Key points are not available for this paper at this time.
In this paper we suggest that the use of conceptual models, as developed in cybernetics and used in cognitive psychology, may help to bridge the gap between educational research and teachers. The notion of model is discussed in the context of explanatory theories, teachers' understanding of students, and students' understanding of mathematics. Piaget's concept of accommodation is explicated in terms of his scheme theory. A plea is made for greater flexibility, both in research methodology and teaching, and for an increased awareness that understanding and motivation to understand require the students' deliberate autonomous operating.
Glasersfeld et al. (Wed,) studied this question.