Reconceptualizing Mathematics Courseware 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. Wheres the Algebra? The Role of Technology Questions and Answers
Overview of the Materials
Five CDs, 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 materialse.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 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
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?
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
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
Wheres the Algebra?
Sample problems Wheres 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@example.com firstname.lastname@example.org Cost:$50/set of 6 CDs (includes shipping) (plus tax if purchasing from within CA)
Contact Information Karen Payne email@example.com@sciences.sdsu.edu Judy Sowder firstname.lastname@example.org@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