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 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 2
STEM Three Curricula The three carefully chosen curricula are: Scott Foresman- Addison Wesley Mathematics UCSMP s Everyday Mathematics Saxon Math 3
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) 4
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? 5
Pentagon Task 1) Find the area 2) Draw a second pentagon with the same area 6
Pentagon Task 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? 7
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 8
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%) 9
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%) 10
Pentagon Task NAEP results Some possible explanations Constraints limit possible solutions No straightforward formula Dynamic situation 11
Task 2 Tables Task 12
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 13
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. 14
Task 2 Tables Task 15
Task 2 Tables Task What s the area unit - squares, triangles, rectangles? Can we use base x height if the length units are different? 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? 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? 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? 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? 20
Task 2 Tables Task AN ALTERNATIVE TASK What would this lesson have looked like had it been taught this way? 21
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. 22
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 23
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 24
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? 25
Dynamic Simulations 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 26
Dynamic Simulations 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/ 27
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 28