Números construtíveis: uma proposta geométrica para o ensino de números irracionais

Abstract

Studies show that teaching geometry requires appropriate languages and procedures for its concepts and symbolic specificities to be understood. These concerns have been on educators’ minds for a long time, as the way Geometry is approached reflects on students’intellectual development, logical reasoning, and their ability to abstract and generalize. In this context, the present work explores how Constructible Numbers can be incorporated into the study of the Set of Real Numbers in Upper Elementary Education. The goal is to encourage the use of Geometric Constructions, performed with a ruler and compass, to teach Real Numbers, thereby simultaneously addressing both Geometry and Algebra concepts. Once a unit of length is established, there are line segments whose lengths are not expressed by rational numbers but by irrational ones. In this way, the study of the Set of Irrational Numbers becomes less abstract and more easily understood. This work presents a didactic proposal with activities related to Geometric Constructions, offering a practical approach to the study of real numbers. Teaching Geometry through Geometric Constructions can enhance learning by making abstract concepts more tangible, allowing a visual and intuitive understanding of the topics covered.