O princípio da casa dos pombos: uma aplicação da modelagem matemática no ensino

Abstract

This research aimed to investigate the implications of applying a teaching sequence about the Pigeonhole Principle (PP) in the learning of 8th grade students. This principle, although simple, allows the resolution of several types of situations of Combinatorial Analysis and, consequently, of Probability, which are areas of Mathematics in which the difficulty faced by students and teachers is remarkable. At the stage of the experimentation of this research, Mathematical Modeling was used as a method for teaching, supported by the theory of Advanced Mathematical Thinking (AMT). To support this practice, a literature review and research on Modeling, AMT and on the PP itself. During the practice, the students created, in a group, a slideshow on the theme “Table Games” and handcrafted boards for Mancala games. During the reflection on the rules and strategies to win this game, students developed a mathematical model representative of counting concepts and combinatory, and, mainly, of the PP. They were, in the end, introduced to the formal concept of this principle and associated it with the model they created. The entire modeling process has been documented and analyzed, and it was observed that the students, when dealing with a topic of interest, felt encouraged to research. The proposed activities developed creativity and allowed the modeling of the desired mathematical concept. It was also noted the creation or improvement of a conceptual image of the PP and later the understanding of the formal concept aimed at, generally in the participating group.