One of the foremost challenges to schema theory in the past has been its lack of specificity. This is a critical issue, of course, because to be useful a theory must provide specific and testable propositions, and schema theory has not always done so. Among the unresolved issues have been questions about schema development, about activation of appropriate schema knowledge, and about the structure of schemas in general (e.g., W. F. Brewer & Nakamura, 1984). These questions have been the focus of most of the previous chapters. The theory presented here addresses these issues and generates statistical and simulation models with which to evaluate them.

A more recalcitrant issue, which has been raised many times but never satisfactorily settled, is the extent to which any schema theory is domain specific. Is it necessary to have a specific schema theory for each domain or is there a general framework that encompasses all schema development and use? This issue, of course, cannot be resolved here, because all the research described in these chapters comes from the domain of arithmetic problem solving. It is the only one, thus far, that has been evaluated fully under the schema theory I propose. A great deal of additional research from many domains is still needed.

My opinion is that schema researchers and theorists will eventually share a common theory of structure but will require specific models of implementation. The issues about general versus specific theory coincide to some extent with the question of whether one is constructing a theory or a model.