As relações entre a álgebra e a aritmética: uma análise comparativa entre os Parâmetros Curriculares Nacionais e a Base Nacional Comum Curricular - Diniz, Ellen Cassiano de Carvalho (2022)
This qualitative research aimed carry out a comparative analysis between the National Curricular Parameters (PCN) and Common National Curricular Base (BNCC), with regard to the relations between the arithmetic and the algebra in these documents. The research problem was proposed in the form of a question: How the relationships between Algebra and Arithmetic are addressed in the two most recent curriculum documents of the Brazilian School Legislation: National Curricular Parameters (PCN) and Common National Curricular Base (BNCC)? We assumed as methodological axis assumptions of Content Analysis from the perspective of Laurence Bardin and before a cursory reading of both documents, we listed six categories of analysis. In the category (C1) - Way of conceiving mathematics - we see that mathematics is understood in both documents as a hypothetical-deductive science, based on systems of postulates and axioms. But while it is stressed in the BNCC that the teaching of mathematics is aimed at developing skills, in the PCN the focus is on training citizens for the world of work. In Category (C2) - Role of Arithmetic - we found that the role it plays in both the BNCC and the PCN is similar, because in both the development of number sense, or numerical thinking is the cornerstone of the teaching and learning process of mathematics since the early years. Regarding Category (C3) - Role of Algebra - we found that in the BNCC Algebra is characterized by the development of algebraic thinking since Elementary School - Early Years, and in the PCN Algebra is characterized by the generalization of Arithmetic. Both documents recognize the close relationship between Algebra and Arithmetic. In the categories (C4) - Knowledge objects and skills in Arithmetic - and (C5) - Knowledge objects and skills in Algebra - we found that in the PCN and also in the BNCC the knowledge objects of Arithmetic are related to skills referring to the development of number sense and the ideas of approximation, proportionality, equivalence, order, among others. The Algebra contents in the BNCC and also, to some extent, in the PCN are related to skills that include notions of equivalence, variation, interdependence, and proportionality. And finally, in chapter entitled Relations between Algebra and Arithmetic in the National Curricular Parameters and the Common National Curricular Base, we verified that the Algebra developed from algebraic thinking since the early years is structured in the various aspects of the work of developing the sense of number and operations, as well as their properties and regularities