Fractais: contribuições para o ensino de geometria nos anos finais do ensino fundamental e no ensino médio

Abstract

Fractals are figures studied by Fractal Geometry which has self-similarity as its main characteristic. Based on the fact that some of them are formed by regular geometric figures, studied from Elementary School onwards, as well as on the proposal of the Base Nacional Comum Curricular (BNCC), on the using of these figures in Geometry classes in High School, it was decided to investigate how fractals have been used in the final years of elementary school and in high school, for teaching geometry, besides to verifying the contributions of these resources to the understanding of geometry at the chosen levels of education. The research consisted of an integrative review, analyzing dissertations published from 2016 to 2020, corresponding to the research objective. The search was conducted in national databases of journals: Catálogo de Teses e Dissertações da Capes and Biblioteca Digital Brasileira de Teses e Dissertações. Once the search was completed and the inclusion and exclusion criteria were applied, three dissertations were selected. The analyzes were based on PCN, PCN+ and BNCC and on studies by Barbosa (2005). At the end of the analysis, it was found that fractals favor the motivation of students for the study of Geometry, besides providing rich experiences in exercising the contents with the manipulation of the studied elements and calculations. The low number of researches and little or no prior knowledge on the part of students showed that fractals have rarely been worked on in the classroom.