Processos de raciocínio matemático mobilizados por estudantes do 5º ano ao argumentar matematicamente a respeito de figuras geométricas planas

Abstract

This qualitative and interpretative research aims to understand the mathematical arguments developed by 5th grade students from a public school in Cornélio Procópio, Paraná, Brazil, when they collaboratively solve a sequence of exploratory tasks involving plane geometric figures. As research questions we listed: (i) what mathematical concepts are used by 5th grade students when making mathematical arguments about plane geometric figures? (ii) what mathematical reasoning processes support these arguments? For this, we present a theoretical study on mathematical reasoning and its processes, on exploratory tasks and their potential for mathematical reasoning, and on the teaching of plane geometry in the Early Years of Elementary School. The research follows the methodological assumptions of Design-Based Research. Data was collected through participant observation supported by audio and video recordings and also by collecting the written records made by the students while solving the tasks. The data were analyzed from the transcript of the discussions between two pairs of students and discussed in light of the theoretical foundation. We conclude that the exploratory tasks applied in this research contributed to the development of mathematical reasoning of the students, enabling arguments between pairs and with the teacher, the development of related concepts of plane geometry specifically related to the area and perimeter of plane figures. Opportunity to develop the processes of mathematical reasoning: conjecture, compare, classify justify, and generalize.