O ensino-aprendizagem das funções de várias variáveis através de modelos matemáticos: Uma investigação qualitativa em sala de aula

Abstract

The present research aims to analyze the possibilities of teaching and learning the functions of various variables from a qualitative investigation of mathematical models in light of aspects of mathematical modeling.To achieve this goal, we used as a sci entific methodology the ten steps proposed by Thomas A. Romberg, making them a kind of “backbone” and enabling the development of this work. Eight students from the fourth semester of the Mathematics Degree course participated in the research, enrolled in the discipline called Differential and Integral Calculus III, in the academic semester 2018.2. These students were prompted to investigate the proposed models in a context of Mathematical Modeling. Data were collected through notes in the re searcher’s field notebook, students’ resolutions from developed activities, recordings, filming and questionnaires applied during the course’s meetings / classes. Our analy sis of the descriptions of the developed activities during the research and the testimo nies collected in the interviews points to the existence of the production of knowledge pertinent to the Differential and Integral Calculus, regarding the Functions of Various Variables, and the Mathematical Modeling had its importance and influence in encou rage students a more intimate and autonomous relationship with the theory used in the process, in the sense of understanding, meaning, application, dialogues between stu dents, student-teacher and execution of resolutions of the activities developed. In the first mathematical models worked, the students’ desire was to apply some mathemati cal operations or substitute values that had no connection, that is, mechanization was evident without seeking an understanding, besides the fear of expressing their doubts. The results show that properly worked mathematical models in the context of mode ling can make significant contributions to the teaching and learning of the functions of various variables. In conclusion, we found the need for a space for the production of meanings by the undergraduates and the relevance of this production so that they are not simple applicators of knowledge produced by others.