1. 2006 School Science & Mathematics Annual Convention,
Write is Right: Improving Students' Problem Solving Using Graphic Organizers Dr. Alan Zollman Northern Illinois University
Graphic Organizers to Help Students Communicate, Connect, Reason, Problem Solve, and Represent Mathematics
Thursday, October 26, :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 Organizer 1 + 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. Adapting for Extended Response Questions
Thinking like a Mathematician
Adapting for Extended Response Questions

22. Brainstorm ways to solve this.
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. Write what you know from the problem.
Second Paragraph
Write what you 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 SANDWICHES Marty loves sandwiches
MARTY’S SANDWICHES Marty loves sandwiches. He likes hamburgers, hot dogs, and fish sandwiches. He loves sandwiches with anything on them!

27. MARTY’S SANDWICHES Marty loves sandwiches
MARTY’S SANDWICHES Marty 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 SANDWICHES Marty loves sandwiches
MARTY’S SANDWICHES Marty 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 algebra TEAM Cheryl:
TEAM Alice: Always works a problem using algebra TEAM Cheryl: Always works a problem making a chart

34. TEAM Alice:. Always works a problem using algebra TEAM Cheryl:
TEAM Alice: Always works a problem using algebra TEAM Cheryl: Always works a problem making a chart TEAM Darrell: Always works a problem drawing a picture

35. TEAM Alice:. Always works a problem using algebra TEAM Cheryl:
TEAM Alice: Always works a problem using algebra TEAM Cheryl: Always works a problem making a chart TEAM Darrell: Always works a problem drawing a picture TEAM Thomas: Always works a problem guessing & testing

36. TEAM Alice:. Always works a problem using algebra TEAM Cheryl:
TEAM Alice: Always works a problem using algebra TEAM Cheryl: Always works a problem making a chart TEAM Darrell: Always works a problem drawing a picture TEAM Thomas: Always works a problem guessing & testing TEAM Marvin: Always works a problem using manipulatives

37. TEAM Alice:. Always works a problem using algebra TEAM Cheryl:
TEAM Alice: Always works a problem using algebra TEAM Cheryl: Always works a problem making a chart TEAM Darrell: Always works a problem drawing a picture TEAM Thomas: Always works a problem guessing & testing TEAM Marvin: Always works a problem using manipulatives TEAM 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

51. Same student
after!

53. Before

55. Same student
after!

57. student favorites

59. later in the semester …

62. Helping students self-reflect
In cooperative groups have students:
Design an abbreviated rubric that includes mathematical knowledge, strategy, and explanation
Assess “student” work using rubric
Give recommendations to the “student”

63. Results

64. PRETEST SCORES 27% average N=186 Students
OPEN-ENDED
RESPONSE QUESTIONS
PRETEST SCORES 27% average N=186 Students
POSTTEST SCORES 70% average N=183 Students
Using ISAT Scoring Rubric

65. PRETEST
State meets or exceeds
4% in Math Knowledge,
19% in Strategic Knowledge
8% in Explanation
N=186 Students
POSTTEST
State meets or exceeds
75% in Math Knowledge,
68% in Strategic Knowledge
68% in Explanation
N=183 Students
Using ISAT Scoring Rubric

66. references:
“Four Square Writing Method for Grades 1-3” written by Judith S. and Evan Jay Gould published by Teaching and Learning Company, Carthage, Illinois. (1999).
“Four Corners Graphic Organizer for Open-Ended Mathematical Problem Solving” Alan Zollman, NIMS Mathematics-Science Partnership. (2004).
“Four Corners Graphic Organizer for Open-Ended Mathematical Problem Solving” Alan Zollman, MSTD Mathematics-Science Partnership. (2005).
“Four Corners Graphic Organizer for Open-Ended Mathematical Problem Solving” Alan Zollman, Raising The MEANs Mathematics-Science Partnership. (2005).
“Four Corners is Better Than Four Squares in Math” Alan Zollman, ICTM 57th Annual Meeting, Springfield, IL. (Oct. 14, 2005).
Illinois Assessment web site:
Council of Chief State School Officers;Surveys of EnactedCurr.(SEC)
“Simmons Middle School Results: East Aurora District 131” Karen Lopez, MEANs Partnership Showcase, DeKalb, IL. (Apr. 6, 2006).

67. Dr. Alan Zollman Dept. of Mathematical Sciences Northern Illinois University Dekalb, IL /