A number of learning theories have been applied to the domain of mathematics. ACT* has been used to develop a computer tutoring program for geometry. Repair theory provides a detailed analysis of the cognitive proceses involved in subtraction. Conversation theory served as the basis for studies in learning probability.
Schoenfeld has developed a comprehensive theory of mathematical problem solving that suggests four kinds of skills are necessary to be successful in mathematics: resources, heuristics, control processes, and beliefs. The Gestalt theory outlined by Wertheimer suggests some general mechanisms of problem-solving that are relevant to mathematics.
The structural learning theory of Scandura has been applied extensively to mathematics. According to this theory, the most fundamental aspect of learning is the acquistion of higher-order rules that describe mathematical procedures. Bruner applies his constructivist framework to mathematics. The algo-heuristic theory of Landa also emphasizes the importance of rules in mathematics learning.
Charles, R. & Silver, E. (1989). The Teaching and Assessing of Mathematical Problem Solving. Hillsdale, NJ: Erlbaum.
Cocking, R. & Mestre, J. (1988). Linguistic and Cultural Influences on Learning Mathematics. Hillsdale, NJ: Erlbaum.
Grouws, D. & Cooney, T. (1988). Perspectives on Research on Effective Mathematics Teaching. Hillsdale, NJ: Erlbaum.
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