Frações na perspectiva de medição e a abordagem instrucional 4A: uma análise dos processos de raciocínio matemático manifestados por estudantes do 5º ano do ensino fundamental

Abstract

The objective of this research was to analyze the mathematical reasoning processes manifested by 5th-grade elementary school students during the teaching of fractions from the measurement perspective, according to the 4A Instructional Approach. The data were collected over four lessons conducted in a class of 30 students from the 5th grade of elementary school in a municipal school located in the north of Paraná, Brazil, using Cuisenaire rods as a pedagogical resource. The proposed activities aimed to develop the concept of fractions from the measurement perspective, focusing on the multiplicative relationships between the rods, moving away from the traditional part-whole approach. The data collection included audio recordings of classroom interactions, students' written records, and the researcher's field journal notes. The analysis was guided by mathematical reasoning processes, based on the studies of Jeannotte and Kieran (2017). The results showed that the 4A Instructional Approach, combined with the use of Cuisenaire rods, supported the emergence of mathematical reasoning processes: comparison, conjecture, classification, justification, and generalization. It was found that the measurement perspective, by focusing on the multiplicative relationships between the rods, enabled students to identify equivalences, compare fractions with the same denominators, and explore properties such as commutativity. In addition to enhancing the understanding of the fraction concept, this approach encouraged the formulation and corroboration of hypotheses, promoting the connection between different mathematical representations. As a result of the research, an e-book was developed as an Educational Product, entitled "Fractions in the Right Measure!", aimed at teachers of Basic Education Mathematics. The e-book contains the planning of a didactic sequence focused on teaching fractions from the measurement perspective for the 5th elementary grade school.