motion and measurement nic gilbertson & funda gonulates strengthening tomorrows education in...
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Motion and Measurement
Nic Gilbertson & Funda GonulatesStrengthening Tomorrow’s Education in
Measurement (STEM) ProjectMichigan State University
Math-in-Action Conference 2012 – Grand Valley State University
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STEMWhat:
Researchanalyzing the capacity of three written elementary
curricula to support robust learning of spatial measurement (length, area, volume)
Professional Developmentwork with pre-service teachers on measurement
lesson study working with facilitators throughout Michigan who
are in turn working with teachers in their areas2STEM 2012- Math-in-Action
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STEM – Three Curricula
The three carefully chosen curricula are:Scott Foresman-
Addison Wesley Mathematics
UCSMP’s Everyday Mathematics
Saxon Math
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STEM – Our Analysis
In our analysis we are looking at every lesson, problem, and activity of teach curricula for two important aspects:Knowledge elements - Spatial measurement
knowledge (conceptual, procedural, conventional)Textual elements - The ways in which this knowledge
is expressed (statements, demonstrations, worked examples, questions, problems, games)
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Some overarching questions…• How might dynamic (as opposed to static)
ways of measuring help develop measurement concepts?
• How might measurement and motion help students better understand formulas?
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Pentagon Task
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1) Find the area
2) Draw a second pentagon with the same area
STEM 2012- Math-in-Action
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Pentagon Task
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With a partner, 1) Share your solutions2) What might students have difficulties with in
solving this problem?3) What would students need to know in order
to solve this problem?
STEM 2012- Math-in-Action
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Pentagon Task – NAEP results
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Scoring Rubric:• Incorrect (both parts a & b incorrect)• Partial (either a or b correct)• Correct (both a & b correct)• Omitted• Off Task
STEM 2012- Math-in-Action
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Pentagon Task – NAEP results
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Scoring Rubric:• Incorrect (both parts a & b incorrect)…48%• Partial (either a or b correct)…47%• Correct (both a & b correct)…2%• Omitted…2%• Off Task…(rounded to 0%)
STEM 2012- Math-in-Action
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Pentagon Task – NAEP results
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Grade 8 – 2005
Scoring Rubric:• Incorrect (both parts a & b incorrect)…48%• Partial (either a or b correct)…47%• Correct (both a & b correct)…2%• Omitted…2%• Off Task…(rounded to 0%)
STEM 2012- Math-in-Action
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Pentagon Task – NAEP results
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Some possible explanations…• Constraints limit possible solutions• No straightforward formula• Dynamic situation
STEM 2012- Math-in-Action
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Task 2 – Tables Task
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Task 2 – Tables Task
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Part 1) Using the isosceles right triangles in your group, find the area of the top of your table.
Part 2) Describe a formula (symbols, words, pictures) for how you can determine the area units any rectangular table top.
Once you are finished let one of us know…
STEM 2012- Math-in-Action
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Task 2 – Tables Task
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Part 3) Using the right triangles in your group, find the area of the top of your table.
Part 4) Describe a formula (symbols, words, pictures) for how you can determine the area for any rectangular table top.
STEM 2012- Math-in-Action
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Task 2 – Tables Task
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Task 2 – Tables Task
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What’s the area unit - squares, triangles, rectangles?Can we use base x height if the length units are different?
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Task 2 – Tables Task
17STEM 2012- Math-in-Action
What’s the area unit - squares, triangles, rectangles?Can we use base x height if the length units are different?
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Task 2 – Tables Task
18STEM 2012- Math-in-Action
What’s the area unit - squares, triangles, rectangles?Can we use base x height if the length units are different?
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Task 2 – Tables Task
19STEM 2012- Math-in-Action
What’s the area unit - squares, triangles, rectangles?Can we use base x height if the length units are different?
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Task 2 – Tables Task
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What’s the area unit - squares, triangles, rectangles?Can we use base x height if the length units are different?
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Task 2 – Tables Task
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AN ALTERNATIVE TASK…
What would this lesson have looked like had it been taught this way?
STEM 2012- Math-in-Action
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Task 2 – Tables Task
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BIG IDEAS…• Different shapes have many different measures• Defining “1 unit” is important• The area unit affects the formula because of how
the space is structured• The formula depends on the unit and attribute• Structuring space is not simple for many students• The formula is a description of a general situation,
not just a procedure to calculate something.
STEM 2012- Math-in-Action
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Some other NAEP items (Grade 8)
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Megan drew a rectangle that has an area of 24 square centimeters. Which of the following could be the dimensions of her rectangle?
• 2 cm by 12 cm• 3 cm by 9 cm• 4 cm by 20 cm• 6 cm by 6 cm• 12 cm by 12 cm
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Some other NAEP items (Grade 8)
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How many square tiles, 5 inches on a side, does it take to cover a rectangular area that is 50 inches wide and 100 inches long?
• Open Response
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Some other NAEP items (Grade 8)
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Make a drawing in the space below to show how the four triangles shown above could fit together without overlapping to make a rectangle that is not a square. Show the dimensions of the rectangle on your drawing. What is the area of this rectangle?
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Dynamic Simulations
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Some Video ResourcesCircumference of Circle http://www.rkm.com.au/ANIMATIONS/animation-pi.html
Area of Circle http://www.rkm.com.au/ANIMATIONS/animation-Circle-Area-Derivation.html Area of Circle 2 http://curvebank.calstatela.edu/circle2/circle2.htm Area of Circle 3 http://www.youtube.com/watch?v=06VSISqNmoI Surface Area of Sphere http://www.rkm.com.au/ANIMATIONS/animation-Sphere-Surface-Area-Derivation.html
STEM 2012- Math-in-Action
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Dynamic Simulations
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Some Applet Resources• STEM’s Simulations -
https://www.msu.edu/~stemproj/simulations.html
• National Library of Virtual Manipulatives http://nlvm.usu.edu/
• NCTM Illuminations – http://illuminations.nctm.org/
• Freudenthal Institute http://www.fi.uu.nl/wisweb/en/
STEM 2012- Math-in-Action
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Thank you!We want to thank the National Science
Foundation for funding this work
We want to thank you for coming!Please take a few minute to fill out our evaluation.
For more information starting you can go to: http://www.msu.edu/~stemproj
If you have any questions please e-mail us at: [email protected]
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