Um estudo sobre a construção de fractais em ambientes computacionais e suas relações como transformações geométricas no plano

Abstract

This research concerns the teaching and learning of Mathematics in the presence of computational tools, particularly in relation to the construction of fractals. The main aim of the work is to contribute to the analysis of the computational transposition process (Balacheff, 1994) of Fractal Geometry in four computational learning environments. The study entails an analysis of the nature of the meanings that each of the educational software environments affords for particular mathematical notions, that is, its epistemological domain of validity . Additionally the idea of microworld is used in relation to Dynamic Geometry environments and those based of Turtle Geometry . The theoretical approach adopted warrants and guides the methodological choices, which involve the qualitative analysis of the set of chosen computational environments. The analyses show that the construction of fractals in two of these environments made use of the concept of the Chaos Game. In these two cases, the formal structures of both softwares present tools based on geometrical transformations of the plane, although with distinct kinds of control, especially in terms of the extent to which relationships between tools and the concepts involved are made explicit. The results also enable the proposal of teaching situations concerning the construction of fractals in these environments, aimed at providing a context for the exploration of notions related to geometrical transformations of the plane and their geometrical and algebraic representations