O pensamento algébrico sob a ótica da teoria da objetivação: uma análise a partir de episódios de trabalho conjunto no 5º ano do ensino fundamental

Abstract

This research focuses on algebraic thinking in the early years of elementary school, and the question to be answered is: If and how are evidences of algebraic learning evidenced by 5th graders in episodes of joint work that encompass covariate algebraic thinking, adapted according to Luis Radford's Objective Theory? In order to understand this issue, we defined as a general objective to analyze the algebraic learning evidenced in episodes of joint work with students from the 5th grade of PE. Bearing this objective in mind, we consider as the theoretical framework of algebraic thinking the Theory of Objectification. Regarding methodological aspects, our research is qualitative and field in nature. The research data consisted of episodes of joint work. The procedures for analyzing these data followed the recursive movements of Discursive Textual Analysis: unitarization, categorization and metatext. The units of analysis were episodes of joint work and algebraic learning; the category of analysis was the generality layer of algebraic thinking in episodes of joint work, with the following subcategories of analysis: factual algebraic thinking; contextual algebraic thinking and standard algebraic thinking, and metatext were constituted from the analyzes performed around the categories. From this, we can infer that evidence of students' algebraic learning was evidenced in the joint work, both in a factual and contextual layer of comprehension. And, that the sequence regularity is more easily objectified by the students, however, after some interventions by the researcher, the covariate relationship of the sequences comes to light. Given this, we consider it important that future research should focus on investigating other possibilities for teacher interventions in working with students, with a view to the emergence of covariate algebraic thinking.