Sistematização de conteúdos em atividades de modelagem matemática numa perspectiva Wittgensteiniana

Abstract

The research aims to investigate, from Wittgenstein’s philosophical perspective, how the systematization of mathematical content occurs in Mathematical Modelling activities developed in the final years of Elementary School. It seeks to understand how language and language games, as well as the activity of following rules, are present when developing Mathematical Modelling activities and in the systematization of the mathematical contents that emerge when modelling a situation, whether for revision or introduction purposes. The adopted methodology is qualitative, and the data were obtained through written records, audio recordings, and videos produced during Mathematics classes, involving 106 students from the final years of Elementary School in a private school located in northern Paraná. The research is organized around two objectives: in the first, we corroborate the action of the mathematical language game and the rules that govern this game, arguing that in order to obtain a mathematical model, a solution, and systematization, it is necessary to follow these rules; in the second, we focus on the role of the teacher who ensures that students act according to such rules, systematizing the mathematical ideas and concepts addressed (revised or introduced) during the activity. Finally, the results highlight the use of language games and rule-following as recurrent in Mathematical Modelling activities, and we emphasize the importance of the teacher being attentive to mediate the systematization of mathematical content that emerges from the situation. As a result of this research, we developed an educational product aimed at teachers of the final years of Elementary School, with the objective of providing suggestions that highlight the language game and contribute to the mathematical systematization through the development of Mathematical Modelling activities.