**ERIC Number:**EJ859753

**Record Type:**Journal

**Publication Date:**2009

**Pages:**3

**Abstractor:**ERIC

**Reference Count:**10

**ISBN:**N/A

**ISSN:**ISSN-0045-0685

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

Unal, Husan

Australian Mathematics Teacher, v65 n3 p22-24 2009

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.)

Descriptors: Symbols (Mathematics), Mathematics Teachers, Geometric Concepts, Arithmetic, Mathematics Instruction, Visualization, Mathematical Logic, Validity, Concept Formation, Mathematical Concepts, Numbers, Teacher Education, Equations (Mathematics)

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

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Higher Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A