PAR OU ÍMPAR: M (2) ou ~M (2)? 2N OU 2N + 1?

Abstract

This article is an excerpt from a Master's research in Mathematics Education that investigated the skills and schemes that students in the 3rd and 5th years of Elementary School present in problem situations and the levels of algebraic reasoning mobilized in these situations. It was supported by a descriptive methodology with a diagnostic approach. The proposed objective was to identify and understand the nature of the strategies presented in the theorems-in-action and relate them to the arithmetic and algebraic field simultaneously. For this purpose, three problem situations from the original research were selected along with extracts from the response protocols of eight students. In the qualitative analysis, we identified in the students' resolving strategies a coexistence between arithmetic and algebra, a relationship of filial continuity. We verified that, in the operational relations adopted in the resolution of problem-situations (or attempts), the student, when generalizing and/or explaining a numeric sequence, even without knowing it, transited between the fields of arithmetic and algebra. The study demonstrated that problem-situations of an arithmetic nature, if mediated by an algebraic bias, could be explored in Mathematics teaching activities from the first school years as a proposal for training early algebraic reasoning.

Keywords: arithmetic; algebra; early years; Elementary School