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Four Corners is Better than Four Squares: Assessment Connections Dr. Alan Zollman Northern Illinois University.

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  1. Four Corners is Better than Four Squares: Assessment ConnectionsDr. Alan ZollmanNorthern Illinois University Successfully adapting the Graphic Organizer "Four Squares" writing method to improve students’ extended responses in mathematical knowledge, strategy, and explanation in problem solving. Friday, April 28, 2006 9:30 am National Council of Teachers of Mathematics Annual Meeting, America's Center 240 St. Louis, MO

  2. question: What’s the new national law that states corporal punishment should only be applied to the right side of a child’s buttocks?

  3. question: What’s the new national law that states corporal punishment should only be applied to the right side of a child’s buttocks? No Child’s Left Behind

  4. Assessing the Curriculum Content Needs of the Students

  5. SURVEYS OF ENACTED CURRICULUM (SEC)Council of Chief State School Officers (CCSSO) • Surveys of Enacted CurriculumTools for Aligning Instruction, Standards, and Assessments • Correlations of teacher-reported enacted curriculum vs. the Illinois State Achievement Test (ISAT)

  6. MSTD Teachers vs. ISAT Exam Correlations Left side slides MSTD Partnership Teachers’ Enacted Curriculum in Math Right side slides Illinois ISAT Exam 2003 Grade 5 Math

  7. One way to assist students in problem solving, communicating, reasoning, making connections, and showing representations in mathematics

  8. Four Squares Graphic Organizer1 + 4 + 3 + T + V • ONE TOPIC • FOUR MAIN POINTS (LAST IS CLOSURE) • THREE SUPPORTING IDEAS FOR EACH POINT • TRANSITION STATEMENTS BETWEEN MAIN POINTS • VIVID DESCRIPTORS OF SUPPORTING IDEAS

  9. NCTM Process Standards • Communications • Problem Solving • Reasoning and Proof • Representation • Connections

  10. AdaptingforExtended Response Questions Thinking like a Mathematician

  11. What do I know? Brainstorm ways to solve this. What do I want to find? Try it here. Things I need to include in my extended-response write up Dr. Alan Zollman, Northern Illinois University Four-Corners Extended Response

  12. Second Paragraph Write whatyou know from the problem. “What I know from the problem is …” Third Paragraph Show your strategies you will try. “So what I first tried to do was …” Fourth Paragraph Show your solution. “Using numbers this is …” First Paragraph Write what you are to find. “First, what I want to find is ..” Fifth Paragraph Explain your answer. “Therefore, what I did was …” Dr. Alan Zollman, Northern Illinois University Four-Corners Extended Response

  13. an extended response example

  14. MARTY’S SANDWICHES

  15. MARTY’S SANDWICHESMarty loves sandwiches. He likes hamburgers, hot dogs, and fish sandwiches. He loves sandwiches with anything on them!

  16. MARTY’S SANDWICHESMarty loves sandwiches. He likes hamburgers, hot dogs, and fish sandwiches. He loves sandwiches with anything on them!He always puts exactly one type of topping on his sandwich: either ketchup, mustard, mayo, or even taco sauce!

  17. MARTY’S SANDWICHESMarty loves sandwiches. He likes hamburgers, hot dogs, and fish sandwiches. He loves sandwiches with anything on them!He always puts exactly one type of topping on his sandwich: either ketchup, mustard, mayo, or even taco sauce.Marty says that for lunch he can eat a different one-topping sandwich everyday for 2 weeks without having the same thing. Can this be true? Explain why.

  18. Helping students use multiple representations to solve extended response problems

  19. TEAM Alice: Always works a problem using algebra

  20. TEAM Alice: Always works a problem using algebraTEAM Cheryl: Always works a problem making a chart

  21. TEAM Alice: Always works a problem using algebraTEAM Cheryl: Always works a problem making a chartTEAM Darrell: Always works a problem drawing a picture

  22. TEAM Alice: Always works a problem using algebraTEAM Cheryl: Always works a problem making a chartTEAM Darrell: Always works a problem drawing a pictureTEAM Thomas: Always works a problem guessing & testing

  23. TEAM Alice: Always works a problem using algebraTEAM Cheryl: Always works a problem making a chartTEAM Darrell: Always works a problem drawing a pictureTEAM Thomas: Always works a problem guessing & testingTEAM Marvin: Always works a problem using manipulatives

  24. TEAM Alice: Always works a problem using algebraTEAM Cheryl: Always works a problem making a chartTEAM Darrell: Always works a problem drawing a pictureTEAM Thomas: Always works a problem guessing & testingTEAM Marvin: Always works a problem using manipulativesTEAM Gwen: Always works a problem graphing it

  25. Before

  26. Same student after!

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  28. Same student after!

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  30. Same student after!

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