ABSTRACT
The discipline of psychology and, more recently, cognitive science has had a seminal influence on how mathematics is taught and learned (Kilpatrick, 1992). From the early part of the century, the teaching and learning of mathematics has received considerable attention from psychologists, as can be seen in E. L. Thorndike’s (1922) book, Psychology of Arithmetic. Thorndike’s work made a significant impact in many a classroom where the chanting of tables (reflecting Thorndike’s “law of exercise”) was a regular occurrence. Psychology has continued to show an interest in mathematics education, as can be seen from the large number of papers presenting a cognitive analysis of children’s mathematical learning (e.g., J. S. Brown & VanLehn, 1982; Collis, 1974; R. B. Davis, 1984; Greeno, 1992; Halford, 1993; Siegler & Jenkins, 1989; Sweller, 1989). Mathematics has been a popular domain of psychological research largely because of its importance in the school curriculum and because its hierachical structure facilitates the construction of tasks of varying levels of difficulty (Kilpatrick, 1992). Mathematical knowledge also lends itself to representation in the computational models of cognitive science.
