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

By Mike U. Smith | Go to book overview

but it does not constitute the major goal of the enterprise. Like problems about quantities in ordinary activity, problems in mathematics arise in a larger context that makes them meaningful. We could refocus our research effort toward problem solving in broader contexts, including the study of abilities of individuals to reason about quantities in situations they can understand. I have presented some preliminary findings from some research that I hope will contribute to that goal.


Acknowledgements

This research was supported by the National Science Foundation, grant BNS-8718918. This paper is based in part on an invited plenary presentation at the North American Chapter of the International Group for the Psychology of Mathematics Education, given at Northern Illinois University in 1988 and published in the proceedings of that meeting.


REFERENCES

Alibert, D.( 1988). Towards new customs in the classroom. For the Learning of Mathematics, 8, 31-35, 43.

Anderson, J. R.( 1982). Acquisition of cognitive skill. Psychological Review, 89, 396-406.

Anderson, J. R. ( 1988). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds.), Complex information processing (pp. 343-370). Hillsdale, NJ: Lawrence Erlbaum Associates.

Anderson, J. R., Boyle, C. F., & Yost, G. ( 1985). The geometry tutor. In A. Joshi (Ed.), Proceedings of the Ninth International Joint Conference on Artificial Intelligence (p. 1-7). Los Altos, CA: Morgan Kaufmann.

Belenky, M. F., Clinchy, B. M., Goldberger, N. R., & Tarule, J. M. ( 1986). Women's ways of knowing. New York: Basic.

Briars, D. J., & Larkin, J. H. ( 1984). An integrated model of skill in solving elementary word problems. Cognion and Instruction, 1, 245-296.

Brown, J. S. (in press). Toward a new epistemology for learning. In C. Frasson & J. Gauthiar (Eds.), Intelligent tutoring systems at the crossroad of AI and education. Norwood, NJ: Ablex.

Brown, J. S., & Burton, R. R. ( 1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2, 155-192.

Brown, J. S., & VanLehn, K. ( 1980). Repair theory: A generative theory of bugs in procedural skills. Cognitive Science, 4, 379-426.

Bundy, A. ( 1975). Analyzing mathematical proofs (or reading between the lines). In P. Winston (Ed.), Proceedings of the 4th International Joint Conference on Artificial Intelligence. Cambridge, MA: Artificial Intelligence Laboratory.

Burton, R. R. ( 1982). Diagnosing bugs in a simple procedural skill. In D. Sleeman & J. S. Brown (Eds.), Intelligent tutoring systems (pp. 157-184). New York: Academic.

Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C., & Loef, M. (in press). Using knowledge of children's mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal.

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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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