This paper discusses the theoretical problem of matching and abstraction of concepts as the processes occur in human minds, and the structures used to represent these processes for use in automated, knowledge based systems. A basic premise of the paper is that hierarchies play a crucial role in structuring knowledge and in solving problems. Data…

Research was conducted investigating properties of skill in learning, in the domain of elementary algebra. Thinking-aloud protocols indicate that early knowledge of the subjects studied was fragmentary, rather than involving systematically flawed procedures. Computational models, developed to simulate observed errors, focused on the role of…