As Recorrências como ferramentas didáticas para o desenvolvimento do raciocínio recursivo

Abstract

This dissertation will initially present a brief history about the development of the study of recurrences and their implications within the study of elementary mathematics. The recurrences and their applications have great participation in solving problems of several areas of mathematics. Some of these applications will be demonstrated here in order to provide the reader with a greater diversity of problems that can be presented to the students in a high school classroom in a captivating way and that instigates these students to feel challenged and motivated to seek the solution of such problems. I will present some classic problems here so that it is possible to do some analysis and seek alternative solutions that demonstrate more simplicity of reasoning and less use of methods of sophisticated mathematical solutions, methods that fall outside the scope of high school. I will analyze some elementary sequences, arithmetic and geometric progressions, cognitive methods of recurrence solutions, as well as some brief explanations and examples of order recurrence classifications. At the end of this work, and as the main objective of this work, three didactic problems created by the author will be presented and developed as a suggestion for the reader as a teacher to present his students as a way to motivate them and to show the vastness and beauty of mathematics.