, though, from all the research on learners in all kinds of situations that what student teachers bring to their teacher education courses in terms of prior knowledge, experience, attitudes, beliefs, goals, fears, hopes, and expectations has to be a key factor in preparing for and teaching those courses and hence for research.