Raciocínio diagramático mobilizado por recursos semióticos em atividades de modelagem matemática no 1º ano do ensino fundamental

Abstract

This research seeks to investigate which semiotic resources are mobilized for diagrammatic reasoning in the knowledge construction of first-year elementary school students when developing mathematical modeling activities. This is a qualitative, interpretive study, anchored in triangulation, based on a theoretical framework that considers mathematical modeling as a pedagogical alternative and Peircean semiotics as the theory of signs, the signs of language. The structure of our research report is presented in a multipaper format, so that our considerations regarding the problem are presented in three scientific articles. In all three articles, our conclusions are based on an interpretative analysis of the mathematical modeling activities developed by first-year elementary school students at a municipal school located in Arapongas, in the state of Paraná, Brazil. In the first article, we sought to identify the semiotic resources that first-year elementary school students chose to develop a mathematical modeling activity. The results indicated that semiotic resources allowed students to articulate signs associated with the phenomenon under study and the mathematical objects that emerged from it, resulting in a solution to the problem through mathematical language. In the second article, we assessed the knowledge of 1st grade elementary school students in a mathematical modeling activity, using a semiotic interpretation of diagrammatic reasoning. The results demonstrated that the mobilization of diagrammatic reasoning was effective in the diagrams produced jointly by students and teacher, primarily to advance the generation of more sophisticated mathematical representations, which led to the construction of new knowledge. The third article aims to understand the knowledge revealed by groups of students using semiotic resources to produce diagrams in mathematical modeling activities. By analyzing the results of the three articles, we found that various semiotic resources were mobilized, such as speech, gestures, technology, written records, tabular records, images and toilet paper rolls. Through these resources, 1st grade elementary school students produced diagrams and engaged in diagrammatic reasoning, revealing mathematical knowledge about number ordering, table and graph construction, addition, multiplication, and other aspects, according to the specificities of the modeling activity. When analyzed together, the three articles allow us to reflect on our research question, inferring that different semiotic resources are mobilized for diagrammatic reasoning in the knowledge construction of students in the 1st year of Elementary School when they develop mathematical modeling activities. Based on this research, we developed an educational product consisting of a notebook with suggested activities for elementary school teachers and researchers interested in implementing mathematical modeling activities in the classroom.