Dos números naturais aos números racionais : como ocorre essa passagem em livros didáticos

Abstract

In this research, the results of analyzes made in some textbooks recommended by National Textbook Plan (Plano Nacional do Livro Didático-PNLD) are presented, with the purpose of investigating how the presentation of the set presents rational numbers and if, in such books, there are ways of overcoming what we consider be one of the obstacles to understanding the theme, the transition from an environment of discrete sets to a dense set. In order to articulate aspects involved with the teaching-learning of rational numbers, we have ascertained, besides documents of the Ministry of Education, texts related to this transition. In this context, we based in three principal categories, the duality discreet/continuous, as fundamental to the comprehension of the notion of numbers in their complete sense, in Brolezzi (1996), the historical aspects present in the origin of numbers, in Caraça (1951) and works related to the difficulties of students with rational numbers, as in Gonçalves 2014), Oliveira (2016) and Pereira and Zúñiga (2015). Our conclusion, after the analysis, is that textbooks present misunderstandings, not only regarding the lack of the notion of density in the characterization of this numerical set, but also in the representation of the elements of the set.