David O. Tall
Encyclopedia
David Orme Tall is a mathematics education theorist at the University of Warwick
. One of his most influential works is the joint paper with Vinner Concept image and concept definition.... 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
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
. 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; (proceptual) 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).
University of Warwick
The University of Warwick is a public research university located in Coventry, United Kingdom...
. One of his most influential works is the joint paper with Vinner Concept image and concept definition.... 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
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
for his longstanding collaboration with Eddie Gray. This partnership, based at the Mathematics Education Research Centre at the University of Warwick
University of Warwick
The University of Warwick is a public research university located in Coventry, United Kingdom...
, resulted in the theoretically important notion of procept
Procept
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...
. 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; (proceptual) 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
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
research between 1976–2006, Tall was revealed to be the most cited mathematics education
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
researcher in the book, with 55 cites to his name (Gutiérrez & Boero, 2006).
Books
- Advanced mathematical thinking. Edited by David Tall. Mathematics Education Library, 11. Kluwer Academic Publishers Group, Dordrecht, 1991.
- Stewart, IanIan Stewart (mathematician)Ian Nicholas Stewart FRS is a professor of mathematics at the University of Warwick, England, and a widely known popular-science and science-fiction writer. He is the first recipient of the , awarded jointly by the LMS and the IMA for his work on promoting mathematics.-Biography:Stewart was born...
and Tall, David: Algebraic number theory. Second edition. Chapman and HallChapman and HallChapman & Hall was a British publishing house in London, founded in the first half of the 19th century by Edward Chapman and William Hall. Upon Hall's death in 1847, Chapman's cousin Frederic Chapman became partner in the company, of which he became sole manager upon the retirement of Edward...
Mathematics Series. Chapman & Hall, London, 1987. xx+262 pp. ISBN 0-412-29690-X 11-01
- 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. ISBN 0-470-26660-0
- 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. ISBN 1-56881-119-5
- Stewart, Ian and Tall, David: Complex analysis. The hitchhiker's guide to the plane. Cambridge University PressCambridge University PressCambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world...
, Cambridge-New York, 1983. ix+290 pp. ISBN 0-521-24513-3; 0-521-28763-4