O raciocínio matemático aos seis anos: Características e funções das representações dos alunos

Abstract

This article focuses on the use of representations by 6 year students and analyses their contribute for the mathematical reasoning of the students. The main purpose of the article is to characterise the representations, specially the diagrams, that students create to solve the problems, and to analyse the functions of that representations. We analyse the mathematical productions of three students created to solve two different problems. The students created idiosyncratic iconic representations and also used conventional symbolic representations, but with very different functions. Diagrams were used by the students to interpret the problematic situation, to relate their elements, to unpack the mathematical structure, to obtain the solution, to review the problem solving process and to support the explanation and/or justification of the reasoning. Conventional symbolic representations were based on the iconic ones, and they were used by the students to display the solutions of the problems or the arithmetic expressions associated to the solution.