Diferentes Interpretações do Número Racional: uma Análise de Livros Didáticos

Abstract

This work aims to analyze which interpretations of rational number are proposed in the collections of textbooks for elementary school. Therefore, it sought theoretical foundation in Lamon ideas, as different interpretations, the rational numbers and the theory of Semiotics Representation Registers, regarding the specifics of mathematics learning. The methodological assumptions adopted following the guidelines of qualitative research and document analysis. Also, we used to organize and analyze the data produced the steps of content analysis. The production data source are two collections of textbooks of mathematics of elementary school, chosen by teachers of a school in a municipality of the Border West of the state of Rio Grande do Sul. The analyzes support the conclusion that interpretation part-whole is more stressed, followed by multiplicative operator and less discussed is measured. Concerning operative invariants of rational numbers (equivalence and order), it appears that equivalence has priority over order. The operations with rational numbers, prioritizes the rules to the detriment of invariants (equivalence) and fundamental interpretations (eg, part-whole, multiplicative operator) essential for assigning meaning to the procedures performed. Regarding cognitive changes, it turns out that was given priority for numerical treatments and conversions prioritized one direction, ie the registration of the natural language for the number.