Acquisition of Proof Skills in Geometry

The ACT theory of learning is applied to the domain of high school geometry. The concern is with how students become skilled at planning a proof of a geometry problem. A general control structure is proposed for integrating backward and forward search in proof planning. This is embodied in a production system framework. Two types of learning are described. Knowledge compilation is concerned. with how students transit from a declarative characterization of the domain to a set of operators for performing a specific task in that domain. Tuning is concerned with how students learn which problem features are predictive of the success of which operators.