ABSTRACT
This chapter discusses the teachers’ descriptions of how their working conditions supported and continue to support the growth of their mathematical knowledge and its organization for teaching. The difference between the two groups in representing the meaning of division by fractions seemed to reflect the influence of the teacher education program on the mathematical knowledge of the prospective teachers. Although the preservice teachers and ninth-grade students had similar algorithmic competence, they displayed two main differences. First, the prospective teachers seemed to have “cleaned-up” mathematical concepts, while their mathematical approach seemed narrowed. Second, unlike the students, the prospective teachers were concerned about teaching and learning. The differences in mathematical knowledge between the Chinese teachers and the two Chinese preteaching groups were of another sort. Chinese teachers not only study teaching materials individually, they also do it with their colleagues. There are also interactions between and among colleagues on the understanding of school mathematics.
