Introdução ao pensamento algébrico: a generalização de padrões

Abstract

This qualitative research aimed to introduce algebraic thinking in an 8th grade classroom of the state education network in Minas Gerais, Brazil. According to the available literature, there is no exact definition of algebraic thinking. Algebraic thinking can be observed through the manifestations of four constituent features: i) observation of regularities; ii) establishment of relationships; iii) modeling; iv) symbolization. Some researches from the 1990s concluded a possible way to introduce algebraic thinking at schools would be through working with the generalization of patterns. Based on the Theory of Objectification, in which knowledge is not acquired or possessed, but set in motion through Activity, we draw the pattern Generalization Activity, and with the cooperation of the teacher of the class with which the field work was conducted, interventions in the school Activity were made. The latter were based on tasks involving actions directed to the observation of visual patterns, repetitive sequences and growth, mediated by the use of artifacts and stimulus to social interaction. During the interventions, we observe, in audio and video recordings, as well as field journaling, the processes of objectification the ways students and teachers turn to artifacts during the teaching-learning processes , analyzing the actions provoked during their course. The analysis showed that, through the use of artifacts, such as oral and sign language and materials, students engaged in the tasks proposed, assuming investigative positions, and it was possible to observe, in the analyzed episodes, characterizing aspects of the algebraic thinking. After the analysis, we develop an educational product: a kit of provocations to work with the algebraic thinking, composed of a box with material resources and a guide with tasks and orientations about how this kit becomes a mediator artifact of potential changes in the school Activity.