David Orme Tall (born 15 May 1941) is 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 In mathematics education, concept image and concept definition are two ways of understanding a mathematical concept.
The terms were introduced by . They define a concept image as such:
:"We shall use the term ''concept image'' to describe the tota ...
" 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 for his longstanding collaboration with Eddie Gray. This partnership, based at the Mathematics Education Research Centre at the
University of Warwick, resulted in the theoretically important notion of
procept In mathematics education, 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.
...
. 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 research between 1976–2006, Tall was revealed to be the most cited
mathematics education 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 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, 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-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'', 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