Higher order rule characterization of heuristics for compass and straight edge constructions in geometry

Abstract

A quasi-systematic method for specifying heuristics in problem solving was proposed and illustrated with compass and straight edge constructions in geometry. Higher order rules (operator combination methods) were constructed for the two loci, similar figures, and auxillary figures problems identified by Pólya [12]. The higher order rules specified were precise, compatible with the heuristics identified by Pólya, and seemed to reflect the kinds of relevant knowledge that successful problem solvers might have. Overall, the analyses demonstrated the viability of the analytic method, and provide further evidence in support of the competence theory [16] on which the analyses were based. Implications of this research for work in simulation and artificial intelligence, and in education were discussed, and future directions indicated.