Estudo das Equações Diferenciais Ordinárias Propostas por Livros-Texto: uma Análise sob a Ótica da Abordagem Qualitativa

Abstract

The present research aims to analyze how the proposals for the study of Ordinary Differential Equations (ODE) presented in textbooks can contribute to the work of mathematics teachers by selecting problem situations involving the concept of function. The theoretical assumptions for the construction of this research refer to the perspectives of the researcher Javaroni (2007) on the study of EDO under the perspective of the Qualitative Approach and through the Analysis of Models, and also the researcher Duval (2003), regarding the Theory of Semiotic Representation Records. To carry out this research were adopted the perspectives of the qualitative research and regarding the procedures, these refer to the assumptions of Content Analysis, according to Bardin (1977). The source of data production was the analysis of 2 textbooks of Differential Equations most cited by the Brazilian courses of Degree in Mathematics. This research allowed us to conclude that Textbook A and Textbook B explore mathematical models to study EDO. The most explored functions are the exponential, quadratic and trigonometric functions, to the detriment of logarithmic function, not addressed in the chapters analyzed. As for the qualitative approach, it has been found that it is used in Textbook A, because the behavior of the solutions is interpreted, but in Book Text B the qualitative approach is limited. As for the registers of representation, the authors of Textbook A approach the ODE by means of different registers like the geometric and the graph. However, this was not verified in Textbook B because some representation records, such as geometric and graphic, are not mobilized in the proposed activities.