Numerical and Algebric Factoration: Ecology of a Protomathematical Object as a Function of the Introduction of New Praxeologies from 1960 to 2021 in Elementary Education

Abstract

We present part of the research on the teaching and learning of numerical and algebraic factoring, specifically, the study of the ecology of its teaching between the 1960s and 2020s, analyzing one collection for each decade and two current collections that follow the guidelines of the BNCC. It is a research whose methodology is defined by Lüdke and André as documentational, having the theoretical framework centered on the Anthropological Theory of Didactics (ATD), for which we opted for the notions of praxeology and ecology, according to Chevallard, which underpinned the methodology of the research through the analysis of the last official national documents that guide Brazilian education (Parâmetros Curriculares Nacionais - PCN and  Base Nacional Comum Curricular - BNCC) and of textbooks from the considered decades. The results show a very stable ecology, if we disregard the one in the 1960s, which represents modern mathematics, as the privileged praxeology in the decades prior to the introduction of the PCN is centered on the use of techniques and a small number of contextualized situations, which reflect only one new cover, which does not make it a real context situation. After the PCN and the BNCC, we observe that the emphasis is given to contextualized problem situations, which reduces the applications of algebraic factorization in the study of algebraic fractions. We consider it important to emphasize that the study of algebraic fractions loses space from 1998 onwards, which indicates the need for greater attention by high school and higher education teachers, particularly when studying Differential and Integral Calculus.