O pensamento funcional de alunos dos anos finais do ensino fundamental em atividades de modelagem matemática

Abstract

This research was developed with students in the 9th grade of elementary school and aimed to investigate and evidence which types of Functional Thinking are manifested by students when developing Mathematical Modeling activities. According to the literature, Functional Thinking can be classified in three ways: Recursive, Covariational and Correspondence Thinking. In view of this, we set out to develop activities with the potential to promote Functional Thinking through Mathematical Modeling activities. Data were collected through audio and video recording, fully transcribed photos, memories of the teacher-researcher and materials produced by students (manuscripts, slides, video). For the analysis, we followed the methodology of qualitative interpretative analysis. We developed and analysed data from three activities developed with a group of 29 students from the 9th grade in which we sought to highlight the phases of Mathematical Modeling: integration, mathematization, resolution, interpretation of results and validation, as well as indications of the types of students' Functional Thinking. By analysing the three activities, we arrived at some conclusions and reflections that revealed evidence of the three types of Functional Thinking. The first activity allowed us to highlight Functional Recursive and Covariational Thinking. In the development of the second activity, it was possible to perceive Recursive, Covariational and Correspondence Functional Thinking. And, the third activity, which also allowed students to express the three types of Functional Thinking. As a result of this research, we elaborated the Educational Product entitled “Functional Thinking and Mathematical Modeling: suggestions for activities for the Final Years of Elementary School”. Finally, we bring considerations about the analyzed activities that made it possible to highlight Functional Thinking, the difficulties and challenges for carrying out this research, and considerations about improvements for carrying out future activities.