Using Action Research
To Empower North Carolina Educators
A Race to the Top Initiative
NC Department of Public Instruction
Educator Effectiveness Division
Algebraic Thinking in the Elementary Classroom
Elizabeth Bertke
g
Charlotte Mecklenburg Schools
Greenway Park Elementary
What is Action Research?
Systematic inquiry conducted by teachers and other educators to find solutions for critical
other educators to find solutions for critical, challenging, relevant issues in their classrooms and schools.
Mills, Geoffrey E, Action Research: A Guide for the Teacher Researcher, Mill
G ff
E A ti R
h A G id f th T h R
h
2014
What is Action Research?
Main Goals Include:
Positively impact student outcomes
impact student outcomes
•Positively
•Identify and promote effective instructional practices
•Create opportunities for teachers to become reflective practitioners
p
•Share research results with other educators
Mills, Geoffrey E, Action Research: A Guide for the Teacher Researcher, 2014
What is Action Research?
A systematic research process to:
● Identify an area of focus (critical, challenging issue)
i
)
●
●
Develop an action research plan
Implement action research plan in classroom/school
●
Collect, analyze, and interpret data
●
Share findings to inform practice
Mills, Geoffrey E, Action Research: A Guide for the Teacher Researcher, 2014
Embedding Algebraic Thinking into Elementary Math Instruction
to e e ta y at
st uct o
•What is the problem of practice investigated?
•Why is this important?
•Who would benefit from reviewing my research?
•How will this innovation benefit students?
Problems of Practice
Poll Everywhere!
Within the operations and algebraic thinking standard
(K-5) which do you believe is the most difficult for
st dents or the most difficult
students
diffic lt for teachers to teach?
Why?
Research on Algebra in the Elementary Classroom
El
t
Cl
• “To
To truly engage in mathematics is to become truly engage in mathematics is to become
curious and intrigued about the regularities and patterns, then describe and explain them.”
-Susan Jo Russell, Deborah Schifter, and Virginia Bastable
Research on Algebra in the Elementary Classroom
El
t
Cl
•“Algebraic thinking tasks alone will not give students the skills they need to reason d
h kill h
d
algebraically. How these tasks are used in instruction is equally important.”
•“Classroom instruction that supports children’s algebraic thinking is marked by rich conversation [and is] a regular part of conversation… [and is] a regular
part of
classroom activity”.
‐Maria L. Blanton
Make K
Knowled
dge Publlic
Analyzze/Interp
pret Daata *The majority of opportunities to
teach and encourage students'
students
investigation of operations and
equality are being missed and
students are not being given time to
engage in generalization sessions.
Co
ollect Daata
*Algebra is not regularly
incorporated into elementary math
lessons and is often taught in
isolation rather than across all
mathematical domains
domains.
Innovattion/Interventio
on
Action
n Researrch Plan
n
Focus Statement
Make K
Knowled
dge Publlic
•
when to notice natural opportunities when
to notice natural opportunities
to engage in algebraic thinking learn to use algebraic thinking strategies that can deepen g
p
understanding of operations and equality.
Analyzze/Interp
pret Daata •
Co
ollect Daata
Use job embedded professional development and coaching to help
development and coaching, to help teachers will learn Innovattion/Interventio
on
Action
n Researrch Plan
n
Purpose of the Study
Data Collection
– Ms. Parke
– Ms. Parke
Ms Parke’ss Students
Students
Make K
Knowled
dge Publlic
•
Analyzze/Interp
pret Daata 5 Second Grade Math Teachers
Co
ollect Daata
•
Innovattion/Interventio
on
Action
n Researrch Plan
n
Study Participants
•Behavior of operations­ regularities of •Behavior of operations
regularities of
operations; specifically in addition, subtraction, and equality
Make K
Knowled
dge Publlic
Analyzze/Interp
pret Daata •Algebra/ Algebraic reasoning­
generalizing mathematical patterns,
generalizing mathematical patterns, regularities, or relationships
Co
ollect Daata
•Job­embedded professional development‐ training that takes place development
training that takes place
during the regular school day through short informational sessions, grade level planning, modeling, and coaching
Innovattion/Interventio
on
Action
n Researrch Plan
n
Study Variables
•Teacher plan opportunities for­
h
l
f
intentionally prepare opportunities to reason
•Student understanding‐ noticing, describing, representing, and explaining Make K
Knowled
dge Publlic
Analyzze/Interp
pret Daata •Teacher engage students in­ help students learn to communicate their
students learn to communicate their reasoning
Co
ollect Daata
•Teacher notice­ identify natural (real‐
time) opportunities to reason
time) opportunities to reason
Innovattion/Interventio
on
Action
n Researrch Plan
n
Study Variables
Make K
Knowled
dge Publlic
Analyzze/Interp
pret Daata Co
ollect Daata
What is the impact of embedded professional b dd d
f i
l
development on teacher ability to notice engage
ability to notice, engage
students in, and plan
opportunities for algebraic pp
g
reasoning?
