Write is Right: Improving Students' Problem Solving Using

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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
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                Right side slides
Grades 3-5 Teachers’            Illinois ISAT Exam
Enacted Curriculum in Math      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
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                                                                                   Third Paragraph

Write what you know from the problem.                                            Show your strategies you will try.
                                                                                 “So what I first tried to do was …”
“What I know from the problem is …”




Fourth Paragraph                                 First Paragraph
                                         Write what you are to find.
Show your solution.
                                        “First, what I want to find is ..”
“Using numbers this 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. He likes hamburgers,
  hot dogs, and fish sandwiches. He loves
      sandwiches with anything on them!
          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. 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:
    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
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


  PRETEST       POSTTEST
  SCORES         SCORES
 27% average    70% average
N=186 Students N=183 Students
        Using ISAT Scoring Rubric
         PRETEST                          POSTTEST
   State meets or exceeds           State meets or exceeds

 4% in Math Knowledge,         75% in Math Knowledge,
19% in Strategic Knowledge     68% in Strategic Knowledge
 8% in Explanation             68% in Explanation

       N=186 Students                   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/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 Zollman
 Dept. of Mathematical Sciences
   Northern Illinois University
        Dekalb, IL 60115
          815/753-6750
    zollman@math.niu.edu

http://www.math.niu.edu/~zollman
http://www.mstd-d41-d4.niu.edu/

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

				
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