1. Tues March 25, 2006NCTM Research PreSession1 Discussant Remarks Jon R. Star Michigan State University

2. Tues March 25, 2006NCTM Research PreSession2 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?

3. Tues March 25, 2006NCTM Research PreSession3 Known strategies or reasoning New situations

4. Tues March 25, 2006NCTM Research PreSession4 “Errors” of “generalization” There are many ways for this process to go awry

5. Tues March 25, 2006NCTM Research PreSession5 Known strategies or reasoning New situations Appropriate generalization?

6. Tues March 25, 2006NCTM Research PreSession6 Known strategies or reasoning New situations Over- generalization?

7. Tues March 25, 2006NCTM Research PreSession7 Known strategies or reasoning New situations Absence of generalization?

8. Tues March 25, 2006NCTM Research PreSession8 Known strategies or reasoning New situations Appropriate generalization?

9. Tues March 25, 2006NCTM Research PreSession9 Known strategies or reasoning New situations How to generalize? ?

10. Tues March 25, 2006NCTM Research PreSession10 “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?

11. Tues March 25, 2006NCTM Research PreSession11 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

12. Tues March 25, 2006NCTM Research PreSession12 Retrieve New situation

13. Tues March 25, 2006NCTM Research PreSession13 Map Blue Round Medium-sized Circle No other shapes New situation Known strategies or reasoning Blue Round Oval Isosceles Triangle

14. Tues March 25, 2006NCTM Research PreSession14 Adapt New situation Known strategies or reasoning

15. Tues March 25, 2006NCTM Research PreSession15 Challenges... Retrieve: –Hard Map: –Harder Adapt: –Hardest

16. Tues March 25, 2006NCTM Research PreSession16 Thanks! Jon R. Star jonstar@msu.edu Michigan State University