Beliefs and negotiations: Case studies of three prospective secondary mathematics teachers

The research undertaken in this study concerned the relationship between the mathematical beliefs, mathematical teaching beliefs, and mathematical learning beliefs of prospective secondary mathematics teachers (PSMTs). The construct of teacher image was also considered in relation to these beliefs. Additionally, the negotiations a PSMT made while teaching were studied.; Most current research in this area has discussed how prior mathematical experiences affect not only what prospective teachers perceive mathematics to be, but also how it will be taught. Furthermore, their background experiences and how those experiences have shaped the meaning of mathematics affect prospective teachers. A more specific discussion of the way in which beliefs relate and how background experiences influence them was needed. The construct of teacher image and the notion of negotiations were necessary in order to better understand how the studied beliefs relate and interact.; Over the course of two semesters, three PSMTs were interviewed and observe different environments and in different roles. The first role was that of a student in a mathematics class. The second role was that of teacher in the classroom. The teaching role was observed during both clinical work and student teaching. Using Green's Model of Belief Structures, data from interviews, observations, and other documents produced by the PSMTs were analyzed using the constant comparative method.; One assertion from this research is that the mathematical beliefs a PSMT has appear to be the driving force for other beliefs studied. Ultimately, all three cases shared a common theme: the mathematical experiences they had proved significant in forming their core beliefs. This conclusion has implications for the types of experiences to give prospective teachers in mathematics. This, in turn, has further implications for the implementation of reforms in mathematics education.; Additionally, the belief structure of each PSMT was strongly related. This is significant because if one works to modify one set of beliefs, this study reveals that the other studied beliefs must be taken into account. Finally, the teacher image proved to be the construct least open to modification.