O estudo da função quadrática com o geogebra à luz da teoria dos registros de representação semiótica

Abstract

The teaching of Mathematics has been undergoing significant changes for a long time and, with the pandemic, there was an intensification of these changes, which highlighted the need for different approaches to content to meet the emerging demands of the post-pandemic scenario and the difficulties presented in mathematical learning. These questions, among others, motivated the present work, which presents an investigation into the study of the quadratic function in GeoGebra based on the Theory of Semiotic Representation Registers – TSRR. In this theory, Raymond Duval, its precursor, emphasizes the role of semiotic representations of mathematical objects and the conversions between them in the learning of these objects, introducing us to the fundamental hypothesis of learning based on the structure of representation as a function of conceptualization. Aiming to investigate cognitive aspects in quadratic function activities in GeoGebra from the perspective of developing a Teaching Proposal (Educational Product), we conducted a bibliographical review on the topic, and, based on the study of the TSRR and the analysis of activities shared in the GeoGebra, we have formulated a Teaching Proposal for the study of the quadratic function. This proposal was developed in GeoGebra and explores the semi-cognitive operations of the function, especially the operation of conversion, to promote a conceptual understanding of the quadratic function. Methodologically, we conducted qualitative, bibliographical, propositional and analytical research. The collection, organization and analysis of data were based on Bardin's Content Analysis. The results of this research involve the theoretical analysis of Geogebra activities, the development of activities and an Educational Product, presenting the TSRR as a contribution and supporting the teaching of the quadratic function using GeoGebra. The activities found, selected and analyzed provide opportunities for teaching and learning the quadratic function with different representations and conversion. The Educational Product presented is a Teaching Proposal in the format of a “book” in GeoGebra titled “Quadractic Function Activity Workbook in Light of TSRR” (originally in portuguese: “Caderno de Atividades de Função Quadrática à Luz da Teoria dos Registros de Representação Semiótica - TRRS”), which contains the analyzed and other elaborated activities that highlight aspects of TSRR. Keywords: