David O. Tall
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David Orme Tall (born 15 May 1941) is Emeritus Professor in Mathematical Thinking at the
University of Warwick , mottoeng = Mind moves matter , established = , type = Public research university , endowment = £7.0 million (2021) , budget = £698.2 million (2020â ...
. 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. Tall is also known within
mathematics education In contemporary education, mathematics education, known in Europe as the didactics or pedagogy of mathematics – is the practice of teaching, learning and carrying out scholarly research into the transfer of mathematical knowledge. Although re ...
for his longstanding collaboration with Eddie Gray. This partnership, based at the Mathematics Education Research Centre at the
University of Warwick , mottoeng = Mind moves matter , established = , type = Public research university , endowment = £7.0 million (2021) , budget = £698.2 million (2020â ...
, resulted in the theoretically important notion of procept. 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. 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 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 Tall’s Three Worlds of Mathematics: (conceptual) embodied; (operational) symbolic; and, (axiomatic) formal (see http://www.warwick.ac.uk/staff/David.Tall/themes/three-worlds.html). In the book commissioned by the International Group for the Psychology of Mathematics Education to review
mathematics education In contemporary education, mathematics education, known in Europe as the didactics or pedagogy of mathematics – is the practice of teaching, learning and carrying out scholarly research into the transfer of mathematical knowledge. Although re ...
research between 1976–2006, Tall was revealed to be the most cited
mathematics education In contemporary education, mathematics education, known in Europe as the didactics or pedagogy of mathematics – is the practice of teaching, learning and carrying out scholarly research into the transfer of mathematical knowledge. Although re ...
researcher in the book, with 55 cites to his name (Gutiérrez & Boero, 2006).Gutiérrez, A., & Boero, P. (Eds.). (2006). Handbook of research on the psychology of mathematics education: Past, present and future. Rotterdam: Sense.


Bibliography

* ''Advanced mathematical thinking''. Edited by David Tall. ''Mathematics Education Library'', 11. Kluwer Academic Publishers Group, Dordrecht, 1991. * Stewart, Ian and Tall, David: ''Algebraic number theory''. Second edition.
Chapman and Hall Chapman & Hall is an imprint owned by CRC Press, originally founded as a British publishing house in London in the first half of the 19th century by Edward Chapman and William Hall. Chapman & Hall were publishers for Charles Dickens (from 1840 ...
Mathematics Series. Chapman & Hall, London, 1987. xx+262 pp.  * Stewart, Ian and Tall, David: ''Algebraic number theory''. Chapman and Hall Mathematics Series. Chapman and Hall, London; A Halsted Press Book, John Wiley & Sons, New York, 1979. xviii+257 pp.  * Stewart, Ian and Tall, David: ''Algebraic number theory and Fermat's last theorem''. Third edition.
A K Peters A K Peters, Ltd. was a publisher of scientific and technical books, specializing in mathematics and in computer graphics, robotics, and other fields of computer science. They published the journals ''Experimental Mathematics'' and the ''Journal ...
, Ltd., Natick, MA, 2002. xx+313 pp.  * Stewart, Ian and Tall, David: ''Complex analysis. The hitchhiker's guide to the plane''.
Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer. Cambridge University Pre ...
, Cambridge-New York, 1983. ix+290 pp. , * Tall, David: (2013). ''How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics'' (Learning in Doing: Social, Cognitive and Computational Perspectives). Cambridge: Cambridge University Press. doi:10.1017/CBO9781139565202


See also

* Criticism of non-standard analysis


References

*. * Gutiérrez, A., & Boero, P. (Eds.). (2006). Handbook of research on the psychology of mathematics education: Past, present and future. Rotterdam: Sense. * 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
Available Online as PDF
* Tall, David; Vinner, Shlomo: "Concept image and concept definition in mathematics with particular reference to limits and continuity", ''
Educational Studies in Mathematics ''Educational Studies in Mathematics'' is a peer-reviewed academic journal covering mathematics education. It was established by Hans Freudenthal in 1968. The journal is published by Springer Science+Business Media and the editors-in-chief are Su ...
'', 12 (May, 1981), no. 2, 151–169. {{DEFAULTSORT:Tall, David 20th-century British mathematicians 21st-century British mathematicians Mathematics educators Mathematical cognition researchers 1941 births Living people Academics of the University of Warwick