Análise combinatória para a Educação Básica: um guia de teorias e aplicações para professores e alunos

Abstract

This work aims to help students and teachers in the combinatorial analysis, which is considered one of the most complex in mathematics, because it requires a potentialized reasoning to solve problems. Due to all the difficulties encountered by students and teachers such as both applied methodologies learning and lack of continuity of content, for example, this is only learned in the 2nd year of high school, we present concepts of combinatorial analysis topics such as Fundamental Principle of Counting, Permutations, Arrangements and Combinations, associated with various application problems for better understanding, as well as topics not much explained in basic education such as Inclusion-Exclusion Principle and Dirichlet Drawer Principle or Pigeon Houses Principle. We take the opportunity to present Olympics problems in several levels with solutions in many ways. Through analysis of NCP's and PROFMAT dissertations, we have demonstrated the importance of combinatorial analysis and its lag in high school students, as well as the need for its teaching in elementary school.