Os desdobramentos teóricos da proporcionalidade na escola de educação básica

Abstract

This work has as an initiative to study the proportionality of a broader and natural perspective to the nature with which the classical mathematics was conceived. To do this, we want to broaden the understanding of the content and present it in a broader perspective, going against the simplistic aspect of bibliographies for Basic Education, in order to obtain necessary resources that justify the proposed Didactic Sequence for 9th grade of Elementary School, on Similarity and Volume Measures. To give substance to the proposal the dissertation was divided into four chapters. The first presents a historical construction of proportionality, where we have the Comensurability, The Elements of Euclid and The Theorem of Thales. Chapter 2 focuses on Cavalieri's Principle and Pappus's Theorem, which has a strong relationship with the following chapter dealing with the proportionality of solids, in particular Polyhedra and Solids of Revolution, in order to broaden the perspective of treatment of this content in the practice of teaching mathematics. Finally, chapter 4 brings the proposal of the Didactic Sequence on Similarity and Volume Measures, directed to the 9th year of Elementary School, with 7 activities with application time of 14 hours class; besides some suggestions of contents in which the proportionality already is or can be used strongly. The purpose of the present proposal is to use preexisting mental schemas to construct others, generating the appreciation of meaningful learning by the teacher who teaches mathematics and meaning to the student within mathematics itself, to stimulate the discovery of both new content and its importance in all aspects of social life.