Modelagem matemática e a formação continuada de professores: a difusão do conhecimento na construção de um guia de formação para o ensino de geometria

Abstract

In the context of mathematics education, methodological alternatives that seek to transform teaching practice and reframe how knowledge is conceived have been widely discussed, with Mathematical Modeling standing out among them. Given this scenario, and considering the role of the mathematics teacher in the face of curricular demands and contemporary transformations, this thesis aimed to understand high school mathematics teachers’ conceptions of Mathematical Modeling in their teaching practices and to analyze how these experiences can support the development of a continuing education guide aimed at promoting the diffusion of knowledge in the teaching of geometry. This qualitative phenomenological study used semi-structured interviews with high school mathematics teachers, Bardin’s Content Analysis, and the ATLAS.ti software to organize and support data interpretation. From the participants’ statements, central categories emerged that express dimensions of the teaching experience, such as continuing education and professional development, knowledge diffusion, Mathematical Modeling as a methodology, geometry teaching, curriculum, and the challenges of practice. The analysis revealed that continuing education is understood as a process of emancipation and reflection on practice, and that Mathematical Modeling, when experienced in a dialogical environment, can promote more meaningful and contextualized learning. Based on these findings, the Continuing Education Guide on Mathematical Modeling for Geometry Teaching was developed as an educational product that synthesizes the results of the study and serves as a support tool for teachers, enabling more reflective and investigative practices aligned with the demands of the BNCC. The integration of theory and practice, research and the construction of a training material validated by the study’s participants, gives this research an innovative and singular character within the field of Mathematics Education. By combining phenomenological investigation, content analysis, and the development of an authentic pedagogical product, this thesis reaffirms the role of the teacher as a transformative agent and diffuser of knowledge, contributing significantly to strengthening teacher education and renewing the teaching of mathematics in the Brazilian context.