O desenvolvimento do conceito de número no sexto ano do ensino fundamental

Abstract

This study aimed to analyze the meanings produced by sixth-grade students in Triggering Learning Situations (TLS) for the development of theoretical thinking regarding the concept of whole numbers (natural numbers including zero). The specific objectives were: (a) to analyze the role of mediating elements (tools and signs) in the development of theoretical thinking concerning the concepts under study; (b) to identify the didactic-pedagogical elements that contributed to fostering learning activity in the development of mathematical thinking; and (c) to collectively analyze the personal meanings and socially shared meanings produced in TLS related to the concept of number. The study sought to answer the following guiding question: which conceptual elaborations collectively produced by students, through processes of meaning-making concerning the concept of number, contribute to the development of their theoretical thinking? Data were generated from the meanings produced during the implementation of an educational product consisting of a set of Triggering Learning Situations in a sixth-grade class of a public school in the municipality of Machado, Minas Gerais, Brazil. The intentional purpose of the TLS was to promote the development of theoretical thinking regarding the concept of whole numbers. Data were collected through field notes, audio and video recordings of the sessions, and students’ written records. This was an exploratory qualitative study, and the analytical framework was based on the methodology of Nuclei of Signification. Data analysis enabled the construction of two Nuclei of Signification: “The Initial Constitution of the Concept of Number in Social Practices and Empirical Thinking” and “Pedagogical Mediation and the Process of Appropriation of the Decimal Numeral System.” The results revealed that, initially, the meanings produced by students were closely linked to social practices and empirical thinking, with numbers being understood primarily as tools for counting and organizing reality. Through pedagogical mediation and the use of TLS, students demonstrated a growing understanding of the relationships underlying the decimal numeral system, including base-ten grouping, place value, numerical composition, and decomposition. The articulation between the two nuclei made it possible to understand that the appropriation of the concept of number occurs as a gradual and socially mediated process marked by the reorganization of students’ thinking. Furthermore, the findings indicate that the intentional organization of teaching, combined with the use of tools and signs and the active participation of students, constitutes a fundamental element in the development of theoretical thinking, with TLS serving as central mediators in the production of meanings and conceptual elaboration in Mathematics.