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 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:
: refers to the process of adding as well as the outcome of the process.
: refers to the process of summing an infinite sequence, and to the outcome of the process.
: 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. Available Online as PDF