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Write is Right: Improving Students' Problem Solving Using Graphic Organizers Dr. Alan Zollman Northern Illinois University PowerPoint PPT Presentation


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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

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

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Write is Right: Improving Students' Problem Solving Using Graphic OrganizersDr. Alan ZollmanNorthern 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:

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


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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


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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 Organizer1 + 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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AdaptingforExtended Response Questions

Thinking like a Mathematician


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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


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Second Paragraph

Write whatyou 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


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Two extended-response

example problems


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MARTY’S SANDWICHES


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MARTY’S SANDWICHESMarty loves sandwiches. He likes hamburgers, hot dogs, and fish sandwiches. He loves sandwiches with anything on them!


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MARTY’S SANDWICHESMarty 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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MARTY’S SANDWICHESMarty 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.


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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 algebraTEAM Cheryl:Always works a problem making a chart


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TEAM Alice: Always works a problem using algebraTEAM Cheryl:Always works a problem making a chartTEAM Darrell:Always works a problem drawing a picture


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TEAM Alice: Always works a problem using algebraTEAM Cheryl:Always works a problem making a chartTEAM Darrell:Always works a problem drawing a pictureTEAM Thomas:Always works a problem guessing & testing


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TEAM Alice: Always works a problem using algebraTEAM Cheryl:Always works a problem making a chartTEAM Darrell:Always works a problem drawing a pictureTEAM Thomas:Always works a problem guessing & testingTEAM Marvin:Always works a problem using manipulatives


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TEAM Alice: Always works a problem using algebraTEAM Cheryl:Always works a problem making a chartTEAM Darrell:Always works a problem drawing a pictureTEAM Thomas:Always works a problem guessing & testingTEAM Marvin:Always works a problem using manipulativesTEAM 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!


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Before

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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OPEN-ENDED

RESPONSE QUESTIONS

PRETESTSCORES 27% averageN=186 Students

POSTTESTSCORES 70% averageN=183 Students

Using ISAT Scoring Rubric


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POSTTEST

State meets or exceeds

75% in Math Knowledge,

68% in Strategic Knowledge

68% in Explanation

N=183 Students

PRETEST

State meets or exceeds

4% in Math Knowledge,

19% in Strategic Knowledge

8% in Explanation

N=186 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/

“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).


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Dr. Alan ZollmanDept. of Mathematical Sciences Northern Illinois UniversityDekalb, IL [email protected]://www.math.niu.edu/~zollman


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

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


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