Innovattion/Interventio
on
Action
n Researrch Plan
n
Research Questions
•
•
•
•
Brief information/practice sessions
i
Coaching during lesson p
planning
g
Coaching during instruction
Modeling
F db k
Feedback on implementation
i l
t ti
Make Kn
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nowledgge Publicc
•
Analyze//Interprret Dataa A
Job Embedded PD/Coaching
Colleect Dataa
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
n
Innovation/Intervention
Representations
Questions
Listening
Generalizing
Make Kn
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nowledgge Publicc
•
•
•
•
Analyze//Interprret Dataa A
How do you encourage algebraic thinking?
Colleect Dataa
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
n
Implementation Through Professional Development
•
•
What does 1 Apple cost?
Solve using cubes
Solve using cubes
Do not use an equation
Make Kn
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nowledgge Publicc
1 Apple and 1 Banana cost $.20
5 Apples and 10 Bananas cost $1.65
Analyze//Interprret Dataa A
Representation: Apples & Bananas
Colleect Dataa
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
n
Implementation Through Professional Development
Draw a representation and label it!
p
Make Kn
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nowledgge Publicc
Yesterday your friend gave you 12 Yesterday
your friend gave you 12
markers. Now you have 19 markers! How many markers did you have before your friend gave you more?
Analyze//Interprret Dataa A
Second Grade Equivalent
Colleect Dataa
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
n
Implementation Through Professional Development
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
n
S
Second Grade Equivalent
d G d E i l
Make Kn
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nowledgge Publicc
Analyze//Interprret Dataa A
Colleect Dataa
Implementation Through Professional Development
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
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What Does the Equal Wh
D
h E
l Sign Really Mean?
Make Kn
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Analyze//Interprret Dataa A
Colleect Dataa
Implementation through Modeling
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
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Why Use a Balance to Wh
U B l
Learn About Equality?
Make Kn
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nowledgge Publicc
Analyze//Interprret Dataa A
Colleect Dataa
Implementation through Modeling
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
n
3+6 = 8+1
3
6 8 1
Is This True?
Make Kn
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nowledgge Publicc
Analyze//Interprret Dataa A
Colleect Dataa
Implementation through Modeling
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
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The Big Question
3 + 6 = 8 + ______
3 + 6 = 8 + Make Kn
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Analyze//Interprret Dataa A
Click here to watch video
from You Tube!
Colleect Dataa
Implementation through Modeling
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
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Lesson Planning: L
Pl
i Integrating Questions & Generalizing Make Kn
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Analyze//Interprret Dataa A
Colleect Dataa
Implementation Through Planning
2. What happens when you add an odd number with an odd number?
b
ih
dd
b ?
3. What happens when you add an even number with an odd number?
number with an odd number?
Create a generalization statement for each of these questions and use your cubes to prove that your rule is always true. Make Kn
M
nowledgge Publicc
1. What
What happens when you add an even happens when you add an even
number with an even number?
Analyze//Interprret Dataa A
Lesson Planning: L
Pl
i Generalizing Odd & Even
Colleect Dataa
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
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Implementation Through Planning
Create a generalization statement for this question and use your cubes to prove that your rule is always true. Make Kn
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nowledgge Publicc
Is 6+18 equal to 18+6?
Analyze//Interprret Dataa A
Seizing the Moment:
S
i i th M
t
Noticing Opportunities
Colleect Dataa
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
n
Implementation Through Coaching
https://todaysmeet.com/Generalize
*Use app Qrafter on iPhone/iPad or type in link
Make Kn
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nowledgge Publicc
Can you think of other general claims that might come up in a K‐5 classroom?
Analyze//Interprret Dataa A
Seizing the Moment:
S
i i th M
t
Noticing Opportunities
Colleect Dataa
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
n
Implementation Through Coaching
Data Collected
d
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
n
Pre­Project Teacher Survey
Make Kn
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Analyze//Interprret Dataa
A
Data Collected
Data Collected
d
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
n
Post­Project Teacher Survey
Make Kn
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Analyze//Interprret Dataa
A
Data Collected
5 + __ = 10 or 5 + 5= __
Pre‐ Results :
P
R l
• 90% (18/20) chose 5+5 Make Kn
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nowledgge Publicc
Which problem is easiest to solve?
