Use of connections between representations by the teacher in the construction of algebraic language

Abstract

Representation is a very important element in the teaching and learning of school Mathematics. Also, some representations help solve concrete problems better than other representations, so knowing how to translate between representations is also crucial when learning mathematics. In this article, we will see how teachers make connections between representations to help students build algebraic language. To do this, we will analyze three episodes taken from two classes by a teacher. The teacher's interventions take place within the framework of a class that develops in a problem-solving environment. We will carry out this analysis using the theoretical framework provided by the Knowledge Quartet, an instrument that allows us to observe how the teacher's knowledge emerges when he helps his students to learn mathematics. This instrument consists of a series of indicators that help us see situations in which the teacher uses his knowledge while interacting with the students. These indicators are classified in four dimensions: fundamentals, transformation, connections, and contingency. This article completes the theoretical framework given by the Knowledge Quartet with a new indicator that we will call “connections between representations” and that will be included in the connection dimension of this instrument.