Abstraction as a natural process of mental compression
 Eddie Gray,
 David Tall
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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 stepbystep 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.
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 Title
 Abstraction as a natural process of mental compression
 Journal

Mathematics Education Research Journal
Volume 19, Issue 2 , pp 2340
 Cover Date
 20070901
 DOI
 10.1007/BF03217454
 Print ISSN
 10332170
 Online ISSN
 2211050X
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Authors

 Eddie Gray ^{(1)}
 David Tall ^{(1)}
 Author Affiliations

 1. Institute of Education, The University of Warwick, CV4 7AL, Coventry, England