MATHEMATICAL KNOWLEDGE FOR TEACHING: THE ROLE OF PLANNING AND REFLECTION IN THE TRAINING OF TEACHERS

Abstract

In this paper I discuss the mathematics knowledge for teaching, particularly the case of the teacher who teaches mathematics in the early years of schooling, specifically the role of the sequence planning – action – reflection may have in the development and consolidation of this knowledge. First I discuss what is expected of the teacher as a mathematics teacher, illustrated with concrete examples, which intend to show that for a teacher it is not enough to know the mathematics he/she has to teach, but also how to teach it and how to assess pupils’ learning. Then I discuss the role of the planning of the class activity and the reflection about the practice to the development of teacher’s professional knowledge. Relating to planning, the “learning trajectory” construct is discussed as well as its components, particularly the teaching sequences and the teacher’s role in their development. The reflection on practice, with reference to the planning done in advance is essential to this process. The paper ends with the presentation and discussion of the case of teacher Maria, a teacher with a great teaching experience, graduated in the In-Service Teacher Training in Mathematics Program, analyzing, from her written portfolio, her planning and reflection about two classes in a second grade classroom.

Key-words: Mathematics knowledge for teaching; Planning; Reflection on practice.