The role of visual representations for structuring classroom mathematical activity

It is our presupposition that there is still a need for more research about how classroom practices can exploit the use and power of visualization in mathematics education. The aim of this article is to contribute in this direction, investigating how visual representations can structure geometry activity in the classroom and discussing teaching practices that can facilitate students’ visualization of mathematical objects. We present one illustrative episode that shows how drawings of geometrical figures have a powerful role in structuring and modifying the mathematical activity in the classroom. It was selected from a database that we have been building to investigate the learning of mathematics in public elementary schools in Brazil. The framework of Activity Theory helped in the characterization of the episode as a system of interconnected activities. We discuss the changes and transformations perceived in those activities; and we explore the idea of miniature cycles of learning actions to focus on the mathematical learning that is taking place. We describe the dynamics and the complexity of the ongoing activity in the calculation of areas; and, how drawings form a part, and show their influence, in it. We argue that part of this influence was associated with the contradiction between abstract mathematical ideas and their empirical representations, revealed by the tensions perceived in the activities analysed; and, simultaneously, that we could see as an impelling force for the learning of the rules and norms which regulate the use of visual representations in school mathematics.