conceptual development in area measurement funda gonulates, lorraine males, & nic gilbertson...
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Conceptual Development in Area Measurement Funda Gonulates, Lorraine Males, & Nic Gilbertson Strengthening Tomorrows Education in Measurement (STEM) Project Michigan State University MCTM Conference 2010 Dakota High School Slide 2 Welcome Wed like to take some time for everyone to introduce themselves Name Position Grade level District/School 2STEM 2010 - MCTM Conference Slide 3 Area Take some time to think about and share your answer to the following: 3STEM 2010 - MCTM Conference What is area? What issues or difficulties do you think students might have with area measurement? Slide 4 Pentagon Task STEM 2010 - MCTM Conference4 1)Find the area 2)Draw a second pentagon with the same area Slide 5 Pentagon Task STEM 2010 - MCTM Conference5 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? Slide 6 Pentagon Task NAEP results STEM 2010 - MCTM Conference6 Scoring Rubric: Incorrect (both parts a & b incorrect) Partial (either a or b correct) Correct (both a & b correct) Omitted Off Task Slide 7 Pentagon Task NAEP results STEM 2010 - MCTM Conference7 Scoring Rubric: Incorrect (both parts a & b incorrect)48% Partial (either a or b correct)47% Correct (both a & b correct)2% Omitted2% Off Task (rounded to 0%) Slide 8 Pentagon Task NAEP results STEM 2010 - MCTM Conference8 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% Omitted2% Off Task (rounded to 0%) Slide 9 STEM Who, Where, and When Who: PI: Dr. Jack Smith Research Assistants: Dan Clark, Kuo-Liang Chang, Leslie Dietiker, Hanna Figueras, Nic Gilbertson, Funda Gonulates, 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 9STEM 2010 - MCTM Conference Strengthening Tomorrows Education in Measurement Slide 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 10STEM 2010 - MCTM Conference Slide 11 STEM Three Curricula The three carefully chosen curricula are: Scott Foresman- Addison Wesley Mathematics UCSMPs Everyday Mathematics Saxon Math 11STEM 2010 - MCTM Conference Slide 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) 12STEM 2010 - MCTM Conference Slide 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 13STEM 2010 - MCTM Conference Slide 14 STEM Area Analysis Flow of Area Topics 14STEM 2010 - MCTM Conference Grain-size perception of area the ability to exploit the structure Holistic perception of area to understand the structure of a region Array of Objects (Numbers, counting) Arrays of Tesselating Objects Rectangles Visual Judgment Cover Measure and Cover Measure w/ Grid w/out Array Structure Measure w/ Array Structure Compute LxW Std. vs Non std. Units Visual Estimation of Area Partition Analysis of area content in all curricula K-4 (Gonulates & Mosier, 2010) Slide 15 Area Lesson Analysis: SFAW Grade 3, P.468A 15STEM 2010 - MCTM Conference What knowledge is required What is in curricula Slide 16 Area Lesson Analysis: SFAW Grade 3, P.468 16STEM 2010 - MCTM Conference What knowledge is required What is in curricula Slide 17 STEM 2010 - MCTM Conference17 SFAW GR3 Area Lesson Analysis Objectives of the Lesson P. 468AP. 468 Conceptual Knowledge Procedural Knowledge Connections Reflection Slide 18 STEM 2010 - MCTM Conference18 SFAW GR3 Area Lesson Analysis Objectives of the Lesson Estimate or find the areas of figures in square units. P. 468AP. 468 Conceptual Knowledge Area as a measurable quantity (Definition and meaning of area measure) Order/Equity Unit Measure Compensation Area as a measurable quantity (Definition and meaning of area measure) Procedural Knowledge Measure area (G, RC) Draw a region Measure area (G, covering, counting, grid) Visual estimation Read an area Draw a region Connections Reflection Slide 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 http://www.msu.edu/~stemproj If you have any questions please e-mail us at: email@example.com firstname.lastname@example.org STEM 2010 - MCTM Conference19