Introdução à álgebra nos anos iniciais do Ensino Fundamental: uma análise a partir da Teoria da Objetivação

Abstract

The purpose of this investigation occurs in the Brazilian cultural context where the systematic teaching-learning of algebra in the early years of elementary school was specifically oriented after the approval of the Common National Curricular Base, at the end of 2017. Thus, as it is a recent demand, we verified, by means of a survey carried out on didactic materials, on portals of journals and on official documents, incipient orientations, especially with regard to the approach of algebra with a focus on the function of the equality symbol in sentences mathematics with an unknown term. In the investigative path, to know, learn and investigate the systematic teaching-learning of algebra in the early years, we chose to follow the socio-cultural perspective of the Theory of Objectivation, which considers thought as a way of acting and reflecting on the world. For that theory, algebraic thinking is based on three vectors: indeterminacy, that is, the presence of the unknown term and the treatment given to it in mathematical situations; the semiotic expression, constituted in the recognition and reference to the indeterminate and the analyticity, which consists of the deductive operation with the unknown. So, the general objective of the research is to characterize, based on the Theory of Objectification, thinking strategies demonstrated by 4th and 5th grade children of Elementary Education at the Center for Childhood Education - Application College of the Federal University of Rio Grande do Norte, in process of introducing algebra, in tasks that address mathematical sentences in which one of the terms is unknown. In this sense, as a specific objective we propose to analyze evidence of the three characteristic vectors of algebraic thinking (analyticity, semiotic expression and indeterminacy) in the thinking strategies raised by children. The research is outlined as qualitative of the descriptive and interpretive type with the method of multisemiotic or multimodal analysis, the Theory of Objectification characteristic. Our analyses indicate that, in the process of introducing algebra, the strategies demonstrated by children show the latent presence of proto-analyticity as a characteristic that makes up this process. We also conclude, from the analysis of the thinking strategies demonstrated by the children that: algebraic thinking presents a break with arithmetic thinking, this differentiation can be demonstrated by the difficulty of children in operating with the unknown; the use of refined arithmetic strategies and the use of mathematical operations properties collaborate in the development and structuring of algebraic thinking; algebraic and / or arithmetic thinking can be expressed in multiple ways, so it is necessary to provide freedom for children to solve problems in their own way, as well as to value their strategies.