Estudo sobre a aprendizagem matemática cuja língua para comunicação do ensino pelo professor não é a língua nativa dos estudantes: reflexões, dificuldades e possibilidades

Abstract

Language is an essential tool for human communication. Through it, people acquire knowledge, express their ideas to be understood, and comprehend those of others. In the teaching and learning process, we understand that the mother tongue facilitates the learning of sciences, especially mathematics, in students' lives. This dissertation focused on the study of mathematical learning in a context where the language used by the teacher for instruction is not the native language of the students. The study was based on the fundamental aspects of problem-solving — additive structures, according to Gérard Vergnaud's theory of conceptual fields, and on the learning of algebra, according to Raymond Duval's Theory of Semiotic Representation Registers. The guiding question of the study was: "What are the contributions of Duval's Theory of Semiotic Representation Registers and Vergnaud's additive structures to the learning of algebraic processes by 3rd and 6th-grade students in primary education, when the language used by the teacher for instruction is or is not the students' native language?"The general objective was to identify the contributions of Duval's Theory of Semiotic Representation Registers and Vergnaud's additive structures to the learning of algebraic processes by 3rd and 6th-grade students in primary education, whose language used by the teacher for instruction is or is not the students' native language. Data were collected through interviews with four students and the application of a didactic sequence in four classes, two of which were 3rd-grade classes and two were 6th-grade classes from public schools: Escola Municipal Guaracy Paraná Vieira, Colégio Cívico-Militar General Antonio Sampaio in the municipality of Ponta Grossa, and Escola Estadual Arandu Miri in the municipality of Inácio Martins.The methodological approach of this research is qualitative, centered on the participation of the investigated subjects. Bardin's Content Analysis (2016) served as the basis for the organization, treatment, and analysis of the collected data. In the data organization, six categories emerged, three related to algebra learning: 1) Participants' prior knowledge of algebra learning; 2) Semiotic Representations: the conversions that occur between the register of numerical language and natural language; 3) Cognitive operations of dual conversion to introduce letters: from numerical language to algebraic expression. And three categories related to additive structures: 1) Problem situation — Composition; 2) Problem situation — Transformation; 3) Problem situation — Comparison. Through the study of algebra learning, problem-solving — additive structures, and interviews, the research results indicate that, for students whose language used by the teacher for instruction is their mother tongue, the difficulties were in the mathematical language, not in the written verbal language. On the other hand, most students whose language used by the teacher for instruction is not their mother tongue demonstrated difficulties in both situations: mathematical language and verbal language. When asked which language they preferred the teacher to use in instruction for better understanding, three of the four interviewed students stated that they would understand the teaching better if the teacher used their mother tongue. We conclude that the learning of algebra, according to Duval, and problem-solving — additive structures, according to Vergnaud, contributed to the researcher discovering the difficulties faced by the students, as the activities require language comprehension.