Higher Order Rule Characterization of Heuristics for Compass and Straight Edge Constructions in Geometry

A quasi-systematic strategy of devising rule sets for problem solving is applied to ruler and compass geometrical constructions. "Lower order" rules consisting of basic skills and "higher order" rules which govern the selection and combination of lower order rules are identified by an analysis of problem types; three types of construction problems are used to generate three specific rule sets. A second level of "higher order" rules, determining how various aspects of the individual rule sets can be combined, results in generalized rule set which describes solutions to a wide-range of instruction problems. This model seems intuitively to reflect the kinds of relevant knowledge that might be applied by successful problem-solvers. The results are suggestive of how the construction of at least certain artificial intelligence systems might be systematized. The results also identify the knowledge underlying reasonably complex kinds of problem solving which could be used as a basis for explicit instruction.