198:" 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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In recent years Tall has been working on what he calls 'three fundamentally different ways of operation' in mathematics, 'one through physical embodiment, including physical action and the use of visual and other senses, a second through the use of mathematical symbols that operate as process and
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David Tall was an avid musician, playing the viola in orchestras and chamber groups, later starting to conduct orchestras and choirs from 1964 onwards. He formed the
Meryfield Choral Society and the Wadham College Orchestra, going on to conduct the Oxford City Operatic Society in
213:. Gray and Tall (1994) noted that mathematical symbolism often ambiguously refers to both process and concept, and that successful learners must be able to flexibly move between these different interpretations.
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Gray, E. & Tall, D. (1994) "Duality, Ambiguity, and
Flexibility: A "Proceptual" View of Simple Arithmetic", Journal for Research in Mathematics Education 25(2) pp. 116–40.
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Gray, E. & Tall, D. (1994) "Duality, Ambiguity, and
Flexibility: A "Proceptual" View of Simple Arithmetic", Journal for Research in Mathematics Education 25(2) pp. 116–40.
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concept (procepts) in arithmetic, algebra and symbolic calculus, and a third through formal mathematics in advanced mathematical thinking'. These three ways have become known as
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Gutiérrez, A., & Boero, P. (Eds.). (2006). Handbook of research on the psychology of mathematics education: Past, present and future. Rotterdam: Sense.
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Gutiérrez, A., & Boero, P. (Eds.). (2006). Handbook of research on the psychology of mathematics education: Past, present and future. Rotterdam: Sense.
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297:. Chapman and Hall Mathematics Series. Chapman and Hall, London; A Halsted Press Book, John Wiley & Sons, New York, 1979. xviii+257 pp.
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355:(Learning in Doing: Social, Cognitive and Computational Perspectives). Cambridge: Cambridge University Press. doi:10.1017/CBO9781139565202
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Tall, David; Vinner, Shlomo: "Concept image and concept definition in mathematics with particular reference to limits and continuity",
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Tall, David; Vinner, Shlomo: "Concept image and concept definition in mathematics with particular reference to limits and continuity",
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for his longstanding collaboration with Eddie Gray. This partnership, based at the
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In the book commissioned by the
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Concept image and concept definition in mathematics with particular reference to limits and continuity
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Monographs in
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How Humans Learn to Think
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researcher in the book, with 55 cites to his name (Gutiérrez & Boero, 2006).
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Tension between
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Tension between
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Mathematics Series. Chapman & Hall, London, 1987. xx+262 pp.
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research between 1976–2006, Tall was revealed to be the most cited
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Complex analysis. The hitchhiker's guide to the plane
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