Analyze//Interprret Dataa
A
Data Collected
d
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
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Student Data Collected
5 + __ = 10 or 5 + 5= __
Post‐ Results :
P
R l
• 50% (10/20) chose 5+5 Make Kn
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nowledgge Publicc
Which problem is easiest to solve?
Analyze//Interprret Dataa
A
Data Collected
d
In
nnovatio
on/Interrvention
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Action
n Researrch Plan
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Student Data Collected
Data Collected
d
In
nnovatio
on/Interrvention
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Action
n Researrch Plan
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What does equal (=) mean?
St d t R
Student Responses
14
12
10
8
6
4
2
0
Pre
Post
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Analyze//Interprret Dataa
A
Student Data Collected
Pre‐ Results:
• 70% (14/20) voiced that these sets of numbers both equaled 8
• 5% (1/20) voiced that the value of 1 came into play
Make Kn
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nowledgge Publicc
How is 5+3 related to 6+2?
Analyze//Interprret Dataa
A
Data Collected
d
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
n
Student Data Collected
Post‐ Results:
• 90% (18/20) voiced that these sets of numbers both equaled 8
sets of numbers both equaled 8
• 25% (5/20) voiced that the value of 1 came into play
Make Kn
M
nowledgge Publicc
How is 5+3 related to 6+2?
Analyze//Interprret Dataa
A
Data Collected
d
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
n
Student Data Collected
Data Collected
d
In
nnovatio
on/Interrvention
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Action
n Researrch Plan
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Field Notes
•
•
Scaffold facilitator From modeling to coaching to observing over 3 month period
Make Kn
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Analyze//Interprret Dataa
A
Data Collected
•
•
•
•
•
•
Within 2 weeks all warm‐up problems contained different unknowns and
contained different unknowns and problem types began to vary
Started RRR approach to problem‐solving to ensure representation and labeling
Formally planned 3 generalization ll l
d
l
sessions including odd & even, adding 1, and adding 9
Noticed 8 opportunities to engage
Noticed 8 opportunities to engage students in generalization discussions
Adjusted 4 math enrichment stations to build student understanding of mathematical patterns and relationships
th
ti l tt
d l ti
hi
Students increased understanding of equality, relationships of related p
problems, and their ability to articulate a y
general claim Make Kn
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nowledgge Publicc
Analyze//Interprret Dataa A
Collect Dataa
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
n
Overall Findings
•
Familiarize teachers with the concept of algebra and algebraic thinking‐
of algebra and algebraic thinking
specifically generalizing
•
Model whole group lessons
g p
•
Model seizing natural moments to question and generalize
•
Plan specific strategies into lessons
•
Plan for specific times to conduct Pl
f
ifi ti
t
d t
generalization sessions
Make Kn
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Analyze//Interprret Dataa A
Collect Dataa
In
nnovatio
on/Interrvention
n
Action
n Researrch Plan
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Recommendations
References
•Jacobs,
Jacobs V.
V R.,
R Franke
Franke, M
M., Carpenter,
Carpenter T
T. P
P., Levi
Levi, L
L., & Battey
Battey, D
D. (2007)
(2007).
Professional development focused on children's algebraic reasoning in
elementary school. Journal For Research In Mathematics Education, 38(3),
258-288.
•Matthews, P., Rittle-Johnson, B., McEldoon, K., & Taylor, R. (2012).
Measure for measure: What combining diverse measures reveals about
children's understanding of the equal sign as an indicator of mathematical
equality.
lit Journal
J
lF
For R
Research
h IIn M
Mathematics
th
ti Ed
Education,
ti
43(3) 316-350.
43(3),
316 350
•Russell, S. J., Schifter, D., & Bastable, V. (2011). Connecting arithmetic to
algebra: Strategies for building algebraic thinking in the elementary grades.
Portsmouth NH: Heinemann.
Portsmouth,
Heinemann
•Warren, E. (2009). Early childhood teachers' professional learning in early
algebraic thinking: A model that supports new knowledge and pedagogy.
Mathematics Teacher Education And Development,
p
, 1030-45.
•Wisconsin Univ., M. e. (2003). Algebraic skills and strategies for elementary
teachers and students. In Brief.
Conclusion of Presentation
•Thank you for your participation!
Contact Information:
Name: Elizabeth Bertke
l b h
k
School/District: CMS
Phone: 980‐343‐5060
Email: elizabeth.pavelecky@cms.k12.nc.us
Website: http://gtnpd177.ncdpi.wikispaces.net/About+the+Project