Processos de raciocínio matemático no ensino fundamental: tarefas exploratórias sobre medidas de comprimento

Abstract

The objective of this research is to analyze the processes of mathematical reasoning developed by students of the fourth year of Elementary School of a municipal school in the city of Londrina in the state of Paraná, Brazil, when solving a sequence of exploratory tasks. This research was carried out with 16 students organized in pairs. The exploratory tasks addressed the content on magnitudes and measures, specifically on measures of length. Data were collected by observing the students, recording audios, videos and written records of the tasks. The research followed a qualitative approach with an interpretative character, with the methodology of Research Based on Design (IBD). As theoretical contributions, we approach the definitions of mathematical reasoning and its processes, about the exploratory tasks and the actions of teachers that support mathematical reasoning and about the teaching of measures. We present data related to three pairs as they solve two of the exploratory tasks. The results allowed us to observe that the students, when solving the tasks, evidenced the contents as addition, subtraction, multiplication, relationships between meter and centimeter measurements and length estimates. They used different strategies and mobilized the processes of conjecturing, comparing and justifying, proving that tasks elaborated and applied in an exploratory teaching-learning perspective contribute to the development of mathematical reasoning.