reconceptualizing mathematics courseware for elementary and middle school teachers amte...
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Reconceptualizing MathematicsCourseware for Elementary and Middle
School Teachers
AMTE Pre-Conference
January 22, 2004
Karen Payne
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
Overview of the Materials
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
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)
Examples from Number & Number Sense Module
“How would you estimate here? – p. 56”
#6 789 x 0.52
#7 148.52+49.351
Example from Shapes & Measurement
P. 7 #5
Example from Chance: Conditional Probability
Example from Chance: Conditional Probability
Example from Chance: Conditional Probability
P(Virus|Pos)=49/248=20%
Example from Data
-Interpreting margins of error and confidence intervals.
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.
Example From Quantitative Reasoning Module:
Quantitative Reasoning Module
Begins with additive reasoning Later moves to multiplicative reasoning Some tasks provoke lengthy discussion
Example from Quantitative Reasoning Module
Examples from Describing Change
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.”
Examples from Describing Change
How do these differ from other materials?
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
Observations on use with Pre- and In-service Teachers
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
Where’s the Algebra?
Sample problems – “Where’s the Algebra?” (p. 28 Shapes notes)
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
From the “Describing Change” Module:
Connections betweens graphs and tables are always in context
Rate of change deeply developed
From the “Describing Change” Module:
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
The Role of Technology
Technology to include
Fathom software Motion detectors Microworld Examples Video Cases
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)
Questions?
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