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

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  • Slide 1
  • Reconceptualizing Mathematics Courseware for Elementary and Middle School Teachers AMTE Pre-Conference January 22, 2004 Karen Payne
  • Slide 2
  • 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
  • Slide 3
  • Overview of the Materials
  • Slide 4
  • Five CDs, Six Modules Number & Number Sense Shapes & Measurement Chance & Data (two modules) Quantitative Reasoning Describing Change Video Clips from Integrating Math and Pedagogy
  • Slide 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 materialse.g. nets for 3-d shapes (very end of notes)
  • Slide 6
  • Examples from Number & Number Sense Module How would you estimate here? p. 56 #6 789 x 0.52 #7 148.52+49.351
  • Slide 7
  • Slide 8
  • Example from Shapes & Measurement P. 7 #5
  • Slide 9
  • Example from Chance: Conditional Probability
  • Slide 10
  • Slide 11
  • P(Virus|Pos)=49/248=20%
  • Slide 12
  • Example from Data -Interpreting margins of error and confidence intervals.
  • Slide 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.
  • Slide 14
  • Example From Quantitative Reasoning Module:
  • Slide 15
  • Quantitative Reasoning Module Begins with additive reasoning Later moves to multiplicative reasoning Some tasks provoke lengthy discussion
  • Slide 16
  • Example from Quantitative Reasoning Module
  • Slide 17
  • Examples from Describing Change
  • Slide 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.
  • Slide 19
  • Examples from Describing Change
  • Slide 20
  • How do these differ from other materials?
  • Slide 21
  • Materials were developed by researchers CD/Module format allows for flexible sequencing Inquiry based exercises where mathematical ideas are developed Quantitative Reasoning
  • Slide 22
  • Observations on use with Pre- and In-service Teachers
  • Slide 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
  • Slide 24
  • Wheres the Algebra?
  • Slide 25
  • Sample problems Wheres the Algebra? (p. 28 Shapes notes)
  • Slide 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
  • Slide 27
  • From the Describing Change Module: Connections betweens graphs and tables are always in context Rate of change deeply developed
  • Slide 28
  • From the Describing Change Module:
  • Slide 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
  • Slide 30
  • The Role of Technology
  • Slide 31
  • Technology to include Fathom software Motion detectors Microworld Examples Video Cases
  • Slide 32
  • Information on obtaining Modules Contact: Judith Leggett jleggett@sciences.sdsu.edu jleggett@sciences.sdsu.edu Cost:$50/set of 6 CDs (includes shipping) (plus tax if purchasing from within CA)
  • Slide 33
  • Questions?
  • Slide 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

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