CCSS
Mathematics
Fellows
ESD 105
Dawn Sparks
Doing Math Together—
Leadership of Self
Select and complete a task that you are not
familiar with at your grade band.
Think about multiple ways that you might
complete this task.
Larger context
Leadership in the Extended
Community
Leadership of Others
Advocate and Systematize
Collaborate
Leadership and
of
Implement
Self
Know and
Model
Purpose of the Fellows
To be a part of and support a system that focuses on math
making sense for all students. --Leadership in the Extended
Community
To be a part of a community of learners that focuses on
putting the shifts into practice to reflect the CCSS vision both
around the student making sense of the mathematics and
demonstrating that understanding. –Leadership of Others and
Self
To deprivatize our practice and take risks in order to facilitate
high quality mathematics instruction and experiences students
have with the mathematics. –Leadership of Self
Why Do Americans Stink at
Math
Assumptions-What assumptions does the
author of the text hold?
Agreements-What pieces of the text do you
agree with?
Aspirations-What pieces of the text do you
aspire to or act upon for yourself and your
colleagues?
Considering our Students
Setting Baseline Tasks
PURPOSE: To deprivatize our practice and take
risks in order to facilitate high quality
mathematics instruction and experiences
students have with the mathematics.
–Leadership of Self
Considering our Students
Setting Baseline Tasks
In order to understand where we are in our
practice, we will use a baseline task to examine
student ideas through the lens of the standards.
This will be operationalized through the content
clusters and Standard for Mathematical Practice 3
and 6 (SBAC Claim 3)
This task will be re-examined at the end of the year
to explore student growth
Assessment Claims for Mathematics
Overall Claim (Gr. 3-8)
Overall Claim (High School)
Claim 1
Concepts and Procedures
Claim 2
Problem Solving
Claim 3
Communicating Reasoning
Claim 4
Modeling and Data Analysis
“Students can demonstrate progress toward college and
career readiness in mathematics.”
“Students can demonstrate college and career readiness in
mathematics.”
“Students can explain and apply mathematical concepts and
interpret and carry out mathematical procedures with
precision and fluency.”
“Students can solve a range of complex well-posed problems
in pure and applied mathematics, making productive use of
knowledge and problem solving strategies.”
“Students can clearly and precisely construct viable
arguments to support their own reasoning and to critique
the reasoning of others.”
“Students can analyze complex, real-world scenarios and can
construct and use mathematical models to interpret and
solve problems.”
Claim 3 – Communicating Reason
Claim 3: Students can clearly and precisely construct viable arguments to support their
own reasoning and to critique the reasoning of others.
A.
B.
C.
D.
E.
F.
G.
Test propositions or conjectures with specific examples.
Construct, autonomously, chains of reasoning that justify or refute
propositions or conjectures.
State logical assumptions being used.
Use the technique of breaking an argument into cases.
Distinguish correct logic or reasoning from that which is flawed,
and—if there is a flaw in the argument—explain what it is.
Base arguments on concrete referents such as objects, drawings,
diagrams, and actions.
Determine conditions under which an argument does and
does not apply.
Making Sense of the Task
Look at the task as though you are a student so
that you can think about misconceptions that
might arise.
Discuss:
What knowledge do your students need to
have to be successful on this task?
Connecting it to the rubrics
Content Cluster Rubric
◦ Focuses on a specific cluster for the task
SBAC Achievement Level Descriptor Rubric
◦ Focuses on Claim 3 broadly
Review the rubrics and consider what a
response might look like based on the task
you completed.
Anchoring Yourself in Student Work
Look at the 3 anchor papers associated with your task. Discuss
as a group:
◦ What Content Cluster score does this student demonstrate?
◦ What SBAC ALD score does this student demonstrate?
What considerations does this illuminate for your students?
Review the official scores for your papers and annotated notes.
◦ What further clarification do you need?
Administering the Tasks Cold—
Leadership of Self
These tasks will be used as a baseline
Please do not give any prior instruction, it is very
important that your students demonstrate what
they know at this time
This data will be used as a baseline—it is more
important that your students grow from this
baseline, than do well at this first administration.
K-1 should read the task for the students and
accept dictation as answers if needed.
Focusing on Student Learning
Protocol—Leadership of Self, Others, and the Extended
Learning Community
Review the protocol
Prior to our second meeting please:
◦ Administer the task to your students “cold”
◦ Track student Content Cluster and SBAC ALD rubric
results
◦ Bring back a few examples of student work
◦ Consider the Implications for teaching
Data Collection for REL…
◦ Your students scores in Content and Claim 3
◦ Your implications for teaching
Module 1 – Teacher Leadership
Framework
ESD 105
September 23, 2014
CSTP Teacher Leadership
Framework
The Teacher Leadership Framework was developed
in 2009 by Washington teachers.
It created a foundational definition of teacher
leadership that includes five areas – adult learning,
communication, collaboration, knowledge of
content & pedagogy, and systems thinking.
Take a few minutes to review and orient yourself to
one area of the Framework.
Objectives
Fellows will be digging into this Framework
over the course of the year to further
develop their leadership.
Introduce the Framework and its 5 areas.
Complete the Framework’s self-assessment
Teacher Leadership SelfAssessment
The Self-Assessment is an opportunity to do some
individual reflecting about your leadership skills and
where you are in each of the 5 areas.
Individual results will be given back to you the next
time we meet. The aggregate results by region will
used to inform the Coordinators’ work with Fellows
and OSPI, so please be thoughtful and take your
time.
