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David Orme Tall (1941-2024) was an Emeritus Professor in Mathematical Thinking at the University of Warwick. One of his early influential works is the joint paper with Vinner "Concept image and concept definition in mathematics with particular reference to limits and continuity". The "concept image" is a notion in cognitive theory. It consists of all the cognitive structure in the individual's mind that is associated with a given concept. Tall and Vinner point out that the concept image may not be globally coherent, and may have aspects which are quite different from the formal concept definition. They study the development of limits and continuity, as taught in secondary school and university, from the cognitive viewpoint, and report on investigations which exhibit individual concept images differing from the formal theory, and containing factors which cause cognitive conflict.
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