Knowledge Compilation: Mechanisms for the Automatization of Cognitive Skills.

Abstract

People get better on a task with practice. In this paper we take this non-controversial statement, elaborate what it means to 'get better', and propose a mechanism that accounts for some of the ways people get better. We trace the development of a skill from the point when it is initially being memorized and applied in a slow and halting fashion to the point where it has become fast and automatic through practice. We are interested in how students learn to use postulates and theorems in geometry tasks. A scenario of how a student (based on two students we have looked at in detail in geometry and three subjects working on an artificial proof system) learns postulates is as follows. The student reads each of several postulates in a section of a textbook. After a brief inspection of the postulates the student goes on to the problems at the end of the section that require the student to use the postulates. In the student's initial attempts with the postulates there is much looking back to them in the textbook because they have not yet been committed to memory. These applications are slow and there is muttering that shows low level matching of the postulates like 'If A is RO and B is NY then I can assert that'. After some practice the student has committed the postulates to memory. After much practice their selection and application is very fast.