Development of expertise in mathematical problem solving

Investigated the distinctive strategies employed by expert and novice problem solvers (forward-chaining and means-ends, respectively) in 7 experiments using 14 mathematics graduates and 162 9-12 yr olds. Exp I studied the course of development of expertise using a subset of kinematics problems. Ss d...

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Bibliographic Details
Published in:Journal of experimental psychology. General 1983-12, Vol.112 (4), p.639-661
Main Authors: Sweller, John, Mawer, Robert F, Ward, Mark R
Format: Article
Language:English
Subjects:
Biological and medical sciences
Cognition. Intelligence
Cognitive Development
Fundamental and applied biological sciences. Psychology
Human
Mathematical Ability
Problem Solving
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Reasoning. Problem solving
Strategies
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Summary:Investigated the distinctive strategies employed by expert and novice problem solvers (forward-chaining and means-ends, respectively) in 7 experiments using 14 mathematics graduates and 162 9-12 yr olds. Exp I studied the course of development of expertise using a subset of kinematics problems. Ss demonstrated the switch from a means-ends to a forward-chaining strategy. This was associated with the conventional concomitants of expertise such as a decrease in the number of moves required for solution. Ss appeared to categorize problems according to the order in which equations would be required. Exps II and III tested the hypothesis that the means-ends strategies used by novices retarded the acquisition of appropriate schemata. The use of nonspecific rather than specific goals was found to enhance the acquisition of expertise, the number of moves required for solution, and the number of equations written without substitutions. Exps IV and V, using geometry problems, duplicated the enhanced rate of strategy alteration found with reduced goal specificity. Results of Exps VI and VII indicated that reduced goal specificity also enhanced the rate at which problem solvers induced appropriate problem categories. It is concluded that in circumstances in which the primary reason for presenting problems is to assist problem solvers in acquiring knowledge concerning problem structure, the use of conventional problems solved by means-ends analysis may not be maximally efficient. (20 ref)
ISSN:0096-3445
1939-2222
DOI:10.1037/0096-3445.112.4.639