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

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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

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

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

Assessing the Curriculum Content Needs of the Students

- 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

- ONE TOPIC
- FOUR MAIN POINTS (LAST IS CLOSURE)
- THREE SUPPORTING IDEAS FOR EACH POINT
- TRANSITION STATEMENTS BETWEEN MAIN POINTS
- VIVID DESCRIPTORS OF SUPPORTING IDEAS

- Communications
- Problem Solving
- Reasoning and Proof
- Representation
- Connections

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.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?

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

Before

Same

student

after!

Before

Before

Same student

after!

Before

Same student

after!

Before

Same student

after!

- 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”

OPEN-ENDED

RESPONSE QUESTIONS

POSTTESTSCORES 70% averageN=183 Students

Using ISAT Scoring Rubric

POSTTEST

State meets or exceeds

75% in Math Knowledge,

68% in Strategic Knowledge

68% in Explanation

N=183 Students

PRETEST

State meets or exceeds

4% in Math Knowledge,

19% in Strategic Knowledge

8% in Explanation

N=186 Students

Using ISAT Scoring Rubric

“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). http://www.mstd-d41-d4.niu.edu/

“Four Corners Graphic Organizer for Open-Ended Mathematical Problem Solving” Alan Zollman, Raising The MEANs Mathematics-Science Partnership. (2005). http://www.means-d131.niu.edu/

“Four Corners is Better Than Four Squares in Math” Alan Zollman, ICTM 57th Annual Meeting, Springfield, IL. (Oct. 14, 2005).

Illinois Assessment web site: http://www.isbe.net/assessment

Council of Chief State School Officers;Surveys of EnactedCurr.(SEC) http://www.ccsso.org/projects/surveys_of_enacted_curriculum/

“Simmons Middle School Results: East Aurora District 131” Karen Lopez, MEANs Partnership Showcase, DeKalb, IL. (Apr. 6, 2006).

Dr. Alan ZollmanDept. of Mathematical Sciences Northern Illinois UniversityDekalb, IL [email protected]://www.math.niu.edu/~zollman

http://www.mstd-d41-d4.niu.edu/

http://www.means-d131.niu.edu/