The Use of Worked Examples as a Substitute for Problem Solving in Learning Algebra

Bibliographic Data

ID23355992
AuthorsJohn Sweller (0000-0001-7855-9160), Graham Cooper (0000-0001-8383-6476), Graham A Cooper
Year1985
Volume2
Issue1
Pages59-89
Publication date1985-03-01
Peer ReviewedYes
Open AccessNo
TypeARTICLE
VenueCognition and Instruction (JOURNAL)
Journal identifiersISSN: 0737-0008 • E-ISSN: 1532-690X
PublisherInforma UK Limited (PUBLISHER • GB)
DOI10.1207/s1532690xci0201_3
OpenAlexW2046675442
LanguageEN
Citations received108
References cited9

The knowledge required to solve algebra manipulation problems and procedures designed to hasten knowledge acquisition were studied in a series of five experiments. It was hypothesized that, as occurs in other domains, algebra problem-solving skill requires a large number of schemas and that schema acquisition is retarded by conventional problem-solving search techniques. Experiment 1, using Year 9, Year 11, and university mathematics students, found that the more experienced students had a better cognitive representation of algebraic equations than less experienced students as measured by their ability to (a) recall equations, and (b) distinguish between perceptually similar equations on the basis of solution mode. Experiments 2 through 5 studied the use of worked examples as a means of facilitating the acquisition of knowledge needed for effective problem solving. It was found that not only did worked examples, as expected, require considerably less time to process than conventional problems, but that subsequent problems similar to the initial ones also were solved more rapidly. Furthermore, decreased solution time was accompanied by a decrease in the number of mathematical errors. Both of these findings were specific to problems identical in structure to the initial ones. It was concluded that for novice problem solvers, general algebra rules are reflected in only a limited number of schemas. Abstraction of general rules from schemas may occur only with considerable practice and exposure to a wider range of schemas.

Abstraction · Algebra over a field · Algebraic number · Cognition · Cognitive psychology · Machine learning · Pure mathematics · Range (aeronautics) · Recall · Schema (genetic algorithms) · Computer Science · Innovative Teaching and Learning Methods · Mathematics · Psychology · Science Education and Pedagogy · Visual and Cognitive Learning Processes

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