can substantially increase the utility of the local knowledge one has available. Without those control structures, the local knowledge only functions by "popping up." With these control structures mediating "dig out" access, local knowledge can be brought to bear much more flexibly upon problems within the domain, and perhaps sometimes beyond the domain.
To summarize, in the fractal picture of mind we are painting, general and local knowledge exist in a symbiotic relationship. Local knowledge does not displace general knowledge as mastery develops. Rather, local knowledge develops through the compilation of general knowledge, but general knowledge continues to serve important control functions that, through "dig out" access, deploy local knowledge much more widely than "pop up" access would allow. This fractal character in problem solving becomes particularly salient and important when novel problems are encountered.
This perspective also has implications for instructional practice. It warns against an exclusive emphasis on local knowledge and on the presumption that local knowledge will automatically prove operative. It recommends attention to multiple levels of generality and to the processes of contextualization and abstraction that mediate between them.
Respecting the literature on expertise, one can acknowledge that general knowledge is helpless without local knowledge. But one must also recognize that local knowledge is rigid without general knowledge. Then what sort of knowledge is powerful? Really, it is the team that is powerful, the fractal structure with concepts occurring in variations at multiple levels of generality. Although developing these ideas in the context of programming, we suggest that this fractal picture of the role of generality in problem solving applies equally well to most other domains (cf. Perkins & Salomon, 1989).
The research reported here was conducted at the Educational Technology Center of the Harvard Graduate School of Education, operating with suport from the Office of Educational Research and Improvement (contract #OERI 400-83-0041). Opinions expressed herein are not necessarily shared by OERI and do not represent Office policy.
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