2023-09-282023-09-282023-09-282022-07-05https://repositorio.ifal.edu.br/handle/123456789/314This work attempts to encourage students of major in Mathematics to give more importance to the Study of real numbers as a way of being future teachers aware of transmitting the clearest and most objective content to Basic Education students, especially to the subject that deals with the origin of irrational numbers. The unwillingness of some teachers to talk about real number theory and history leads the student to believe that they exist by chance, wlich leads students to accept ready-made formulas. In some cases the teacher itself omits this topic, without attaching much importance to learning, and many students finish high school without knowing why real(ou irrational?) numbers exist and go unnoticed as to how the set of real numbers can be described. The main aim of this work is a critical study of real numbers, from the point of view of a mathematics teacher, this ondergraduate student herself, based on experiences lived in the school career, which can be seen that many undergraduates in mathematics also face a lot of difficulty in trying to understand a subject that seems simple at first, but there are several divergences, as a result, we will analyze the ideal procedures that suit our reality in mathematics teaching, as well as propose to future teachers ways of passing the content to students in a didactic and comprehensive approach, offering students a deeper view of the subject, so they may enjoy the proposed content. Work, uses bibliographic research and a qualitative approach, based on a bibliographic approach, in an explanatory way.Acesso AbertoEnsino BásicoMatemáticaNúmeros ReaisBasic EducationMathReal NumbersTrabalho de Conclusão de CursoCIENCIAS EXATAS E DA TERRA