A INTERPRETAÇÃO DE UMA AVALIAÇÃO DIAGNÓSTICA SOBRE O PENSAMENTO ALGÉBRICO À LUZ DA TEORIA DOS CAMPOS CONCEITUAIS

Abstract

In this article, we aim to describe and analyze the solutions of 8th-grade students from elementary school to questions proposed in a diagnostic assessment on algebraic thinking, in light of the theory of conceptual fields. The theory of conceptual fields is a cognitive theory that seeks to provide a framework for understanding learning processes. According to this theory, a concept is never learned in isolation; it is associated with other concepts, establishing a conceptual field. A concept, in turn, is constituted by the situations that give meaning to it, the operative invariants present in the schemes mobilized to handle these situations, and its symbolic representations. The diagnostic test was administered to a class of 40 students from the public school system of Duque de Caxias, Rio de Janeiro, during a 100-minute session. Although the test consists of six questions, we emphasize here two questions: one focused on the simplification of algebraic expressions and another focused on solving equations. We conclude that, although the students have schemes to deal with the situations, they are not aware of the domain of validity of their schemes. There is implicit knowledge in these schemes, but some consist of false theorems-in-action.

Keywords: conceptual field theory; diagnostic assessment; algebraic reasoning; elementary School.