Conceitos de análise matemática na reta para bem compreender os números reais no ensino médio.

Abstract

We have realized that some concepts related to the real numbers studied by math teachers, when they were students at the university in the Mathematical Analysis discipline, end up distancing themselves from the concepts brought in high school textbooks. Thus, the present work intends to establish a connection between the real numbers study approaches in basic education and in mathematics degree course. Our focus is on teachers’ look to this subject, how to help them see that real numbers can be better understood using concepts from the Mathematical Analysis discipline and that these concepts could help them to approach this subject in their classrooms. To do it, we will analyze and describe how real numbers are treated in high school and college. Next, we will discuss what real numbers can be marked on the real line so we can demystify the impression expressed by textbooks that it is possible to mark all of the numbers. We will also present a definition of completeness of real numbers that could be taught in Mathematical Analysis disciplines in mathematics degree courses, using the Nested Intervals Theorem, making it more intelligible and close to concepts used in High School. Through this work, We hope to contribute to the approximation of the contents studied in the discipline of Analysis with the contents addressed in high school textbooks, in order to contribute to the teaching practice and to make clear the importance of disciplines such as Mathematical Analysis for teachers training.