PUBLIC SCHOOLS OF NORTH CAROLINA
Squirrels:
Problem Solvers?
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
A challenge!
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
Common Core State Standards for
Mathematical Practice
Numero Uno: Problem Solving
Proficient students expect mathematics to make
sense. They take an active stance in solving
mathematical problems. When faced with a nonroutine problem, they have the courage to plunge in
and try something, and they have the procedural
and conceptual tools to carry through. They are
experimenters and inventors, and can adapt
known strategies to new problems. They think
strategically. See … www.corestandards.org
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
NCDigIns, Problem Solving and
Squirrels
-------------------
National Conference on
Student Assessment
June 2013
Mike Gallagher
Math Test and Measurement Consultant
North Carolina Deptartment of Public Instruction
michael.gallagher@dpi.nc.gov
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
NCDigIns Data Focus
Mostly Qualitative ….
• Trickle out one problem at a time.
• Guide the student to be the data user.
• What did I and my classmates do well?
• What could I do better?
• …. Pretty similar to post-game
analysis done by sports teams!
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
The Givens and Our Niche
• Given: Teachers are becoming more
versed in the principles of formative
assessment.
• Given: Teachers are pretty busy.
• Niche: NCDigIns gives teachers mathspecific tools and a template for
formative assessment.
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
NCDigIns
• NCDigIns were created by NC
teachers and test developers as a pilot
project for grades 4, 7 and Algebra 1.
• Teachers deconstructed the North
Carolina released test questions
(based on the 2003 Standard Course
of Study).
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
Data to Guide Descriptive
Feedback for each problem
• Start with expert teachers’ view on
likely sources of error and what to do
next.
• Then focus on each student’s work.
• Where did the class go with the
problem? Common errors/approaches
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
Template for NCDigIns
1. Question on a single page. (Not
intended for use as a quiz.)
2. Feedback hints on common errors.
3. Feedback hints on Problem-Solving
Strategies.
4. Concepts/Skills for Improvement
5. Where to go next (resources)
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DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
NCDigIns - - Example
Grade 4 DigIn Number 11, Question 3
“Bowling Pins”
• 2003 SCS Objective 1.03
• CCSSM 4.OA.3
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
Each Question One Page
Willy went bowling with his family. The
bowling pins were set up as shown.
--GRAPHIC with 10 pins –
If Willy knocked over 2/5 of the pins,
how many pins were left standing?
A
2
C
5
B
4
D
6
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
Feedback: Common Errors
A The student may not have read the
problem carefully or saw the
numerator as the number of pins
knocked over.
B The student may have found the
equivalent fraction correctly, but may
not have read the problem carefully
and picked 4 because it was the
number of pins knocked down.
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
Common Errors …cont.
C The student may not have a good
understanding of fractions and just
chose the denominator.
D Correct answer.
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
Feedback: Problem Solving
Strategies -> -> tied to 1 sheet!
1. Understand the problem.
•
Can you make a sketch?
2. Make a Plan
3. Carry it out.
4. Check your answer.
•
Is your answer reasonable?
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
Key concepts / skills
• Subtracting like fractions.
• Equivalent fractions.
• Understanding the relative size of
fractions. For example, 2/5 is less than
½.
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
Resources
• Three links are provided to free sites
with information and practice.
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
Build your own DigIns…
• Develop a classroom culture of peer
and self descriptive feedback along
the format of NCDigIns.
• This is a great way to find out the
learning progressions of your students,
which often do not match the logic of
textbooks.
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
Using NCDigIns
• Teacher feedback is most effective for
common errors … one to many
• Self and peer assessment expands
feedback … many to many
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
Problem Solving
“I’d unravel any riddle, for any individ’le
In trouble or in pain .. Oh, I would tell
you why, The ocean’s near the shore. I
could think of things I never thunk
before …” If I only had a brain.
Scarecrow in The Wizard of Oz.
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
There’s a Problem …
… with Problem Solving
Grade 4 Question from NAEP 2003
Estella wants to buy 2 notebooks that cost
$2.79 each, including tax. If she has onedollar bills and no coins, how many onedollar bills does she need?
A 3
B 4
C 5
C 6
Nationally, 31% of the students correctly
selected D. And 41% chose A.
nces.ed.gov/nationsreportcard/itmrls/
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STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
PUBLIC SCHOOLS OF NORTH CAROLINA
FA -> CCSSO Definition
Definition: “Formative assessment is a
process used by teachers and
students during instruction that
provides feedback to adjust teaching
and learning to improve students
achievement of intended instructional
outcomes.”
CCSSO 2008, adopted by N.C. Board of
Education
STATE BOARD OF EDUCATION
DEPARTMENT OF PUBLIC INSTRUCTION
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PUBLIC SCHOOLS OF NORTH CAROLINA
FA -> Key User = Student!
When it comes to learning, students are the
key assessment users: “Am I succeeding?
Am I improving over time? What should I do
next to succeed? Does my teacher think I
am capable of success? Do I think I am
capable of success?”
…from Student-Involved Classroom Assessment, 3rd
Edition. Richard J. Stiggins, 2001, Prentice-Hall.
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DEPARTMENT OF PUBLIC INSTRUCTION
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