Ensino e aprendizagem da integral de Riemann de funções de uma variável real: possibilidades de articulação da utilização de mapas conceituais com a teoria dos registros de representações semióticas

Abstract

The purposes of the present research are to identify the contributions of: 1) the theory of Semiotic Representation Registers, allied to theory of Didactic Situations, to the construction of the concept of Riemann‘s Integral for functions of a real variable (named as Definite Integral along the text); 2) the use of Concept Maps in order to notice the development of conceptualization of Definite Integral. It is a qualitative research, of exploratory nature, which has adopted the Didactical Engineering as research methodology. The theoretical support is based on Theories of Didactic Situations and Theory of Semiotic Representation Registers. For monitoring, the Concept Maps were used as didactic instruments. After literature review, it was developed and applied a didactic sequence, through a mini course for thirteen students of 1st to 3rd grade levels of Civil Engineering, Environmental Engineering, Production Engineering and License in Chemistry. During the didactic sequence applied from 6th to 15th of August of 2012, on five occasions, it was required the production and/or alteration of a Concept Map, in the software Cmap Tools, involving the contents of the activities. The softwares Geogebra and wxMaxima were used as didactic resources for solving the respective activities. It was observed that group discussion and computational exploration can bring about important contributions for the concepts learning. Furthermore, the analysis of the Concept Maps produced by students, allows the teacher to recognize features that should be strengthened to improve the understanding of Definite Integral content. It also allows to identify possible didactic difficulties, and to confront key-concepts of teachers and students. It was noticed that, activities planned in order to provide autonomy and attitude in the students, based on different registers of semiotic representation, are more likely to provide meanings to the taught contents.