Concept image and concept definition are two ways of understanding a mathematical concept distinguished by the mathematics educators David Tall and Shlomo Vinner. A concept definition is the formal, agreed form of words used to specify a mathematical concept precisely, while a concept image is the whole cognitive structure a person actually associates with the concept in their own mind, built up gradually through experience with examples, non-examples, pictures, procedures and impressions encountered over time. Tall and Vinner observed that a person's concept image can differ substantially from the formal concept definition, and different parts of an individual's concept image can even be evoked in different contexts without the person noticing that those parts conflict with one another or with the formal definition, a state they called a potential conflict factor; such a conflict becomes an actual source of confusion or error only when the incompatible parts are evoked together and the person notices the clash. The distinction has been widely used in research on mathematics learning to explain why students who can correctly state a mathematical definition may still reason incorrectly about the concept it defines, because their day-to-day mental image of the concept has not caught up with, or has drifted away from, the formal definition itself.
Facts
Core ClaimA concept image is the total cognitive structure associated with a mathematical concept, including all mental pictures and properties built up through experience, while a concept definition is the formal form of words used to specify the concept, and the two can diverge for an individual learner. 1 FAQs
Does a concept definition in this theory always mean the formal definition from mathematics?
A concept definition can be personal to a learner and can differ from the formal definition the mathematical community accepts.
No. In the account by Tall and Vinner, a concept definition is similar to the usual notion of a definition in mathematics, with the distinction that it is personal to an individual. A learner's personal concept definition can differ from the formal concept definition, which is the one accepted by the mathematical community at large. This is separate from the concept image, which is the total cognitive structure a person associates with the concept.
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Source Concept Image and Concept Definition (Wikipedia)
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1. Concept Image and Concept Definition (Wikipedia)
WikipediaConcept image and concept definition, definitions given for both terms
We shall use the term concept image to describe the total cognitive structure that is associated with the concept, which includes all the mental pictures and associated properties and processes.
Concept image and concept definition, bibliography entry for Tall and Vinner
Tall, David; Vinner, Shlomo (May 1981), "Concept image and concept definition in mathematics with particular reference to limits and continuity"
Lead paragraph, education-level
In mathematics education, concept image and concept definition are two ways of understanding a mathematical concept.
Developed By: David Tall, Lead
The terms were introduced by Tall & Vinner (1981).
In Group: Mathematics Learning Frameworks, Lead
In mathematics education, concept image and concept definition are two ways of understanding a mathematical concept.
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