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

Write is Right: Improving Write is Right: Improving Students' Problem Solving Students' Problem Solving Using Graphic OrganizersUsing Graphic Organizers

Dr. Alan ZollmanDr. Alan ZollmanNorthern Illinois UniversityNorthern Illinois University

Write is Right: Improving Write is Right: Improving Students' Problem Solving Students' Problem Solving Using Graphic OrganizersUsing Graphic Organizers

Dr. Alan ZollmanDr. Alan ZollmanNorthern Illinois UniversityNorthern Illinois University

Graphic Organizers to Help Students Communicate, Connect, Reason, Problem Solve, Graphic Organizers to Help Students Communicate, Connect, Reason, Problem Solve, and Represent Mathematicsand Represent MathematicsThursday, October 26, 2006 2:30 pm Thursday, October 26, 2006 2:30 pm

2006 School Science & Mathematics Annual Convention,2006 School Science & Mathematics Annual Convention,

Missoula, MontanaMissoula, Montana

question:question:

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

question:question:

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

No Child’s Left BehindNo 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 slidesGrades 3-5 Teachers’Enacted Curriculum in Math

Right side slidesIllinois ISAT Exam2003 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

Adaptingfor

Extended Response Questions

Thinking like a Mathematician

What do I want to find?

What do I know? Brainstorm ways to solve this.

Try it here.

Things I need to include in my extended-response write up

Dr. Alan Zollman, Northern Illinois UniversityFour-Corners Extended Response

First ParagraphWrite what you are to find.

“First, what I want to find is ..”

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 …” Fifth Paragraph

Explain your answer.“Therefore, what I did was …”

Dr. Alan Zollman, Northern Illinois UniversityFour-Corners Extended Response

Two extended-responseexample problems

MARTY’S SANDWICHESMARTY’S SANDWICHES

MARTY’S SANDWICHESMARTY’S SANDWICHES

Marty loves sandwiches. He likes hamburgers, Marty loves sandwiches. He likes hamburgers, hot dogs, and fish sandwiches. He loves hot dogs, and fish sandwiches. He loves

sandwiches with sandwiches with anythinganything on them! on them!

MARTY’S SANDWICHESMARTY’S SANDWICHES

Marty loves sandwiches. He likes hamburgers, Marty loves sandwiches. He likes hamburgers, hot dogs, and fish sandwiches. He loves hot dogs, and fish sandwiches. He loves

sandwiches with sandwiches with anythinganything on them! on them!

He always puts exactly one type of topping on He always puts exactly one type of topping on his sandwich: either ketchup, mustard, mayo, or his sandwich: either ketchup, mustard, mayo, or

even taco sauce!even taco sauce!

MARTY’S SANDWICHESMARTY’S SANDWICHES

Marty loves sandwiches. He likes hamburgers, Marty loves sandwiches. He likes hamburgers, hot dogs, and fish sandwiches. He loves hot dogs, and fish sandwiches. He loves

sandwiches with sandwiches with anythinganything on them! on them!

He always puts exactly one type of topping on He always puts exactly one type of topping on his sandwich: either ketchup, mustard, mayo, or his sandwich: either ketchup, mustard, mayo, or

even taco sauce.even taco sauce.

Marty says that for lunch he can eat a different Marty says that for lunch he can eat a different one-topping sandwich everyday for 2 weeks one-topping sandwich everyday for 2 weeks

without having the same thing. without having the same thing.

Can this be true? Can this be true? Explain why.Explain why.

Oil is gushing out of an oil rig leak on the Oil is gushing out of an oil rig leak on the ocean, radiating outward in a ocean, radiating outward in a circularcircular film film

on the surface of the water.on the surface of the water.

Oil is gushing out of an oil rig leak on the Oil is gushing out of an oil rig leak on the ocean, radiating outward in a ocean, radiating outward in a circularcircular film film

on the surface of the water.on the surface of the water.

If the radius of this circular film is increasing If the radius of this circular film is increasing at the rate of 2 meters per minute, how fast at the rate of 2 meters per minute, how fast is the area of the oil film growing when the is the area of the oil film growing when the

radius reaches 100 meters?radius reaches 100 meters?

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

BeforeBefore

Same student

after!

Same student

after!

BeforeBefore

Same student

after!

Before

Same student

after!

Before

Same student

after!

student favoritesstudent favorites

later in the semester …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

PRETESTSCORES

27% averageN=186 Students

POSTTESTSCORES

70% averageN=183 Students

OPEN-ENDED RESPONSE QUESTIONS

Using ISAT Scoring Rubric

PRETESTState meets or exceeds

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

N=186 Students

POSTTESTState meets or exceeds

75% in Math Knowledge, 68% in Strategic Knowledge68% in Explanation

N=183 Students

Using ISAT Scoring Rubric

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). 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/assessmentCouncil 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 60115

815/753-6750zollman@math.niu.edu

http://www.math.niu.edu/~zollman

Dr. Alan ZollmanDept. of Mathematical Sciences

Northern Illinois UniversityDekalb, IL 60115

815/753-6750zollman@math.niu.edu

http://www.math.niu.edu/~zollman

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

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

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

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