Abstraction as a Natural Process of Mental Compression

Autor/inn/en	Gray, Eddie; Tall, David
Titel	Abstraction as a Natural Process of Mental Compression
Quelle	In: Mathematics Education Research Journal, 19 (2007) 2, S.23-40 (18 Seiten)Infoseite zur Zeitschrift PDF als Volltext (1); PDF als Volltext kostenfreie Datei (2) Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1033-2170
Schlagwörter	Symbols (Mathematics); Brain; Arithmetic; Mathematics Instruction; Abstract Reasoning; Cognitive Processes; Foreign Countries; Mathematical Concepts; Graduate Students; Concept Formation; United Kingdom (England) + Suchen Sie Ihr Suchwort? Gehirn; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Mathematics lessons; Mathematikunterricht; Abstraktes Denken; Denken; Cognitive process; Kognitiver Prozess; Ausland; Graduate Study; Student; Students; Aufbaustudium; Graduiertenstudium; Hauptstudium; Studentin; Concept learning; Begriffsbildung
Abstract	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. (Author).
Anmerkungen	Mathematics Education Research Group of Australasia. MERGA-GPO Box 2747, Adelaide, South Australia 5001, Australia. Web Site: http://www.merga.net.au/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10