1. Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne

2. Outline of Talk Overview of the Materials How do these differ from other materials? Observations on use with pre- and in-service teachers. Where’s the Algebra? The Role of Technology Questions and Answers

3. Overview of the Materials

4. Five CD’s, Six Modules – Number & Number Sense – Shapes & Measurement – Chance & Data (two modules) – Quantitative Reasoning – Describing Change Video Clips from Integrating Math and Pedagogy

5. Materials for each module: Student Version – Blank margins Instructor Version – Consider p. 31 “2.2 Organizing Shapes” Instructor Notes – “Bubble Note #9” – refer to back of notes (p. 14) – Margin note p. 31 and 32 Auxiliary Materials – Sample test items – Other materials…e.g. nets for 3-d shapes (very end of notes)

6. Examples from Number & Number Sense Module “How would you estimate here? – p. 56” #6 789 x 0.52 #7 148.52+49.351

8. Example from Shapes & Measurement P. 7 #5

9. Example from Chance: Conditional Probability

11. P(Virus|Pos)=49/248=20%

12. Example from Data -Interpreting margins of error and confidence intervals.

13. Survey Methods Results are based on telephone interviews with 381 speech watchers, aged 18 and older, conducted Jan. 20, 2004. For results based on the total sample of speech watchers, one can say with 95% confidence that the margin of sampling error is ±5 percentage points.

14. Example From Quantitative Reasoning Module:

15. Quantitative Reasoning Module Begins with additive reasoning Later moves to multiplicative reasoning Some tasks provoke lengthy discussion

16. Example from Quantitative Reasoning Module

17. Examples from Describing Change

18. Student 1: “First I started walking up a hill. Then the hill flattened out. Then there was another, steeper hill that I walked up.” Student 2: “I rode my bike down a street. Then I turned right and rode for awhile. Then I turned left and rode a long way.”

19. Examples from Describing Change

20. How do these differ from other materials?

21. Materials were developed by researchers CD/Module format allows for flexible sequencing Inquiry based exercises where mathematical ideas are developed Quantitative Reasoning

22. Observations on use with Pre- and In-service Teachers

23. Pre-Service Teachers “Just the facts please” Dissonance due to unfamiliarity of… – Conversation – Concepts – Current curricula In-service Teachers Think of it as Professional Development, to some extent Continuously searching for classroom connections

24. Where’s the Algebra?

25. Sample problems – “Where’s the Algebra?” (p. 28 Shapes notes)

26. In the Quantitative Reasoning Module Keeping track of the quantity, rather than #’s or symbols representing the quantity Keeping track of HOW quantities are related

27. From the “Describing Change” Module: Connections betweens graphs and tables are always in context Rate of change deeply developed

28. From the “Describing Change” Module:

29. Observations on use with Middle School Teachers Supporting generalization – recording 4, 4+3, 4+3+3, 4+3+3+3, to see 4+3(n-1) rather than 4, 7, 10, 13 etc. – Connections to algebra: Simplest terms for fractions, writing as product of factors rather than dividing out common term, connection to algebra

30. The Role of Technology

31. Technology to include Fathom software Motion detectors Microworld Examples Video Cases

32. Information on obtaining Modules Contact: Judith Leggett jleggett@sciences.sdsu.edu jleggett@sciences.sdsu.edu Cost:$50/set of 6 CD’s (includes shipping) (plus tax if purchasing from within CA)

33. Questions?

34. Contact Information Karen Payne kpayne@sciences.sdsu.edukpayne@sciences.sdsu.edu Judy Sowder jsowder@sciences.sdsu.edujsowder@sciences.sdsu.edu Web resources: http://pdc.sdsu.edu more info on Professional Development Collaborative http://www.sci.sdsu.edu/CRMSE/IMAP/main.html more info on IMAP video clips