# Write is Right: Improving Students' Problem Solving Using by E7G8pPd

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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, 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
Assessing the
Curriculum Content
Needs of the
Students
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                Right side slides
Grades 3-5 Teachers’            Illinois ISAT Exam
Enacted Curriculum in Math      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 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
NCTM Process Standards
•   Communications
•   Problem Solving
•   Reasoning and Proof
•   Representation
•   Connections
Thinking like a Mathematician

for
Extended
Response
Questions
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                                                                                   Third Paragraph

Write what you know from the problem.                                            Show your strategies you will try.
“So what I first tried to do was …”
“What I know from the problem is …”

Fourth Paragraph                                 First Paragraph
Write what you are to find.
“First, what I want to find is ..”
“Using numbers this is …”
Fifth Paragraph
“Therefore, what I did was …”

Dr. Alan Zollman, Northern Illinois University
Four-Corners Extended Response
Two extended-response
example problems
MARTY’S SANDWICHES
MARTY’S SANDWICHES

Marty loves sandwiches. He likes hamburgers,
hot dogs, and fish sandwiches. He loves
sandwiches with anything on them!
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’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.
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
Helping students use
multiple
representations to
solve extended
response problems
TEAM Alice:
Always works a problem using algebra
TEAM Alice:
Always works a problem using algebra
TEAM Cheryl:
Always works a problem making a chart
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 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 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 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
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!
student favorites
later in the semester …
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”
Results
OPEN-ENDED
RESPONSE QUESTIONS

PRETEST       POSTTEST
SCORES         SCORES
27% average    70% average
N=186 Students N=183 Students
Using ISAT Scoring Rubric
PRETEST                          POSTTEST
State meets or exceeds           State meets or exceeds

4% in Math Knowledge,         75% in Math Knowledge,
19% in Strategic Knowledge     68% in Strategic Knowledge
8% in Explanation             68% in Explanation

N=186 Students                   N=183 Students

Using ISAT Scoring Rubric
references:
“Four Square Writing Method for Grades 1-3” written by Judith S. and Evan Jay
“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 Zollman
Dept. of Mathematical Sciences
Northern Illinois University
Dekalb, IL 60115
815/753-6750
zollman@math.niu.edu

http://www.math.niu.edu/~zollman
http://www.mstd-d41-d4.niu.edu/

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

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