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Motion and Measurement

Motion and Measurement. Nic Gilbertson & Funda Gonulates Strengthening Tomorrow’s Education in Measurement (STEM) Project Michigan State University. Math-in-Action Conference 2012 – Grand Valley State University . STEM. What: Research

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Motion and Measurement

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  1. Motion and Measurement Nic Gilbertson & FundaGonulates Strengthening Tomorrow’s Education in Measurement (STEM) Project Michigan State University Math-in-Action Conference 2012 – Grand Valley State University

  2. 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 STEM 2012- Math-in-Action

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

  4. 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) STEM 2012- Math-in-Action

  5. 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? STEM 2012- Math-in-Action

  6. Pentagon Task • Find the area • Draw a second pentagon with the same area STEM 2012- Math-in-Action

  7. Pentagon Task With a partner, • Share your solutions • What might students have difficulties with in solving this problem? • What would students need to know in order to solve this problem? STEM 2012- Math-in-Action

  8. Pentagon Task – NAEP results 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

  9. Pentagon Task – NAEP results 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

  10. Pentagon Task – NAEP results 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

  11. Pentagon Task – NAEP results Some possible explanations… • Constraints limit possible solutions • No straightforward formula • Dynamic situation STEM 2012- Math-in-Action

  12. Task 2 – Tables Task STEM 2012- Math-in-Action

  13. Task 2 – Tables Task 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

  14. Task 2 – Tables Task 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

  15. Task 2 – Tables Task STEM 2012- Math-in-Action

  16. Task 2 – Tables Task What’s the area unit - squares, triangles, rectangles? Can we use base x height if the length units are different? STEM 2012- Math-in-Action

  17. Task 2 – Tables Task What’s the area unit - squares, triangles, rectangles? Can we use base x height if the length units are different? STEM 2012- Math-in-Action

  18. Task 2 – Tables Task What’s the area unit - squares, triangles, rectangles? Can we use base x height if the length units are different? STEM 2012- Math-in-Action

  19. Task 2 – Tables Task What’s the area unit - squares, triangles, rectangles? Can we use base x height if the length units are different? STEM 2012- Math-in-Action

  20. Task 2 – Tables Task What’s the area unit - squares, triangles, rectangles? Can we use base x height if the length units are different? STEM 2012- Math-in-Action

  21. Task 2 – Tables Task AN ALTERNATIVE TASK… What would this lesson have looked like had it been taught this way? STEM 2012- Math-in-Action

  22. Task 2 – Tables Task 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

  23. 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 STEM 2012- Math-in-Action

  24. Some other NAEP items (Grade 8) 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 STEM 2012- Math-in-Action

  25. Some other NAEP items (Grade 8) • 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? STEM 2012- Math-in-Action

  26. Dynamic Simulations Some Video Resources Circumference of Circle http://www.rkm.com.au/ANIMATIONS/animation-pi.htmlArea of Circle http://www.rkm.com.au/ANIMATIONS/animation-Circle-Area-Derivation.htmlArea of Circle 2 http://curvebank.calstatela.edu/circle2/circle2.htmArea of Circle 3 http://www.youtube.com/watch?v=06VSISqNmoISurface Area of Sphere http://www.rkm.com.au/ANIMATIONS/animation-Sphere-Surface-Area-Derivation.html STEM 2012- Math-in-Action

  27. Dynamic Simulations Some Applet Resources • STEM’s Simulations - https://www.msu.edu/~stemproj/simulations.html • National Library of Virtual Manipulativeshttp://nlvm.usu.edu/ • NCTM Illuminations – http://illuminations.nctm.org/ • Freudenthal Institute http://www.fi.uu.nl/wisweb/en/ STEM 2012- Math-in-Action

  28. 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: stemproj@msu.edu STEM 2012- Math-in-Action

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