ABSTRACT
In this chapter, I consider how individuals acquire skill in the task of solving problems in formal domains, domains involving a considerable amount of rich semantic knowledge but characterized by a set of principles logically sufficient to solve problems in the domain. Formal domains are different from toy domains (block worlds, puzzles, etc.) in that the number of such principles is large and the amount of additional knowledge needed to apply them skillfully is considerable. Examples of formal domains include mathematics, applied mathematics, most of what are called “hard sciences,” as well as sophisticated games (e.g., chess, go). Formal domains are only a subset of what have been called semantically rich domains (Bhaskar & Simon, 1977). For example, biology, psychology, and English literature are not formal domains, because it is extremely hard to formulate an unambiguous set of principles sufficient to solve problems in these domains. Formal domains are interesting first because their apparent superficial structure provides a starting point for hypothesizing about the organization of knowledge in the domain. In addition, formal domains are educationally important, increasingly so as technology becomes more advanced. How then is skill acquired in solving problems in formal domains?
