A modelagem matemática a partir da teoria da atividade: reconstrução/reconfiguração de ambientes em uma escola

Abstract

This study, grounded in Cultural-Historical Theory (CHT) and Activity Theory (AT), investigates how the significations generated by students through a Modeling Activity in Mathematics Education, focused on the reconstruction of school environments, contribute to the development of geometric concepts. The study was conducted with 18 first-year high school students from a public state school in Minas Gerais, Brazil, and centered on the reconstruction and reconfiguration of school environments. The organization of teaching was structured around investigative situations related to circulation, accessibility, and the use of school spaces, in which students analyzed concrete problems and mobilized geometric concepts to develop models and support decision-making. The research adopted a qualitative approach and used video recordings, students’ written and graphical records, observations, and the teacher-researcher’s field journal as data sources. Data analysis was carried out using the methodology of Signification Cores, proposed by Aguiar and Ozella (2006, 2013), with the aim of understanding the movements of thought produced throughout the students’ activity. The findings indicate processes of reorganization in the significations produced by the students, expressed through shifts from initially empirical and fragmented understandings toward more integrated ways of analyzing space, in which relationships among measurement, area, slope, and spatial organization progressively guided their decisions and justifications. Collaborative work, pedagogical mediation, and the development of models fostered the production of significations that connected everyday experiences with systematized geometric knowledge. The study indicates that the organization of teaching, by creating conditions for students to engage with meaningful problems related to the school environment, can foster the production of significations and create opportunities for movement toward theoretical thinking in Geometry.