Four Corners is Better than Four Squares: Assessment Connections Dr. Alan Zollman Northern Illinois University - PowerPoint PPT Presentation

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Four Corners is Better than Four Squares: Assessment Connections Dr. Alan Zollman Northern Illinois University

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Successfully adapting the Graphic Organizer 'Four Squares' ... We had chickens, pigs, dairy cows. We grew alfalfa, clover, soybeans, tobacco, oats, wheat, ... – PowerPoint PPT presentation

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Title: Four Corners is Better than Four Squares: Assessment Connections Dr. Alan Zollman Northern Illinois University


1
Four Corners is Better than Four Squares
Assessment Connections Dr. Alan
ZollmanNorthern Illinois University
  • Successfully adapting the Graphic Organizer "Four
    Squares" writing method to improve students
    extended responses in mathematical knowledge,
    strategy, and explanation in problem solving.
  • Friday, April 28, 2006 930 am
  • National Council of Teachers of Mathematics
    Annual Meeting,
  • America's Center 240
  • St. Louis, MO

2
question
  • Whats the new national law that states corporal
    punishment should only be applied to the right
    side of a childs buttocks?

3
question
  • Whats the new national law that states corporal
    punishment should only be applied to the right
    side of a childs buttocks?
  • No Childs Left Behind

4
  • Assessing the Curriculum Content Needs of the
    Students

5
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 MSTD Partnership
Teachers Enacted Curriculum in Math
Right side slides Illinois ISAT Exam 2003 Grade 5
Math
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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
23
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
First Paragraph Write what you are to
find. First, what I want to find is ..
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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an extended response example
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MARTYS SANDWICHES
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MARTYS SANDWICHESMarty loves sandwiches. He
likes hamburgers, hot dogs, and fish sandwiches.
He loves sandwiches with anything on them!
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MARTYS 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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MARTYS 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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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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  • 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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Assessing for mathematical knowledge, strategy,
and explanation in problem solving
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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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One-class sample results
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Here is the overall data
Category of students who scored an exceeds of students who scored an exceeds of students who scored a meets of students who scored a meets of students who scored less than a meets of students who scored less than a meets
Squares and vertices problem Pre Post Pre Post Pre Post
Mathematic knowledge 0 31 25 38 75 31
Strategy score 0 44 0 37 100 19
Explanation score 0 31 6 38 94 31

Tiling the patio problem Pre Post Pre Post Pre Post
Mathematic knowledge 0 10 5 38 95 52
Strategy score 0 38 5 38 95 23
Explanation score 0 10 0 38 100 52
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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 OfficersSurveys
    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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  • closure

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The growing of good corn
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  • I was raised on a farm in Indiana.
  • We had chickens, pigs, dairy cows. We grew
    alfalfa, clover, soybeans, tobacco, oats, wheat,
  • and especially corn.

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  • Everyone who plants corn wants to have a good
    crop of corn.
  • Initially, it requires money for good seed,
    fertilizers, insecticides, herbicides, and then a
    lot of
  • time and effort.

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  • No one can make corn grow.
  • You nurture the corn
  • to allow it to grow.

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  • You cant plant one lone seed of corn to get
    corn. You cant plant one row of corn to get
    corn.
  • Corn cross-pollinates.
  • Fields of corn are needed.

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  • You get the best corn when you and all your
    neighbors all grow good corn.
  • You need your neighbors to grow good corn if you
    want good corn.

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  • Thank you for helping me grow good corn by being
    good neighbors!
  • - Alan

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dr. alan zollmandept. of mathematical sciences
northern illinois universitydekalb, il
60115815/753-6750zollman_at_math.niu.eduhttp//ww
w.math.niu.edu/zollman
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