Processos de objetificação no desenvolvimento do pensamento algébrico: o caso de Evandro

Abstract

This article is a clipping of a professional master's research conducted between May and September 2016 with 17 students aged 13 to 15 years, who were in the eighth grade of elementary school in a public school in the state network of Minas Gerais, in the city from Belo Horizonte. The focus of the research was the observation of six didactic interventions made with the objective of provoking the development of algebraic thinking, characterized as an analytical way of thinking in situations of indetermination. We developed six tasks that had the generalization of patterns as a guiding thread, in order to provoke students to think algebraically. The interventions were filmed and field notes were taken. We observed that actions were triggered by the mediation of different artifacts and social interaction. The analysis of such actions had as theoretical foundation the Objectification Theory of knowledge, in which learning is considered a process through which it is possible, through the use of artifacts, to become aware of cultural ways of thinking, the processes of objectification. In this conception, we bring to this clipping, the objectification processes experienced by Evandro, when engaging in tasks of observing patterns and generalizing algebraically. The results show that, by coordinating different resources, Evandro moved between different stages of generalization (detecting a commonality, extending it and using it to derive a rule) and thereby reaching the different layers of generality, using, to express their thinking during tasks, from gestures and material resources, to the elaboration of a rule in oral language.