View source for Procept

A '''procept''' is an amalgam of three components: a '''process''' which produces a mathematical '''object''' and a '''symbol''' which is used to represent either process or object. It derives from the work of Eddie Gray and [[David O. Tall]], and is a much used construct in [[mathematics education]] research.

The notion was first published in a paper in the [https://web.archive.org/web/20051025030243/http://my.nctm.org/eresources/journal_home.asp?journal_id=1 Journal for Research in Mathematics Education] in 1994, and is part of the process-object literature. This body of literature suggests that mathematical objects are formed by encapsulating processes, that is to say that the mathematical object 3 is formed by an encapsulation of the process of counting: 1,2,3...

Gray & Tall's notion of procept improved upon the existing literature by noting that [[mathematical notation]] is often ambiguous as to whether it refers to process or object. Examples of such notations are:

:<math>3+4</math> : refers to the process of adding as well as the outcome of the process.

:<math>\sum_{n=0}^{\infty}(a_n)</math> : refers to the process of summing an infinite sequence, and to the outcome of the process.

:<math>f(x)=3x+2</math> : refers to the process of mapping x to 3x+2 as well as the outcome of that process, the function f(x).

==References==
*Gray, E. & Tall, D. (1994) "Duality, Ambiguity, and Flexibility: A "Proceptual" View of Simple Arithmetic", Journal for Research in Mathematics Education 25(2) p.116-40. [http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot1991h-gray-procept-pme.pdf Available Online as PDF]

==External links==
* [http://www.warwick.ac.uk/staff/David.Tall/themes/procepts.html Procepts]

[[Category:Mathematics education]]


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