A General Learning Theory and Its Application to the Acquisition of Proof Skills in Geometry.
Abstract
Generating a proof in geometry is analyzed into the stages of proof planning and proof generation. This report focuses on the processes of proof planning. In this stage the student searches for a proof tree which relates the givens to what is to be proven. This search is performed by operators that reason forward from the givens and that reason backwards from the to-be-proven statement. We discuss three types of learning which underlie this search. There is acquiring the operators in procedural form, learning to represent the problem in a way the operators can apply, and tuning the operators so that they will apply more appropriately. The paper focuses discussion on the first and third. The mechanisms underlying the first process are composition and instantiation. They transform information processing from interpretative application of procedural knowledge. The mechanism underlying knowledge tuning are analogy, generalization, discrimination, and composition. They serve to add further constraints to the productions that embody these rules. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 20, 1980
- Accession Number
- ADA087189
Entities
People
- John R. Anderson
Organizations
- Carnegie Mellon University