What Can the Teacher Learn in the Classroom?

Our research is concerned with teacher’s knowledge, and especially with teacher’s processes of learning, in the classroom, from observing and interacting with students’ work. In the first part of the paper, we outline the theoretical framework of our study and distinguish it from some other perspectives. We argue for the importance of distinguishing a kind of teacher’s knowledge, which we call didactic knowledge. In this paper, we concentrate on a subcategory of this knowledge, namely observational didactic knowledge, which grows from teacher’s observation and reflection upon students’ mathematical activity in the classroom. In modeling the processes of evolution of this particular knowledge in teachers, we are inspired, among others, by some general aspects of the theory of didactic situations. In the second part of the paper, the model is applied in two case studies of teachers conducting ordinary lessons. In conclusion, we will discuss what seems to be taken into account by teachers as they observe students’ activity, and how in-service teacher training can play a role in modifying their knowledge about students’ ways of dealing with mathematical problems.