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Conceptual Development in Area Measurement

Conceptual Development in Area Measurement. Funda Gonulates, Lorraine Males, & Nic Gilbertson Strengthening Tomorrow’s Education in Measurement (STEM) Project Michigan State University. MCTM Conference 2010 Dakota High School. Welcome.

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Conceptual Development in Area Measurement

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  1. Conceptual Development in Area Measurement Funda Gonulates, Lorraine Males, & Nic Gilbertson Strengthening Tomorrow’s Education in Measurement (STEM) Project Michigan State University MCTM Conference 2010 Dakota High School

  2. Welcome We’d like to take some time for everyone to introduce themselves • Name • Position • Grade level • District/School STEM 2010 - MCTM Conference

  3. Area Take some time to think about and share your answer to the following: • What is area? • What issues or difficulties do you think students might have with area measurement? STEM 2010 - MCTM Conference

  4. Pentagon Task • Find the area • Draw a second pentagon with the same area STEM 2010 - MCTM Conference

  5. 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 2010 - MCTM Conference

  6. 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 2010 - MCTM Conference

  7. 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 2010 - MCTM Conference

  8. 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 2010 - MCTM Conference

  9. STEM – Who, Where, and When Strengthening Tomorrow’s Education in Measurement Who: • PI: Dr. Jack Smith • Research Assistants: Dan Clark, Kuo-Liang Chang, Leslie Dietiker, Hanna Figueras, Nic Gilbertson, FundaGonulates, Pat Greeley, Jia He, Kosze Lee, Lorraine Males, Aaron Mosier, Matt Pahl, Gulcin Tan Sisman, Shannon Sweeny, Alexandria Theakston When: • 2007 – present Where: • Michigan State University • Work beginning in various districts throughout Michigan including Eastern UP, Grand Rapids, Jackson, Kalamazoo, & Oakland STEM 2010 - MCTM Conference

  10. STEM – What What: Research • analyzing the capacity of three written elementary curricula to support robust learning of spatial measurement (length, area, volume) Professional Development • worked with pre-service teachers during their year-long internship on measurement lesson study • working with facilitators throughout Michigan who are in turn working with teachers in their areas STEM 2010 - MCTM Conference

  11. STEM – Three Curricula The three carefully chosen curricula are: • Scott Foresman-Addison Wesley Mathematics • UCSMP’s Everyday Mathematics • Saxon Math STEM 2010 - MCTM Conference

  12. 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 2010 - MCTM Conference

  13. STEM – Area Core Principles • Area as a measurable quantity • Conservation under partitioning. •  Conservation under motion  • Identical Units • Unit iteration  • Transitivity • Spatial structure of rectangular arrays • Multiplicative composition from lengths STEM 2010 - MCTM Conference

  14. “Holistic perception of area” to understand the structure of a region Visual Judgment Std. vs Non std. Units Partition Cover Visual Estimation of Area Measure and Cover “Grain-size perception of area” the ability to exploit the structure Array of Objects (Numbers, counting) Measure w/ Grid w/out Array Structure Measure w/ Array Structure Arrays of Tesselating Objects Compute LxW Rectangles STEM – Area AnalysisFlow of Area Topics Analysis of area content in all curricula K-4 (Gonulates & Mosier, 2010) STEM 2010 - MCTM Conference

  15. Area Lesson Analysis: SFAW Grade 3, P.468A STEM 2010 - MCTM Conference

  16. Area Lesson Analysis: SFAW Grade 3, P.468 STEM 2010 - MCTM Conference

  17. STEM 2010 - MCTM Conference

  18. STEM 2010 - MCTM Conference

  19. 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 this fall you can go to: http://www.msu.edu/~stemproj If you have any questions please e-mail us at: stemproj@msu.edu STEM 2010 - MCTM Conference

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