Análise de modelos em atividades de modelagem matemática com alunos do ensino médio

Abstract

This research, conducted within the scope of the Graduate Program in Mathematics Education at the Federal University of Technology - Paraná, adopts the approach of Mathematical Modeling and Model Analysis as a pedagogical alternative to investigate how students analyze and critically evaluate mathematical models. For this purpose, three mathematical modeling activities were planned and implemented in which 3rd-year high school students collected data through experimentation and the availability of digital technologies. The analysis of the data collected from the development of one of the activities was carried out using a qualitative approach based on Content Analysis. The discussion of the results was based on three categories of analysis: teacher intervention, resources used, and manipulation and experimentation, arising from the analysis and coding of the data collected by the researcher. The synergy between the two pedagogical alternatives—Mathematical Modeling and Model Analysis—was evident, enhancing the analysis and critical evaluation of the studied mathematical models. The analysis shows that students were engaged in developing a mathematical model, analyzing it, comparing it with a classical model from the literature, and refining it, which allowed them to study new mathematical content and give more meaning to the mathematics learned in the classroom. An important outcome of the research is the Educational Product "Mathematical Modeling Activities with Model Analysis for High School," which consists of a website aimed at guiding Mathematics teachers and related fields, providing Mathematical Modeling activities with an emphasis on Model Analysis. The material aims to offer students the opportunity to apply their knowledge in everyday situations, critically evaluating mathematical models and highlighting their potentialities and limitations.