This paper reviews current trends in the training of teachers, particularly in the areas of content knowledge and pedagogical content knowledge, pedagogical reasoning, training, and beliefs. Content knowledge consists of the key facts, concepts, principles, and explanatory framework in the discipline, in this case mathematics. Pedagogical content knowledge or subject-specific pedagogical knowledge is defined as knowledge of students and learning, knowledge of curriculum and school context, and knowledge of teaching. Pedagogical reasoning is the process of transforming content knowledge into forms that are pedagogically powerful and adaptive to particular groups of students. The discussion of training includes a 15-point list of essential training principles as gleaned from a synthesis of the research. Beliefs are considered the attitudes and assumptions of entering preservice teachers, beginning teachers, and experienced teachers, and the power of these beliefs to effect change in education. As teacher educators think about the reform movement, especially in the areas discussed, they need to ask themselves whether they and their programs have realized the importance of nurturing these qualities and standards in their own practice. They need to ask what teacher education programs have done to prepare teachers to be active participants in learning and teaching. In conclusion, the paper proposes that the need for a theory of reform in the education of teachers is urgent. (Contains 52 references.) (JB)