A construção dos conceitos de função afim e quadrática mediada pelo livro didático no ensino médio : um estudo à luz da teoria de Vigotski

Abstract

This study aims to present how Secondary Education mathematics textbooks, indicated by PNLD 2021, can mediate the construction of concepts of affine and quadratic functions. The theoretical basis of this research was built on ideas from Vygotsky's socio-interactionist theory: mediation, internalization, social interaction, zone of proximal development and, in particular, the theory of concept formation. The research corpus consisted of three teaching books which, together, are present in almost 80% of state and federal public schools in the municipality of Caxias do Sul. The selected textbooks were analyzed based on the discursive textual analysis of Moraes and Galiazzi (2011), and the categories that emerged from this process were: presentation of contexts, presentation of definitions, proposals for activities and retakes of prerequisites. The third category was divided into three subcategories: proposals for questions and tests, proposals for activities using digital technology and proposals for explorations and investigations. The results indicate that textbooks have the potencial to mediate the construction of the concepts of affine and quadratic functions, especially if taking up concepts that are prerequisites through probing, presents contextual situations related to the concepts to be studied, states definitions in symbolic language combined with mother tongue and proposes varied activities such as contextualized questions, problematizations using digital technology, explorations and investigations that prioritize social interaction, verbal communication and written production. These four aspects, presented in an articulated way, enhance the mediation of the didactic work in the process of constructing concepts of affine and quadratic functions. This potential is integrated with the teacher's role as a mediator in the learning process, through explanations, guidance and interventions that contribute to the construction and internalization of these concepts. [resumo fornecido pelo autor]