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ERIC Number: EJ720049
Record Type: Journal
Publication Date: 2004
Pages: 9
Abstractor: ERIC
ISSN: ISSN-0819-4564
Playing Outside: An Introduction to the Jazz Metaphor in Mathematics Education
Neyland, Jim
Australian Senior Mathematics Journal, v18 n2 p8-16 2004
The trouble with mathematics is that it looks a little more logical and consistent than it is. Mathematics has a universally recognised exactitude. It also has an inexactitude that tends to remain concealed. This author contends that the trouble with mathematics is that it is neither structured, nor unstructured. It is nearly structured, but not fully. It is neither tamed nor wild. It is both nearly tamed and forever untameable. The author uses the jazz metaphor as a useful way of understanding complexity, and explains that his analysis of the jazz metaphor and its relation to mathematics teaching has led to the identification of five key components of jazz: (1) structure; (2) improvision; (3) playing outside; (4) pursuit of ideals; and (5) "ways of the hand". This article concentrates on the third component: "playing outside", which, in jazz refers to a radical form of improvisation that deliberately transcends the established structures. Playing outside is essential in the study of mathematics, where proof is not enough for establishing mathematical truth.
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:; Web site:
Publication Type: Journal Articles; Reports - Evaluative
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A