Here is the link to the online self-assessment:
https://www.surveymonkey.com/s/X7VRWTJ
Teacher Leadership:
Reflective Discussion
How does your work as Fellows connect to the
Knowledge, Skills and Dispositions outlined in the
Framework? Where did you find yourself thinking about
your Fellows role as you were taking the self
assessment?
What did you realize about your own Knowledge, Skills
and Dispositions as you took the self assessment?
What do you think the group should concentrate on in
terms of building our leadership capacity as defined in
the self-assessment?
Teacher Leadership: Next
Steps
4 Modules designed for Fellows:
Introduction to Teacher Leadership
Adult Learning and Group Dynamics
Systems Thinking
Case Study Dilemmas
Extension Activity or
Homework
Take out the Knowledge of Content and Pedagogy
page.
Connect – what specific bullet points or phrases
connect to the work you do as a Fellow?
Extend – what areas on this page do you think you
think you could do as an extension of the work
you are currently doing?
Challenge – what on this page would represent a
challenge for you?
Fellows Plan Document
Review the document
◦Highlight something that squares with
your thinking (you expected to do this
as part of your fellows work)
◦Put a question mark over something
that you are not sure about
Creating your plan
Review sample plans from last year
Reflect:
◦ When will be a good time to meet with your
administrator?
◦ What are some initial ideas you have about your
Common Core work this year?
◦ What implications does the NY times article have on your
plan?
◦ Are there any potential barriers you foresee in beginning
this work?
◦ How can I support you?
Lunch- See you in an hour!
Updates from OSPI and
Washington State
Deep Dive into
SMP
3&6
Improving Student Learning
What do students need to know and
do?
How do we know if they know it?
How are we going to help get them
there?
Looking
Deeper at
Mathematic
al Practice 3
and 6
Simulation for Generating an
Argument ~Instructional Model
1. Identify the Task and Question
2. Generate a Tentative Argument
3. Argumentation Session
4. The Reflective Discussion
5. Final Written Argument
Stage One: Generating a Question
and Beginning the Task
Everything I ever learned about
soup came from Seinfeld!
Selling Soup
• Martha wants to set up a
soup stall at a Farmer’s
Market and raise money for
charity.
• What questions do you have
for Martha?
P-35
Selling Soup
• Martha wants to set up a soup
stall at a Farmer’s Market.
• She hopes to sell 500 mugs of
soup, each with a white or
brown bread roll.
•She wants to make as much
profit as she can.
•She doesn't want to waste
food at the end.
•She needs to know how
much of each flavor soup
to buy and how many of
each kind of bread roll to
buy.
P-36
Stage 2: The Generation of a
Tentative Argument
1. Take turns to explain your idea of how to
respond to Martha’s Soup Question.
2. Listen carefully to each other and ask questions
if you don’t understand.
3. Once you understand each other’s work, agree
together in your group on the best approach
for completing the problem.
4. Outline on your large sheet of paper the
approach you are going to use.
P-37
Stage 2: Generation of a Tentative
Argument
Claim: The answer to
Martha’s question.
Evidence: Data to support
your answer. (data charts,
equations, graphs, tables,
explanations, etc.)
The Research Question:
What exactly should I buy so that I can
make the most profit and not have lots of
soup and rolls left over at the end?
Your group’s claim:
Justification: A rationale
that explains why the
evidence you use is relevant
or important, along with any
assumptions you have made
regarding the problem.
Your evidence:
Your justification of
the evidence:
Stage 3: The Argumentation Session
Students are given an opportunity to share,
evaluate and revise the products or process of
their investigation with their classmates.
• Visit other groups.
• Use the Gallery Walk
Interview Questions to
guide your discourse.
• Give feedback and be
ready to take back ideas
to your group.
Stage 4:
A Reflective Discussion
Meet with your group
◦ Discuss anything you learned from other groups
◦ Discuss feedback on your group’s ideas
Modify/Revise original ideas based on feedback
Teacher facilitates whole class discussion
◦ Encouraging students to share what they learned
◦ Common challenges faced by groups
Stage 5: The Production of a
Final Argument
Each student makes sense of their experiences by
producing a final argument
State the question and claim you are trying to
support
Include evidence (data + analysis + interpretation)
Provide a justification of your evidence
Organize your argument in a way that enhances
readability
Correct grammar, punctuation, and spelling errors
Reviewing the Stages of the Generate an
Argument Instructional Model
Identify the Task and Question
Generate a Tentative Argument
Argumentation Session
The Reflective Discussion
Final Written Argument
Next Steps…
How does the process of the Argument
Instructional Model assist with student
mathematical discourse?
How could you use a process like this in your
classroom?
How does this instructional model help students
develop skills to meet the intent of Mathematical
Practice 3 and 6?
Productive vs.
Unproductive
Beliefs
Beliefs
“Teachers’ beliefs influence the decisions
that they make about the manner in which
they teach mathematics… Students’ beliefs
influence their perception of what it means
to learn mathematics and their dispositions
toward the subject.” (NCTM, 2014)
Productive and Unproductive
Beliefs
On a 3x5 card,
individually
brainstorm
Productive and
Unproductive
Beliefs teachers
have about
mathematics.
Practice
Mathematics
Beliefs
Productive vs. Unproductive
Card Sort
Unproductive Beliefs
Productive Beliefs
Homework
1. Baseline Tasks due before 11/10
2. Meet with Admin and fill out Section A of the Fellows
Plan before 11/10
3. Principles to Action…
4. Read Pgs. 29 to 35 by our next meeting.
 Mark or note 3 instances of your current practice
 Mark or note 2 areas you would like to insert into your
current practice
 Mark or note 1 question you have about the reading