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Motion and Measurement Nic Gilbertson & Funda Gonulates Strengthening Tomorrows Education in Measurement (STEM) Project Michigan State University Math-in-Action Conference 2012 – Grand Valley State University

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STEM What: Research analyzing the capacity of three written elementary curricula to support robust learning of spatial measurement (length, area, volume) Professional Development work with pre-service teachers on measurement lesson study working with facilitators throughout Michigan who are in turn working with teachers in their areas 2STEM 2012- Math-in-Action

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STEM – Three Curricula The three carefully chosen curricula are: Scott Foresman- Addison Wesley Mathematics UCSMPs Everyday Mathematics Saxon Math 3STEM 2012- Math-in-Action

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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) 4STEM 2012- Math-in-Action

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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? 5STEM 2012- Math-in-Action

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Pentagon Task 6 1)Find the area 2)Draw a second pentagon with the same area STEM 2012- Math-in-Action

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Pentagon Task 7 With a partner, 1)Share your solutions 2)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 8 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 9 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 10 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 11 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 12STEM 2012- Math-in-Action

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Task 2 – Tables Task 13 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 14 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 15STEM 2012- Math-in-Action

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Task 2 – Tables Task 16STEM 2012- Math-in-Action Whats 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 Whats 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 Whats 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 Whats 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 20STEM 2012- Math-in-Action Whats 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 21 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 22 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) 23STEM 2012- Math-in-Action 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) 24STEM 2012- Math-in-Action 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) 25STEM 2012- Math-in-Action 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 26 Some Video Resources Circumference 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 STEM 2012- Math-in-Action

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Dynamic Simulations 27 Some Applet Resources STEMs Simulations - https://www.msu.edu/~stemproj/simulations.html https://www.msu.edu/~stemproj/simulations.html National Library of Virtual Manipulatives http://nlvm.usu.edu/ http://nlvm.usu.edu/ NCTM Illuminations – http://illuminations.nctm.org/http://illuminations.nctm.org/ Freudenthal Institute http://www.fi.uu.nl/wisweb/en/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 http://www.msu.edu/~stemproj If you have any questions please e-mail us at: stemproj@msu.edu stemproj@msu.edu 28STEM 2012- Math-in-Action

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