Realidade, matemática e modelagem: as referências feitas pelos alunos

Abstract

In this dissertation, I present a study of qualitative nature, about relationships between reality and mathematics in mathematical modelling environments. The objective of the research was to understand the references that students make to reality and to mathematics in modelling environments, and the relationships established between them. To substantiate the research, I have relied on some philosophical discussions and in work of the mathematical educator Ole Skovsmose about reference to reality and to mathematics in learning environments. In empirical terms, I conducted a modelling project with students of a class of first year of high school at a state public school of the city of Belo Horizonte, MG, Brazil. The project was developed face-to-face, in mathematics classes, and also in a virtual environment, in which the students inserted videos, reportages and links related to the project, and comments on the project development. The methodological approach was the participant observation, in which I took notes in a field notebook, where they were registered the development of the project, some speeches and actions of participants. To provide support to such the observations, the classes were recorded on audio and video. From the analysis of the data, it was possible to infer that the relations established in modelling environments between references to reality and to mathematics are connected to other routine activities of the students, and to the actual and previous experiences of the participants. Additionally to that, both the perspective of modelling in mathematics education, that oriented the project, as the use of information technology, characterized by the use of computer software, they contributed to question the use of mathematics regarding situation of the reality investigated. The results of this study also signaled that in modelling environments, mathematics or mathematical model may be changed to confirm certain hypothesis about the situation of reality, and so characterizing a role reversal, compared with the conventional classes mathematics in which real situations are often changed to fit exercise patterns. In view of this, this research pointed out a consideration beyond the field of modelling: the relevance to consider not only to the incorporation of real situations, but also the use of mathematics in the face of such situations of reality.