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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

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question: Whats the new national law that states corporal punishment should only be applied to the right side of a childs buttocks?

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question: No Childs Left Behind

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Assessing the Curriculum Content Needs of the Students

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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)

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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

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GRAPHIC ORGANIZER One way to assist students in problem solving, communicating, reasoning, making connections, and showing representations in mathematics

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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

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NCTM Process Standards Communications Problem Solving Reasoning and Proof Representation Connections

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Adapting for Extended Response Questions Thinking like a Mathematician

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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 University Four-Corners Extended Response

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First Paragraph Write 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 University Four-Corners Extended Response

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Two extended-response example problems

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MARTYS SANDWICHES MARTYS SANDWICHES

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MARTYS SANDWICHES Marty loves sandwiches. He likes hamburgers, hot dogs, and fish sandwiches. He loves sandwiches with anything on them!

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MARTYS 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!

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MARTYS 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.

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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.

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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?

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Helping students use multiple representations to solve extended response problems

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TEAM Alice: Always works a problem using algebra

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TEAM Alice: Always works a problem using algebra TEAM Cheryl: Always works a problem making a chart

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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

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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

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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

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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

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Assessing for mathematical knowledge, strategy, and explanation in problem solving

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Before

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Same student after! Same student after!

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Before

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Same student after!

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Before

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Same student after!

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Before

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Same student after!

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student favorites

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later in the semester …

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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

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Results

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PRETEST SCORES 27% average N=186 Students POSTTEST SCORES 70% average N=183 Students OPEN-ENDED RESPONSE QUESTIONS Using ISAT Scoring Rubric

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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

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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/ 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/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/assessmenthttp://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).

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

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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/

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