Números reais : concepções dos licenciandos e formação matemática na licenciatura

Abstract

Real numbers: conceptions of perspective mathematics teacher. The authors believe that a specific approach to the numeric sistems – especially designed for the teaching degrees – should be developed. They propose that such an approach should spring from whatever conceptual idealizations are current among undergraduate students and reach a global understanding that will actually aid teaching at the fundamental and high school level. This article presents some analysed results of a survey conducted among 84 students of Mathematics with the Federal Universities of Minas Gerais and Santa Catarina, Brazil, aimed at a greater understanding of their “conceptual images” about the set of the real numbers. It was noted that very few students are aware of the meaning of the incommensurability of two line segments, and the consequent need for the irracional numbers. This may be the core of the usual difficulties found among Brazilian students to comprehend various concepts related to the structure of the real number set.