Processos de raciocínio matemático mobilizados por alunos do ensino fundamental

Abstract

The mathematical reasoning has been highlighted by researches and curriculum documents as one of the most relevant goals of the school Mathematics teaching. Thus, we set the objective of this research as analyse which mathematical reasoning processes 6 th and 7th grade Brazilian students use when they solve a mathematical task and how they use them to solve the tasks, about geometry in the case of 6th grade students, and about sequences in the case of 7th grade students. From the theoretical background adopted, we seek for characterize the mathematical reasoning, finding that it can be viewed from two aspects: the structural aspect and the processes aspect. The mathematical reasoning processes are our focus. Then, we effort to characterize this processes and understand how they relate with each other. This research has a qualitative and interpretative aspect. The data collected was the written production and the audio record of the students talk when they solved the task. After that, the audio recordings were transcript and analysed aiming to identify the mathematical reasoning processes used by the students. The analyses showed that students employed the mathematical reasoning processes of justifying, generalizing, conjecturing, exemplifying and pattern identifying. We verify that as students justify, they make their conjectures and generalizations better. The Educational Product accomplished from the research was a fictitious newspaper, named The Conjecture, which aims to present mathematical reasoning processes in mathematical tasks to school mathematics teachers.