Sequências e séries : conhecendo e construindo estratégias de abordagem

Abstract

Teaching series and sequences in High School, in college and the proposed problems in the High School Mathematical Olympics, have very diverse proposals. The teaching of this topic is covered in a mechanical manner while the problems posed in the Olympics requires a logical reasoning developed from the behavior of several series and sequences. Hence, it is necessary that knowledge by the teacher and the student, both in high school, goes beyond the limits traditionally treated in the pedagogical practice of teaching sequences and series. Thus, it is necessary to have knowledge of what the convergence of a sequence, its properties, convergence tests that can be used in high school, behavior of several series and sequences such as the Fibonacci sequence, the harmonic series, arithmetic progressions various orders, etc.. Taking into account the mathematical stage of high school student, the teacher should develop the student skills and acquiring tools that allow this to solve problems that may break with math memorization. Thus, the use of games, the use of geometry to the understanding of convergence among others, the use of various knowledge elds where the teaching of series and sequences can be used and troubleshooting of series and sequences of math olympics are tools necessary for the teacher to learn how to learn and thus lead their students to emancipation of mathematical thinking.