ABSTRACT
The fundamental premise of this book is that teachers’ classroom practices and their underlying cognitions must be predominantly student centered for students to learn mathematics with understanding. In the preceding chapters, we described the development and use of our model as a way to understand and appreciate the complexity of student-centered teaching. This chapter consists of fi ve case studies that show various issues and concerns that arise when student teachers engage in the process of refl ection and self-assessment about their cognitions and instructional practices. For the student teachers, Maria, Iris, Mindy, Elizabeth, and Kyungso, we describe their experiences and their professional growth by organizing their comments under the following headings: Identifying the Problem, Owning the Problem and Searching for Resolution, and Growth in Self-Understanding. Furthermore, we include a commentary section to share our own analysis of the student teachers’ experiences and to suggest probable trajectories for their progress in becoming student-centered professionals. As you read the comments of these student teachers, watch for the unspoken contradictions in what they say and what they do, feel their emotional struggles as they try to make their practice consistent with their cognitions, and share in their breakthrough moments when they confront and seek resolution of acknowledged problems. In shadowing their experiences, you get a glimpse of the complexity of the dynamic interplay between goals, knowledge, and beliefs and classroom practice and an appreciation of what it takes to understand one’s own teaching.
