Incomensuráveis: abordagem dos números irracionais na educação básica

Abstract

This study addresses the construction of numerical sets, with particular emphasis on irrational numbers, in order to examine their teaching in Brazilian Basic Education. The research begins with a review of the historical and conceptual foundations of irrational numbers, highlighting the discovery of incommensurables in Ancient Greece. The analysis of basic education textbooks reveals superficial and fragmented approaches to irrational numbers, affecting students’ conceptual understanding. The importance of adopting a historical-epistemological approach to contextualize irrational numbers and avoid circularity in the definition of real numbers is also discussed. It is concluded that the teaching of irrational numbers needs to be rethought, seeking a more meaningful and in-depth approach, valuing teacher training, and promoting the use of technological resources and problem situations to stimulate conceptual understanding and the solving of mathematical problems.