Funções lineares no ensino médio: contextualizações e representações

Abstract

The present study has had as its aim to analyze conceptions and practices of contextualization and representations of linear functions, by Mathematics teachers in High School. We have adopted studies from Gérard Vergnaud, Raymond Duval as our theoretical reference center, besides bringing other writers’ contributions as well. The investigation, with qualitative level, was led by questions comprising essential elements for Mathematical concepts constructions, relations between contextualization and representations of linear function concept, the nature of proposed situations as far as potentiality in order to contribute to increase the meaning of the linear function concept by the students, and the role of class books in the job of the teachers. The study was made from data collected through interviews, by observing classroom practice with three teachers at state public High Schools located in the city of Campina Grande, Paraiba state, from notebooks notes of two students of those related teachers participants of the study, and with class books used by them. Along the interviews, we could highlight the teachers’ conceptions about the necessary elements to Mathematical concept formation, and about contributions of the representations and contextualization for elaborating the concept of linear function. The analysis on the students’ notebooks and the observations allowed us have an overview on the teachers’ work, in the classroom, with the contextualization and representations of a linear function, and about the class books, we checked possible contributions of the proposals presented in them, for the developments of elements remarked in our investigation. We can hold that the situations and representations cannot happen in an isolated way, but they imply in fundamental elements in the constructions of mathematical concepts, which must be developed in a integrated way. The analysis of information referent to the teachers revealed an limited comprehension of which can be said as contextualization, lack of knowledge about the importance of working with potentiating situations of the meaning of a concept, and lack of skill to mobilize more than a kind of representation simultaneously, in the construction of a mathematical concept by the student. The class books go further just a little on the proposal of work, with representations of a linear function in a contextualized approach, in the perspective that we come to support here.