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ERIC Number: EJ780177
Record Type: Journal
Publication Date: 2007
Pages: 18
Abstractor: Author
Reference Count: 40
ISBN: N/A
ISSN: ISSN-1033-2170
Abstraction as a Natural Process of Mental Compression
Gray, Eddie; Tall, David
Mathematics Education Research Journal, v19 n2 p23-40 2007
This paper considers mathematical abstraction as arising through a natural mechanism of the biological brain in which complicated phenomena are compressed into thinkable concepts. The neurons in the brain continually fire in parallel and the brain copes with the saturation of information by the simple expedient of suppressing irrelevant data and focusing only on a few important aspects at any given time. Language enables important phenomena to be named as thinkable concepts that can then be refined in meaning and connected together into coherent frameworks. Gray and Tall (1994) noted how this happened with the symbols of arithmetic, yielding a spectrum of performance between the more successful who used the symbols as thinkable concepts operating dually as process and concept (procept) and those who focused more on the step-by-step procedures and could perform simple arithmetic but failed to cope with more sophisticated problems. In this paper, we broaden the discussion to the full range of mathematics from the young child to the mature mathematician, and we support our analysis by reviewing a range of recent research studies carried out internationally by research students at the University of Warwick.
Mathematics Education Research Group of Australasia. MERGA-GPO Box 2747, Adelaide, South Australia 5001, Australia. Web Site: http://www.merga.net.au/
Publication Type: Information Analyses; Journal Articles; Reports - Evaluative
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: United Kingdom (England)