Mathematical representations in pre-service of Basic Education teachers

Abstract

Mathematical representations increasingly occupy a central place in mathematics classes and in the planning of tasks with meaning that imply thinking and doing, rather than memorizing definitions and procedures. The main reference documents that regulate mathematical activity point to the knowledge and use of multiple representations as one of the central objectives of mathematical learning. In this sense, the main objective of this study is the identification of different types of representations, from a more informal pictorial representation to mathematical symbolic representations, used by university students, future teachers, and the development of the ability to understand and use different conventional representations, choosing the most appropriate to each problematic situation.
The research is part of a qualitative and interpretative approach, developed with a total of sixty-eight students, who solved a set of three tasks that require a wide range of representations in order to understand, explore, register and to find a solution. The data collection instruments used were documentary analysis of student productions, observation, field notes and audio recording.
The results show that students have ease in building varied mathematical representations. For comprehension of the utterance predominate the informal representations of the pictorial or iconic type; but for resolution and response appear as more common the mathematical symbolic representations of the arithmetic type. The nature of the task seems to influence the choice of one or another type of representation. It is also evident to accept other forms of representation, different from those produced, the students needed an explanation and consequent understanding of them.