Resolução de problemas combinatórios: uma abordagem estratégica baseada no método de Polya para o ensino médio

Abstract

Combinatorial Analysis is often pointed out by High School teachers as the most difficult part of Mathematics to teach, and studies reveal that students, when faced with combinatorial problems, have difficulties in understanding the problem and in the appropriate choice of counting techniques. Given this scenario, this work aimed to investigate the contribution of George Polya's Method as a strategy for solving combinatorial problems in High School. A qualitative, theoretical-analytical research was carried out, based on a literature review and the analysis of selected problems from the Exame Nacional do Ensino Médio (ENEM - National High School Exam). The selected problems were solved following the steps of the method, and then a general analysis of this application was performed. The results indicate that the adapted inquiries in each step of the method contributed not only to a better understanding of the problem, but also helped to avoid the choice of concepts and strategies not applicable to the problems. Thus, it is concluded that George Polya's Method is promising for the improvement of the understanding and resolution of combinatorial problems.