As mudanças geradas pela Base Nacional Comum Curricular (BNCC) em uma coleção de livros didáticos para o ciclo de alfabetização na abordagem do pensamento algébrico

Abstract

In this work, we present a qualitative documentary research, whose main objective is to compare the praxeologies, according to Chevallard, in the approach of algebraic reasoning of two editions of a collection of textbooks for the literacy cycle — from the first to third year of elementary education - one prior to the homologation of the Base Nacional Comum Curricular (BNCC) (National Common Curricular Base); and another guided by it. For this, we analyzed the BNCC of the early years of Elementary School, using as reference the categories of algebraic thought proposed by Blanton and Kaput; and then we analyzed the activities of two editions of the same collection of books for the Literacy Cycle, through the praxeological organization of Chevallard, which provided conditions to compare the tasks, techniques and technological-theoretical discourses of the activities, in the light of the categories Blanton and Kaput. The chosen textbook collection had an edition approved by the Programa Nacional do Livro Didático (PNLD) 2016 (National Textbook Program 2016), when the BNCC was not yet approved; and another edition approved by PNLD 2019 in which the collections sought to adjust to the skills and competencies proposed by the BNCC. The analyzes showed that there was a reorganization. Several tasks started to be better distributed over the three years. However, most categories have decreased, making room for more intentional work like patterns, including the description of a rule that describes them and their creation; and with equality, proposing more activities with the explicit sign of equality and addressing, also, verification and justification of equality, with a more structural and argumentative character. We can say that the approaches concerning algebraic reasoning have increased, however, our concern is that the decimal numbering system, as well as sequences and equality - the three most adressed subjects in the current collection — would decrease the presence of other contexts, which are also relevant. In the context of the praxeological organization, it became evident that the technological-theoretical discourse of tasks with the potential to develop algebraic reasoning related not only to the algebraic field, but also to other mathematical fields, which was expected in the context of algebraic reasoning, whose proposal is not to work with Algebra, but to develop aspects of thought that are fundamental to the learning of Algebra, crossing different mathematical fields