conceptual development in area measurement funda gonulates, lorraine males, & nic gilbertson...
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Conceptual Development in Area MeasurementFunda Gonulates, Lorraine Males, & Nic Gilbertson
Strengthening Tomorrow’s Education in Measurement (STEM) Project
Michigan State University
MCTM Conference 2010 Dakota High School
WelcomeWe’d like to take some time for everyone to introduce themselvesNamePositionGrade levelDistrict/School
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AreaTake some time to think about and share your answer to the following:
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What is area?What issues or difficulties
do you think students might have with area measurement?
Pentagon Task
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1) Find the area
2) Draw a second pentagon with the same area
Pentagon Task
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With a partner, 1) Share your solutions2) What might students have difficulties with in
solving this problem?3) What would students need to know in order
to solve this problem?
Pentagon Task – NAEP results
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Scoring Rubric:• Incorrect (both parts a & b incorrect)• Partial (either a or b correct)• Correct (both a & b correct)• Omitted• Off Task
Pentagon Task – NAEP results
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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%)
Pentagon Task – NAEP results
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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 – 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 UniversityWork beginning in various districts throughout Michigan including
Eastern UP, Grand Rapids, Jackson, Kalamazoo, & Oakland9STEM 2010 - MCTM Conference
Strengthening Tomorrow’s Education in Measurement
STEM – WhatWhat:
Researchanalyzing the capacity of three written elementary
curricula to support robust learning of spatial measurement (length, area, volume)
Professional Developmentworked 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 areas10STEM 2010 - MCTM Conference
STEM – Three Curricula
The three carefully chosen curricula are:Scott Foresman-
Addison Wesley Mathematics
UCSMP’s Everyday Mathematics
Saxon Math
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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)
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STEM – Area Core Principles Area as a measurable quantityConservation under partitioning. Conservation under motion Identical UnitsUnit iteration TransitivitySpatial structure of rectangular arraysMultiplicative composition from lengths
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STEM – Area AnalysisFlow of Area Topics
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• “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)
Area Lesson Analysis: SFAW Grade 3, P.468A
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Area Lesson Analysis: SFAW Grade 3, P.468
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SFAW GR3 Area Lesson Analysis
Objectives of the Lesson
P. 468A P. 468Conceptual Knowledge
Procedural Knowledge
Connections
Reflection
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SFAW GR3 Area Lesson Analysis
Objectives of the Lesson Estimate or find the areas of figures in square units.
P. 468A P. 468Conceptual 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
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: [email protected]
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