1 or 0? Cantorian Conundrums in the Contemporary Classroom

Autor/inn/en	Sriraman, Bharath; Knott, Libby
Titel	1 or 0? Cantorian Conundrums in the Contemporary Classroom
Quelle	In: Australian Senior Mathematics Journal, 20 (2006) 2, S.57-61 (5 Seiten) PDF als Volltext (1); PDF als Volltext kostenfreie Datei (2) Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0819-4564
Schlagwörter	Mathematics Instruction; Teaching Methods; Mathematical Concepts; Elementary Education; Theories; Preservice Teachers; Logical Thinking; Preservice Teacher Education; Elementary School Mathematics + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Teaching method; Lehrmethode; Unterrichtsmethode; Elementarunterricht; Theory; Theorie; Lehramtsstudiengang; Lehrerausbildung; Elementare Mathematik; Schulmathematik
Abstract	In set theory, one comes across the notion of "vacuous truth." A statement is vacuously true if it is true but does not quite say anything. The structure of a vacuously true statement is typically of the form: everything with property A also has property B, with the caveat being that there is nothing in property A. For instance one could say: all humans with gills are sharks. This statement is vacuously true because there are no humans with gills. It is natural to dismiss such examples as absurd and pathologies within the framework of set theory. However the notion of vacuous truth arises in some pedagogical situations. The reader is undoubtedly curious whether a situation requiring the examination of "vacuous" truth can arise in a contemporary mathematics classroom. In fact such situations do arise. In this article, the author describes one such situation in a preservice elementary mathematics classroom. This unusual set-theoretic pedagogical situation is known as Cantonian conundrums. (Contains 1 footnote.) (ERIC).
Anmerkungen	Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide, South Australia 5001. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au.
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10