Procept
Encyclopedia
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).
David O. Tall
David Orme Tall is a mathematics education theorist at the University of Warwick. One of his most influential works is the joint paper with Vinner Concept image and concept definition.... The "concept image" is a notion in cognitive theory. It consists of all the cognitive structure in the...
, and is a much used construct in mathematics education
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
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
Mathematical notation
Mathematical notation is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics, the physical sciences, engineering, and economics...
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).