Logaritmo e exponencial: uma breve abordagem histórica e suas aplicações no ensino médio

Abstract

The present work had as object of study research on the logarithmic and exponential functions, with regard to their origins, as well as the way in which they are approached in high school. In this research, the National Curricular Parameters (PCN), the Guidelines and Orientations in the Official Documents were used: Law of Guidelines and Bases of Education (LDB) and National Common Curricular Base (BNCC), in addition to some textbooks where it was possible to analyze how the Logarithmic and exponential functions are addressed in high school, according to the authors Paiva (2009), Dante (2006) and Giovanni & Bonjorno (2005). In fact, among the teaching texts that we used in this research, the following items were analyzed: how each one presents the theme of logarithmic and exponential functions; whether this topic is clearly presented to students; if the theme is presented in a contextualized way; whether the examples presented by the authors motivate students to seek more information and deepen their knowledge of these functions. In addition, we also research in mathematics exams and competitions such as the National High School Examination (ENEM) and the Brazilian Public School Mathematics Olympics (OBMEP), questions where the logarithmic function and the exponential function are charged. Where we observe the importance of having mastery of knowledge, correlated to the concept of logarithms and exponential, as well as the importance of knowing how to apply this knowledge, determined by problem situations.