Theories of problem-solving are dominated by the work of Newell & Simon on GPS (General Problem Solver). This work established the information processing paradigm for the study of problem-solving and the concepts of "means-ends-analysis" and "problem space". According to the GPS framework, problem-solving involves the identification of subgoals and the use of methods (especially heuristics) to satisfy the subgoals.
The Gestalt psychologist Wertheimer also conducted research on problem-solving and emphasized the importance of understanding the structure (i.e., the relationship among parts) of the problem. In his lateral thinking theory, DeBono stressed the importance of looking at a problem with a fresh perspective.
Schoenfeld presents a theory of problem-solving in mathematics that involves four aspects: resources, heuristics, control, and beliefs. Although this framework was specifically developed for mathematical problem-solving, it seems more generally applicable. Bransford et al. present a problem-solving approach to the use of hypermedia in their anchored instructional theory.
Problem-solving skills appear to be related to many other aspects of cognition (Frederiksen, 1984) such as schema (the ability to remember similar problems), pattern recognition (recognizing familiar problem elements) and creativity (developing new solutions). The issue of transfer is highly relevant to problem solving. A good summary of problem-solving research as it applies to instruction is provided by Tuma & Rief (1980). Problem-solving skills are fundamental to many professional domains such as engineering or medicine.
Frederiksen, N. (1984). Implications of cognitive theory for instruction in problem solving. Review of Educational Research, 54 (3), 363-407.
Tuma, D. & Reif, F. (1980). Problem Solving and Education. Hillsdale, NJ: Erlbaum.
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