2006 School Science & Mathematics Annual Convention,

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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

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 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

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 Adapting for Extended Response Questions

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

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

Two extended-response
example problems

MARTY’S SANDWICHES

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!

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’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.

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 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:
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:
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:
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:
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:
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

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

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

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).

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