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

1. 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

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 Grades 3-5 Teachers’ Enacted Curriculum in Math Right side slides Illinois ISAT Exam 2003 Grade 5 Math

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

17. 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

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

21. AdaptingforExtended Response Questions Thinking like a Mathematician

22. 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

23. 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

24. Two extended-response example problems

25. MARTY’S SANDWICHES

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

27. 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!

28. 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.

29. Oil is gushing out of an oil rig leak on the ocean, radiating outward in a circular film on the surface of the water.

30. 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?

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

32. TEAM Alice: Always works a problem using algebra

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

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

35. 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

36. 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

37. 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

38. Assessing for mathematical knowledge, strategy, and explanation in problem solving

41. Before

43. Same student after!

45. Before Before

47. Same student after!

49. Before