Uma análise dos processos visuais na apreensão de conceitos da geometria fractal

Abstract

Some principles of Euclidean Geometry are developed in basic school, such as concepts of plane figures, areas and volumes. Considering some structures that are present in nature, such as clouds, mountains and lightning, the geometry learned at school cannot accurately describe them. Fractal Geometry is a branch of mathematics that describes and models some forms found in nature, bringing a more appropriate description, but not perfect, such as those exemplified. In this context, the research developed here aims to analyze which visual procedures are used in solving activities involving mathematical content and Fractal Geometry by Basic Education teachers. To achieve this objective, a case study research was carried out, using a qualitative approach, in which it was analyzed how Mathematics teachers in Basic Education relate fractal-type figures and mathematical content. In addition, with the help of the GeoGebra software, the understanding of concepts of this geometry was sought with the teachers, based on a workshop in which mathematical contents described in documents such as the National Common Curricular Base were explored, enabling a study of the Fractal Geometry. In this investigation, it can be concluded that, during the activities proposed in the workshop, the participants used different visual processes such as translation and rotation of figures. In addition, the use of the GeoGebra software was positive, even though the participants did not fully master its tools.