Processos de raciocínio matemático em tarefas exploratórias

Abstract

The present work aims to analyze and identify the processes of mathematical reasoning and its contributions to the learning of mathematics. To compose the theoretical basis of this research, studies were conducted based on different authors about what is mathematical reasoning, its structural aspects and processes, as well as its relevance to mathematical learning. This is an interpretative qualitative research, carried out through the application of an exploratory task in a first year high school class in a private school in the state of Paraná, Brazil. The applied task was solved by 30 students, organized freely in groups of three and constituted by questions that instigate reasoning, providing a constructive communication between teacher and students. We made audio recordings of the students solving the task. The audios were transcribed by the author and make up the corpus of analysis of this research. As one of the main results, we highlight the presence, in a more evident way and in both circumstances, the preparation of conjectures and the attempt to validate them based on empirical implications, use of generic examples and, at times with the aid of external authority of the teacher. Here, the role of the teacher's interventions in both groups is highlighted, in which the questions were fundamental actions for the development of reasoning, supporting the student's work and resisting the provision of indications for the development of the resolution.