Matemática financeira: aplicações de progressões aritméticas e geométricas no ensino de juros e amortizações à luz de uma abordagem teórico-prática para o ensino médio

Abstract

This study aims to analyze the application of the concepts of Arithmetic Progression (AP) and Geometric Progression (GP) in the teaching of simple interest, compound interest and amortization systems in high school, using a theoretical-practical approach aligned with the guidelines of the National Common Curricular Base (BNCC). Considering the relevance of Financial Education in the formation of critical and conscious citizens, the study adopts a methodology based on bibliographic research highlighting the speech of authors such as Skovsmose (2001), Dante (2009) and Silva and Powell (2013), among others. A qualitative approach was also carried out with the application of questionnaires to students in the 3rd year of high school, aiming to identify the students' financial concepts and habits. The results indicate that, although many students present immediate behaviors in relation to consumption, there are signs of understanding about how investments and purchasing strategies work. The research highlights the importance of making the teaching of Financial Mathematics more contextualized, using practical examples, educational games and everyday situations. Arithmetic and geometric progressions have proven effective in illustrating the concepts of linear and exponential growth applied to interest and amortization. It is concluded that the integrated teaching of these contents favors the development of mathematical reasoning and financial autonomy of students, contributing to a more meaningful mathematical education focused on citizenship.