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![Page 1: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/1.jpg)
Reconceptualizing MathematicsCourseware for Elementary and Middle
School Teachers
AMTE Pre-Conference
January 22, 2004
Karen Payne
![Page 2: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/2.jpg)
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
![Page 3: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/3.jpg)
Overview of the Materials
![Page 4: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/4.jpg)
Overview of the Materials
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
![Page 5: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/5.jpg)
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)
![Page 6: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/6.jpg)
Examples from Number & Number Sense Module
“How would you estimate here? – p. 56”
#6 789 x 0.52
#7 148.52+49.351
![Page 7: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/7.jpg)
![Page 8: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/8.jpg)
Example from Shapes & Measurement
P. 7 #5
![Page 9: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/9.jpg)
Example from Chance: Conditional Probability
![Page 10: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/10.jpg)
Example from Chance: Conditional Probability
![Page 11: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/11.jpg)
Example from Chance: Conditional Probability
P(Virus|Pos)=49/248=20%
![Page 12: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/12.jpg)
Example from Data
-Interpreting margins of error and confidence intervals.
![Page 13: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/13.jpg)
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.
![Page 14: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/14.jpg)
Example From Quantitative Reasoning Module:
![Page 15: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/15.jpg)
Quantitative Reasoning Module
Begins with additive reasoning Later moves to multiplicative reasoning Some tasks provoke lengthy discussion
![Page 16: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/16.jpg)
Example from Quantitative Reasoning Module
![Page 17: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/17.jpg)
Examples from Describing Change
![Page 18: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/18.jpg)
Examples from Describing Change
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.”
![Page 19: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/19.jpg)
Examples from Describing Change
![Page 20: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/20.jpg)
How do these differ from other materials?
![Page 21: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/21.jpg)
How do these differ from other materials?
Materials were developed by researchers CD/Module format allows for flexible
sequencing Inquiry based exercises where mathematical
ideas are developed Quantitative Reasoning
![Page 22: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/22.jpg)
Observations on use with Pre- and In-service Teachers
![Page 23: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/23.jpg)
Observations on use with Pre- and In-service Teachers
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
![Page 24: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/24.jpg)
Where’s the Algebra?
![Page 25: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/25.jpg)
Sample problems – “Where’s the Algebra?” (p. 28 Shapes notes)
![Page 26: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/26.jpg)
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
![Page 27: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/27.jpg)
From the “Describing Change” Module:
Connections betweens graphs and tables are always in context
Rate of change deeply developed
![Page 28: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/28.jpg)
From the “Describing Change” Module:
![Page 29: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/29.jpg)
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
![Page 30: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/30.jpg)
The Role of Technology
![Page 31: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/31.jpg)
Technology to include
Fathom software Motion detectors Microworld Examples Video Cases
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Information on obtaining Modules
Contact: Judith Leggett [email protected]
Cost:$50/set of 6 CD’s (includes shipping) (plus tax if purchasing from within CA)
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Questions?
![Page 34: Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne.](https://reader036.fdocuments.in/reader036/viewer/2022062407/56649d415503460f94a1bb3d/html5/thumbnails/34.jpg)
Contact Information
Karen Payne [email protected]
Judy Sowder [email protected]
Web resources:http://pdc.sdsu.edu
more info on Professional Development Collaborativehttp://www.sci.sdsu.edu/CRMSE/IMAP/main.html
more info on IMAP video clips