Função afim, quadrática, exponencial e logarítmica nos livros didáticos: uma análise à luz da teoria de representações semióticas

Abstract

We know that mathematics is often feared by our students for different reasons, including the lack of understanding of mathematical objects and the lack of understanding of the various ways of representing such objects. In the present work, we present Raymond Duval's register theory of semiotic representations that can help in the teaching-learning process of mathematics. In possession of this theory, we will analyze functions in textbooks, from the first year of high school, of state schools in the city of Itapajé in the state of Ceará. We will start by explaining the difficulties faced by our students and the performance of Brazil in tests such as: International Student Assessment Program (PISA). In the second section, we present the theory as well as its particularities. In the third section, we analyze the contents of affine, quadratic, exponential and logarithmic functions in books in the light of this theory. During the fourth section, we will see how the analyzed functions appear in the descriptors of the SPAECE and Saeb reference matrices, and how the semiotic registers are present in the questions of external evaluations. About ENEM, we will see some questions about function and we will identify the representations of the mathematical objects analyzed in this work. The fifth section will have the final considerations.