Abstract
Faced with the current scenario of education, where the teaching of mathematics takes
place, each day more, in a mechanical way and far from critical thinking, the present work
approaches a proposal for the use of the history of mathematics as a teaching methodology for
the introduction of the content of irrational numbers and construction of the set of real numbers,
based on reflections and discussions about the notion of infinity, for a ninth grade elementary
school class, with the aim of building a meaningful teaching and learning process for students.