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Discussant Remarks

Discussant Remarks. Jon R. Star Michigan State University. Reframe the problem. Push a bit on what you are calling “error” and “generalization” Challenge: Are you over-generalizing? Is focus on “errors” on target?. New situations. Known strategies or reasoning.

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Discussant Remarks

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  1. Discussant Remarks Jon R. Star Michigan State University NCTM Research PreSession

  2. Reframe the problem... • Push a bit on what you are calling “error” and “generalization” • Challenge: • Are you over-generalizing? • Is focus on “errors” on target? NCTM Research PreSession

  3. New situations Known strategies or reasoning NCTM Research PreSession

  4. “Errors” of “generalization” • There are many ways for this process to go awry NCTM Research PreSession

  5. Appropriate generalization? New situations Known strategies or reasoning NCTM Research PreSession

  6. Over- generalization? New situations Known strategies or reasoning X X NCTM Research PreSession

  7. Absence of generalization? New situations Known strategies or reasoning NCTM Research PreSession

  8. Appropriate generalization? New situations Known strategies or reasoning NCTM Research PreSession

  9. How togeneralize? New situations Known strategies or reasoning ? NCTM Research PreSession

  10. “Errors”? • Useful for researchers and teachers to understand how students decide to apply known strategies and reasoning to new situations • What features of the source are useful in deciding to how to apply strategies or reasoning in new situations? NCTM Research PreSession

  11. Analogical reasoning • Retrieve strategy from memory • Map elements of new problem to elements of known strategy • Adapt known strategy for use in new problem Gick & Holyoak, 1980; Novick & Holyoak, 1991; Novick, 1988, 1995; Reed, 1989; Ross, 1987; Gentner, 1983 NCTM Research PreSession

  12. Retrieve New situation NCTM Research PreSession

  13. Map Known strategies or reasoning New situation BlueRoundOvalIsosceles Triangle BlueRoundMedium-sizedCircleNo other shapes NCTM Research PreSession

  14. Adapt Known strategies or reasoning New situation NCTM Research PreSession

  15. Challenges... • Retrieve: • Hard • Map: • Harder • Adapt: • Hardest NCTM Research PreSession

  16. Thanks! Jon R. Star jonstar@msu.edu Michigan State University NCTM Research PreSession

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