Modelagem matemática e tecnologias digitais na aprendizagem da teoria dos conjuntos Fuzzy no ensino médio

Abstract

The aim of the work is to propose a didactic sequence to introduce the teaching of fuzzy sets theory in high school, having as a motivation the rupture of a tailings dam. The methodology uses communications technologies that utilize digital information and interactivity. Fuzzy logic is introduced and the main differences with classical mathematical logic are highlighted. Students build, with the help of an expert in hydraulics and sanitation, a Fuzzy Rule-Based System, using the free software FisPro, which controls the risk of rupture or risk of leakage of the tailings from the dam. An acrylic model was built of a dam prototype, with the aid of a 3D printer. Thus, students interact, using a smartphone, with a sensor placed on the dam, entering data from the input variables of the Fuzzy Rule-Based System. The input variables of this system are: age, height and volume of tailings from the dam. Depending on the output value of this system, the dam will break a number of colored gel balls, which represent the tailings. This didactic sequence was applied in a short course for high school students. The evaluation of the content learning was carried out through a game created in the free software RPG Maker. The results of the quantitative assessment were significant. It is noteworthy that the most important thing is to introduce a theory that mathematically considers uncertainty using digital technologies and a current issue.