Rational Number with Meaning of Fraction: relational aspect, ordering, equivalence and representations

Abstract

This article is about a research that aimed to analyze the process of teaching and learning the rational number, with the meaning of fractions, as well as their ordering and equivalence. 7th grade elementary school students, from a public school in São Paulo, who did not demonstrate understanding for any meaning of the rational number, experienced didactic-pedagogical activities, systematized to promote the development and coordination of competencies and skills associated with the rational number, such as: observe, perceive and understand. The activities were based on theoretical assumptions, considering the relational aspect for understanding a fraction and the role of semiotic representations in the development of mathematical concepts. The data of these activities were analyzed qualitatively in light of the theoretical framework of the research. According to the results, the use of the relational aspect for the concept of fraction and treatments and conversions between representations was fundamental for the elaboration of the meaning of the rational number as a fraction and for its ordering. However, for the concept of equivalence, the results presented by all students were diffuse, allowing inferring their non-consolidation given the conceptual non-permanence to the detriment of the fractions used and their representations. It is concluded that, for these students, the understanding of the rational number, with the meaning of the part-whole relationship and its ordering, was significantly elaborated considering the relational aspect and its representations.