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
http://www.math.niu.edu/~zollman
Dr. Alan ZollmanDept. of Mathematical Sciences
Northern Illinois UniversityDekalb, IL 60115
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/