Two Geo-Arithmetic Representations of n[superscript 3]: Sum of Hex Numbers

Autor/in	Unal, Husan
Titel	Two Geo-Arithmetic Representations of n[superscript 3]: Sum of Hex Numbers
Quelle	In: Australian Mathematics Teacher, 65 (2009) 3, S.22-24 (3 Seiten) PDF als Volltext (1); PDF als Volltext kostenfreie Datei (2) Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0045-0685
Schlagwörter	Symbols (Mathematics); Mathematics Teachers; Geometric Concepts; Arithmetic; Mathematics Instruction; Visualization; Mathematical Logic; Validity; Concept Formation; Mathematical Concepts; Numbers; Teacher Education; Equations (Mathematics) + Suchen Sie Ihr Suchwort? Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Elementare Geometrie; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Mathematics lessons; Mathematikunterricht; Visualisation; Visualisierung; Mathematical logics; Mathematische Logik; Gültigkeit; Concept learning; Begriffsbildung; Zahlenraum; Lehrerausbildung; Lehrerbildung; Equations; Gleichungslehre
Abstract	Studies have shown that students' understanding is typically analytic and not visual. Two possible reasons for this are when the analytic mode, instead of the graphic mode, is most frequently used in instruction or, when students or teachers hold the belief that mathematics consists simply of skillful manipulation of symbols and numbers. The National Council of Teachers of Mathematics (NCTM) states that: "Different representations support different ways of thinking about and manipulating mathematical objects. An object can be better understood when viewed through multiple lenses" (2000, p. 360). This article presents two ways of visualising a series in "proof without words" (PWW) style (Nelsen, 1993; 2000). The contention is not that one representation is superior to another, only that students often construct vastly different personal and idiosyncratic representations which lead to different understandings of a concept. (Contains 9 figures.) (ERIC).
Anmerkungen	Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. 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