Strategies young children used to correct errors in nesting seriated cups changed substantially with age, becoming increasingly more flexible and involving more extensive restructuring of the relationships among the cups. The same trend toward increasing flexibility of thought and action also appeared in procedures children used to combine the…

How computers have affected diagnosis in mathematics is discussed. A distinction is made between errors and mistakes, followed by consideration of computers as a diagnostic tool. The development of algorithms to diagnose errors and of models of student performance is described. (MNS)

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)…