Toward a Unified Theory of Problem Solving: Views from the Content Domains

By Mike U. Smith | Go to book overview

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).


Acknowledgements

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.


REFERENCES

Anderson, J. R. ( 1983). The architecture of cognition. Cambridge, MA: Harvard University Press.

Bereiter, C. ( 1984). "How to keep thinking skills from going the way of all frills". Educational Leadership, 42, 75-77.

Bereiter, C., & Scardamalia, M. ( 1982). "From conversation to composition: The role of instruction in a developmental process". In R. Glaser (Ed.), Advances in instructional psychology (Vol. 2, pp. 1-64). Hillsdale, NJ: Lawrence Erlbaum Associates.

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Toward a Unified Theory of Problem Solving: Views from the Content Domains
Table of contents

Table of contents

  • Title Page *
  • Contents *
  • Preface *
  • 1 - A View from Biology 1
  • Acknowledgment 17
  • References 17
  • 2 - A View from Chemistry 21
  • References 32
  • 3 - A View from Medicine 35
  • References 43
  • 4 - A View from Programming 45
  • Acknowledgements 63
  • References 63
  • 5 - A View of Mathematical Problem Solving in School 69
  • Acknowledgements 95
  • References 95
  • 6 - A View from Physics 99
  • References 113
  • 7 - A View from Trouble-Shooting 115
  • References 148
  • Author Index 155
  • Subject Index 161
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