Concepções de professores de Matemática sobre números reais e seu ensino

Abstract

This dissertation presents an exploratory research about conceptions of Mathematics teachers about real numbers and their teaching. In the literature review, the concept of professor of mathematics teacher is discussed, in the light of different authors, followed by a historical presentation on the construction of real numbers, especially the irrational ones and the question of incommensurability. Next, a set of texts on the teaching of real numbers under different perspectives and contexts is discussed. The reviews of the textbook collections on real numbers presented in the National Textbook Program (PNLD) 2018 are also highlighted, with the aim of portraying how textbooks have discussed this theme from the point of view of the PNLD reviewers. The exploratory research was carried out with teachers of Basic and Higher Education, also active in Basic Education, and aimed to discuss in an extension course offered in a virtual learning environment, their conceptions and practices on rational and irrational numbers, as a mean for the formalization of fundamental ideas about real numbers. The data reveal that the need to (re)visit, (re)think and (re)construct concepts related to real numbers is urgent, since many conceptual inaccuracies have been perceived, pointing to a need for re-adaptation of objectives and approaches of the subjects of Real Analysis in the Pre service teachers training in Mathematics, understanding its role in the mathematical formation for the teaching in Basic Education