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Beyond the Union of Rational and Irrational Numbers: How Pre-Service Teachers Can Break the Illusion of Transparency about Real Numbers?  

Lee, Jihyun (Incheon National University)
Publication Information
Journal of Educational Research in Mathematics / v.25, no.3, 2015 , pp. 263-279 More about this Journal
Abstract
The introduction of real numbers is one of the most difficult steps in the teaching of school mathematics since the mathematical justification of the extension from rational to real numbers requires the completeness property. The author elucidated what questions about real numbers can be unanswered as the "institutional didactic void" in school mathematics defining real numbers as the union of the rational and irrational numbers. The pre-service teachers' explanations on the extension from rational to real numbers and the raison d'$\hat{e}$tre of arbitrary non-recurring decimals showed the superficial and fragmentary understanding of real numbers. Connecting school mathematics to university mathematics via the didactic void, the author discussed how pre-service teachers could break the illusion of transparency about the real number.
Keywords
didactic transposition; double discontinuity; infinite decimal; real numbers; pre-service mathematics teacher education;
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Times Cited By KSCI : 1  (Citation Analysis)
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