WE TEACH WHAT WE KNOW, BUT DO WE KNOW WHAT WE TEACH? THE PRACTICAL "DISTINCTION" BETWEEN SQUARES AND RECTANGLES IN A PRIMARY SCHOOL CLASS

The knowledge and understanding that each one of us possesses about each topic of the national maths curriculum, as well as our perception about the way they relate to each other shapes our own way of being a teacher and, consequently, the way our students see the mathematical content and the teaching process. Aiming for a "comprehensive" approach to each topic of the mathematical curriculum is essential for the teacher, not only to have an in-depth knowledge about each topic, but also the right technique to deliver it to the students, in order to make it understandable to them, by anticipating their thinking, difficulties and their motivations. In this paper we will present an extract of a lesson in a Portuguese primary school in which the teacher reviews the distinction between squares and rectangles. We will look into the components of the professional knowledge (Ball, Thames & Phelps, 2008) as an integral part of it, discussing its implications in teacher training.