Generalização, particularização e analogia na metodologia de resolução de problemas de George Pólya

Abstract

This work is situated in a branch of Mathematics Education studies called Problem Solving. Our study focused on generalization, particularization, and analogy, mental operativos considered important by George Pólya (1887-1985), a Hungarian mathematician and founder of the Problem Solving methodology. The study was conducted through bibliographic research, with Pólya’s book How to Solve It as the primary reference. After distinguishing between problems and exercises, we classified problems into determination problems and demonstration problems. The second chapter contains the main results of the work, where we show how to generalize determination and demonstration problems; how to use particularization to obtain counterexamples or test a result; and some uses of the concept of analogy. This chapter also includes a generalization of the Pythagorean Theorem, made by Pólya, to illustrate the use of particularization, generalization, and analogy; and a solution to the two-pancake problem, adapted from the book by Davis and Hersh, where particularization and generalization are used by one of the authors to overcome a classic “crisis of understanding” in the classroom, generated by an excessively formal demonstration.