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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


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 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


NCTM Process Standards

  • Communications

  • Problem Solving

  • Reasoning and Proof

  • Representation

  • Connections


AdaptingforExtended Response Questions

Thinking like a Mathematician


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


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


Two extended-response

example problems


MARTY’S SANDWICHES


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


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’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.


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 algebraTEAM Cheryl:Always works a problem making a chart


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


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


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


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


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


OPEN-ENDED

RESPONSE QUESTIONS

PRETESTSCORES 27% averageN=186 Students

POSTTESTSCORES 70% averageN=183 Students

Using ISAT Scoring Rubric


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


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).


Dr. Alan ZollmanDept. of Mathematical Sciences Northern Illinois UniversityDekalb, IL 60115815/753-6750zollman@math.niu.eduhttp://www.math.niu.edu/~zollman


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

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


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