Strategies to Help Your Measurement Instruction Measure Up Jack Smith & Lorraine Males STEM Project,...
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Transcript of Strategies to Help Your Measurement Instruction Measure Up Jack Smith & Lorraine Males STEM Project,...
Strategies to Help Your Measurement Instruction Measure Up
Jack Smith & Lorraine MalesSTEM Project, College of Education, Michigan State
Math In Action Conference
February 25, 2009
Introduction & Overview
• Welcome!• Your presenters & you• This session: A problem & one good idea• Math focus: Units of length measure• Teaching focus: Doing more with assigned
textbook materials• Disclaimer: One hour is not enough!
2
Into the Content
The Toothpick Problem[NAEP, Grade 4, 2003, Open response]
“What is the length of the toothpick?”
3
Toothpick Performance Data[Grade 4, large national sample]
Response % Responding
2.5 inches (correct) 20
10.5 inches 14
3.5 inches 23
Other 42
Omitted 24
Lessons from Toothpick
• We are not doing so well nationally• Too many kids don’t understand length
measurement, rulers, or both• Some errors are sensible; some remain
mysterious• Not obvious what we are doing wrong• => Not obvious what we should change
5
A Bit About Our Project
• Premise: Part of the problem may be our curriculum materials
• Carefully examine 3 elementary programs– Everyday Mathematics– Scott-Foresman/Addison-Wesley Mathematics– Saxon Mathematics
• Look for every instance of measurement content• Code each as an “opportunity” to learn some bit of
conceptual or procedural knowledge• Length analysis is complete for K through Grade 3
6
A Bit More(attention to Conceptual Knowledge)
• Lots of different conceptual and procedural elements
• Focus on two conceptual elements– Unit-Measure Compensation– Unit Iteration
• Both important; Unit Iteration appears less frequently than we would like
7
Unit-Measure Compensation
Larger units of length produce smaller measures of length; smaller units of length produce
larger measures.
• All curriculum mention this idea with some frequency & in different grades
• Could do more but not the heart of the problem
8
Unit Iteration
Measures of length are produced by iterating a length unit (repeatedly adjoining) from one end of an object, segment, or distance to the other and then finding the number of iterations (e.g., by counting). Iterated units may not overlap or leave gaps.
• Insufficient attention in all 3 curricula• N = 19 instances from K to Grade 3!!• Many are partial statements
9
Unit Iteration (idea by idea)
Measures of length are produced by iterating a length unit (repeatedly adjoining)
10
Unit Iteration (idea by idea)
Measures of length are produced by iterating a length unit (repeatedly adjoining) from
one end of an object, segment, or distance to the other
11
Unit Iteration (idea by idea)
Measures of length are produced by iterating a length unit (repeatedly adjoining) from one end of an object, segment, or distance to the other and then finding the number of iterations (e.g., by counting).
12
Unit Iteration (idea by idea)
Measures of length are produced by iterating a length unit (repeatedly adjoining) from one end of an object, segment, or distance to the other and then finding the number of iterations (e.g., by counting). Iterated units may not overlap or leave gaps.
• How does this relate to Toothpick?
13
Some Work with Activities in Existing Curricula
• Case 1: EM, grade 2• Case 2: SFAW, grade 1• May not be your curricula, but• We hope you will see how to adapt our
main points to your situation
14
Some Issues in the Activities
• Tiling is not the same as Iterating• Both depend on Partitioning (conservation)• Tiling and Iterating are closely related, but• Do young children see that?• Shouldn’t we do more to help them?• Tiling and Iterating are “built into” Rulers • Shouldn’t we help them there too?
15
Seeing Tiling & Iterating
• Besides using bodies, what else?• We developed some animations
– Measuring a pencil– Non-standard unit (a rectangular tile)
• Seek your reactions & judgments– Where you see differences– How your kids would react (same/different)
• Differences that arise could lead to good discussion and learning
16
Tiling
Sufficient number of tiles - numbered17
Iterating I
Insufficient number of tiles – numbered with trace 18
Iterating II
Insufficient number of tiles – not numbered with tick marks 19
Iterating III
Insufficient number of tiles – not numbered with tick marks and alignment marks 20
Closing• Thank you for coming & engaging• You are essential for our work to have
meaning & impact• Engage with us
– Feedback form– Indicate an interest in measurement– Are you using one of our target curricula?– Look for us around the state, at NCTM, and in
NCTM’s journals– Jack Smith ([email protected])
Lorraine Males ([email protected]) 21