THE RELATIONSHIP BETWEEN TEACHERS ’ MATHEMATICAL KNOWLEDGE AND TEACHING IN CALCULUS

In this paper we address some issues about the nature of secondary teacher mathematical knowledge in the area of Calculus. Our research data comes from observing classroom teaching of nine teachers and from interviews with them. In particular, we indicate some qualitative characteristics of the specialised mathematical knowledge for teaching that allow the teacher to create a rich mathematical communication in the classroom. These characteristics include teacher’s ability to make connections between different mathematical areas; to be aware of the role of these connections in the discipline of mathematics; to extend these connections to other disciplines; to blend mathematical and pedagogical dimensions. The last two decades a number of studies have attempted to define the nature and the components of teacher knowledge that is necessary for mathematics teaching. In most of these studies the investigation of this knowledge is based on the analysis of data that come from the actual teaching practice. It seems that the teacher knowledge required for teaching is rooted in the mathematical demands of teaching itself and it differs from the knowledge that a teacher has acquired in the formal education (Ball and Bass, 2003; Cooney an