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Write is Right: Improving Students' Problem Solving Using Graphic Organizers Dr. Alan Zollman Northern Illinois Universi

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## Write is Right: Improving Students' Problem Solving Using Graphic Organizers Dr. Alan Zollman Northern Illinois Universi

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**Write is Right: Improving Students' Problem Solving Using**Graphic OrganizersDr. Alan ZollmanNorthern Illinois University Graphic Organizers to Help Students Communicate, Connect, Reason, Problem Solve, and Represent Mathematics Thursday, October 26, 2006 2:30 pm 2006 School Science & Mathematics Annual Convention, Missoula, Montana**question:**What’s the new national law that states corporal punishment should only be applied to the right side of a child’s buttocks?**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**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)**MSTD Teachers vs. ISAT Exam Correlations**Left side slides Grades 3-5 Teachers’ Enacted Curriculum in Math Right side slides Illinois ISAT Exam 2003 Grade 5 Math**GRAPHIC ORGANIZER**One way to assist students in problem solving, communicating, reasoning, making connections, and showing representations in mathematics**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**NCTM Process Standards**• Communications • Problem Solving • Reasoning and Proof • Representation • Connections**AdaptingforExtended Response Questions**Thinking like a Mathematician**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**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**Two extended-response**example problems**MARTY’S SANDWICHESMarty loves sandwiches. He likes**hamburgers, hot dogs, and fish sandwiches. He loves sandwiches with anything on them!**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’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.**Oil is gushing out of an oil rig leak on the ocean,**radiating outward in a circular film on the surface of the water.**Oil is gushing out of an oil rig leak on the ocean,**radiating outward in a circular film on the surface of the water.If the radius of this circular film is increasing at the rate of 2 meters per minute, how fast is the area of the oil film growing when the radius reaches 100 meters?**Helping students use multiple representations to solve**extended response problems**TEAM Alice: Always works a problem using algebraTEAM**Cheryl: Always works a problem making a chart**TEAM Alice: Always works a problem using algebraTEAM**Cheryl: Always works a problem making a chartTEAM Darrell: Always works a problem drawing a picture**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**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**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**Assessing for mathematical knowledge, strategy, and**explanation in problem solving**Same**student after!**Before**Before**Same student**after!