O jogo das operações semióticas na aprendizagem da integral definida no cálculo de área

Abstract

In this research, it was possible to investigate how students from a graduation course from Mathematics were using semiotic operations in integral learning of area calculation. It refers to a qualitative research whose empirical interventions were proceeded in academic field, taking part of the process of teaching and learning calculation. Having as a background the Theory of Registers and Semiotic Representation by Raymond Duval and from elements of Didactics Engineering Methodology, organizing a didactics sequence formed by 5 blocks of activities. Each block contained specific goals, which, together, aimed at understanding the object in study. The didactic sequence has explored the diversity of registers of semiotic representation and operations, mainly treatments and conversions. The software GeoGebrapara was used for the sketch of curves and for conversions of representations produced in graphical-geometric and algebraic records, promoting to the students an experimentation environment. In the development of activities, students were challenged to deal, in an articulated way, the reasoning, viewing and writing. Students were also led to build knowledge, based on ideas confrontation, elaboration and refutation of hypothesis and conjectures. The analysis of results points that the didactic sequence makes possible the understanding of integral in area calculation, once students were capable to develop, autonomously, the activities proposed, reaching the goals aimed in each block. Furthermore, the equivalence of areas, a subject that is not approached in text books of calculation, is an element that can be introduced together with the study of the integral. Besides, the problems involving area require the mobilization of multiple semiotic operations, and, thus, we confirmed that conversion is, in fact, an operation non neutral and creator of new knowledge, as stated by Duval.