Title: Four Corners is Better than Four Squares: Assessment Connections Dr. Alan Zollman Northern Illinois University
1Four 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
2question
- Whats the new national law that states corporal
punishment should only be applied to the right
side of a childs buttocks? -
3question
- 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
5SURVEYS 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)
6 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
7(No Transcript)
8(No Transcript)
9(No Transcript)
10(No Transcript)
11(No Transcript)
12(No Transcript)
13(No Transcript)
14(No Transcript)
15One way to assist students in problem solving,
communicating, reasoning, making connections, and
showing representations in mathematics
16(No Transcript)
17Four 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
18(No Transcript)
19(No Transcript)
20NCTM Process Standards
- Communications
- Problem Solving
- Reasoning and Proof
- Representation
- Connections
21AdaptingforExtended Response Questions
Thinking like a Mathematician
22What 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
23Second 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
24an extended response example
25MARTYS SANDWICHES
26MARTYS SANDWICHESMarty loves sandwiches. He
likes hamburgers, hot dogs, and fish sandwiches.
He loves sandwiches with anything on them!
27MARTYS 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!
28MARTYS 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.
29Helping students use multiple representations to
solve extended response problems
30TEAM Alice Always works a problem using
algebra
31TEAM Alice Always works a problem using
algebraTEAM Cheryl Always works a problem
making a chart
32TEAM Alice Always works a problem using
algebraTEAM Cheryl Always works a problem
making a chartTEAM Darrell Always works a
problem drawing a picture
33TEAM 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
34TEAM 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
35TEAM 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
36(No Transcript)
37 38(No Transcript)
39 40(No Transcript)
41Before
Before
42(No Transcript)
43Same student after!
44(No Transcript)
45Before
46(No Transcript)
47Same student after!
48(No Transcript)
49Before
50(No Transcript)
51Same student after!
52(No Transcript)
53student favorites
54(No Transcript)
55later in the semester
56(No Transcript)
57(No Transcript)
58Assessing for mathematical knowledge, strategy,
and explanation in problem solving
59(No Transcript)
60Helping 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
61One-class sample results
62Here 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
63references
- 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).
64 65The growing of good corn
66- 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.
67- 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.
68- No one can make corn grow.
- You nurture the corn
- to allow it to grow.
69- 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.
70- 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.
71- Thank you for helping me grow good corn by being
good neighbors! - - Alan
72dr. alan zollmandept. of mathematical sciences
northern illinois universitydekalb, il
60115815/753-6750zollman_at_math.niu.eduhttp//ww
w.math.niu.edu/zollman