This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the…

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…

A theory of how people learn certain procedural skills is presented. It is based on the idea that the teaching and learning that goes on in a classroom is like an ordinary conversation. The speaker (teacher) compresses a non-linear knowledge structure (the target procedure) into a linear sequence of utterances (lessons). The listener (student)…