Premissas sobre equações de recorrências : teoria, aplicações e propostas de resolução de problemas no ensino básico

Abstract

The core of this work is to present, through the study of recurrence equations, having prior knowledge of basic education subjects, that we can model practical problem situations in several areas of knowledge, resulting from recursive reasoning, mathematically formulating special types of expressions, namely, recurrence equations and display possible solutions to the addressed problems. In addition to the theoretical content, we will explain examples of difference equations of two kinds, first and second order difference equations, emphasizing aspects that provide support for problem solving that develops the knowledge acquisition process, both by elaborating solutions of classic phenomena, which were support for the theory, the more objectively, arising from the various questions taken from the assessments and notebooks of the Brazilian Mathematical Olympiads. Finally, we present some proposals for intervention in basic education, having a direct interaction with the student, proposing situations in which they can glimpse recursive patterns in classic phenomena of theory that are molded with the use of low-cost manipulable materials, promoting a healthy interaction in search of knowledge in this area of knowledge.