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 jleggett@sciences.sdsu.edu

Cost:$50/set of 6 CD’s (includes shipping) (plus tax if purchasing from within CA)

Questions?

Contact Information

Karen Payne kpayne@sciences.sdsu.edu

Judy Sowder jsowder@sciences.sdsu.edu

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