@article {MATHEDUC.06428513,
author = {da Silva, Benedito Antonio and Penteado, Cristina Berndt},
title = {Fundamentals of real numbers: conceptions of teachers and feasibility of a beginning study of density in high school. (Fundamentos dos n\'umeros reais: concep\c{c}\~oes de professores e viabilidade de inic\'{\i}o do estudo da densidade no ensino m\'edio.)},
year = {2009},
journal = {Educa\c{c}\~ao Matem\'atica Pesquisa},
volume = {11},
number = {2},
issn = {1516-5388},
pages = {351-371},
publisher = {Pontif\'{\i}cia Universidade Cat\'olica de S\~ao Paulo (PUC-SP), S\~ao Paulo},
abstract = {Summary: The paper discusses, at first, the knowledge mobilized by high school teachers when developing activities about real numbers, and later discusses the feasibility of the introduction of the property of density study in basic education. This approach allows the teacher questions, in a sequence that let them use two procedures: When does the discussion of the density of rational numbers begin. The procedure proposed is based on the arithmetic average, which enables to find infinite rational numbers between two given numbers. But in case of one of the numbers is irrational, a change of the digits is suggested in its infinite decimal representation. The possibility expressed by this investigation participants is reported to use this intervention proposed at their classes, by judging it is appropriate and feasible, besides providing a first step towards the understanding of this property of real numbers.},
msc2010 = {F54xx (D34xx)},
identifier = {2015c.00617},
}