motion and measurement nic gilbertson & funda gonulates strengthening tomorrows education in...

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

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

STEM – Three Curricula

The three carefully chosen curricula are:Scott Foresman-

Addison Wesley Mathematics

UCSMP’s Everyday Mathematics

Saxon Math

3STEM 2012- Math-in-Action

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)


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?


Pentagon Task

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1) Find the area

2) Draw a second pentagon with the same area

STEM 2012- Math-in-Action

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?


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



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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%)



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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%)



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Some possible explanations…• Constraints limit possible solutions• No straightforward formula• Dynamic situation


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…



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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.




What’s the area unit - squares, triangles, rectangles?Can we use base x height if the length units are different?


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AN ALTERNATIVE TASK…

What would this lesson have looked like had it been taught this way?



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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.


Some other NAEP items (Grade 8)


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



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



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?

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


http://www.rkm.com.au/ANIMATIONS/animation-pi.html

http://www.rkm.com.au/ANIMATIONS/animation-Circle-Area-Derivation.html

http://curvebank.calstatela.edu/circle2/circle2.htm

http://www.youtube.com/watch?v=06VSISqNmoI

http://www.rkm.com.au/ANIMATIONS/animation-Sphere-Surface-Area-Derivation.html

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/


https://www.msu.edu/~stemproj/simulations.html

http://nlvm.usu.edu/

http://illuminations.nctm.org/

http://www.fi.uu.nl/wisweb/en/

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]


http://www.msu.edu/~stemproj

mailto:[email protected]

motion and measurement nic gilbertson & funda gonulates strengthening tomorrows education in...

Documents

task stem

action slide

tables task

area stem

alternative task

action whats

pentagon task naep results

action conference