Fellows Meeting 4
APRIL 21, 2015
ESD 105
Fellows Meeting #4
A candy jar contains 5 Jolly Ranchers (squares) and
13 Jawbreakers (circles). Suppose you had a new
candy jar with the same ratio of Jolly Ranchers to
Jawbreakers, but it contained 100 Jolly Ranchers.
How many Jawbreakers would you have? Explain
how you know.
◦ Please try to do this problem in as many ways as you can.
◦ If done, share your work with a neighbor.
Road Map of Our Day
8:30-10:00 Principles to Action Book Study
10:00-10:15 Break
10:15-11:30 CSTP- Fellows Groups Together
11:30-12:30 Lunch
12:30-1:30 Discourse and English Language Learners
1:30-1:45 Break
1:45-2:45 SBAC Claims and Depth of Knowledge
2:45-3:30 Next Steps-Evaluations
Best Math Lesson Ever
Turn and Talk
What made it so successful?
What was the math teacher doing?
What were the students doing?
What mathematics was being learned?
Teaching Practices that Support
Common Core Implementation
• Establish Mathematics Goals to Focus Learning
• Implementing Tasks that Promote Reasoning and
Problem Solving
• Use and Connect Mathematical Representations
• Facilitate Meaningful Mathematical Discourse
• Pose Purposeful Questions
• Build Procedural Fluency from Conceptual
• Support Productive Struggle in Learning Mathematics
• Elicit and Use Evidence of Student Thinking
Turn and Talk
How has the book study around the 8 teaching
practices deepened your understanding around
your vision of mathematics reform efforts?
How has the study impacted your work with your
Facilitate Meaningful Mathematical Discourse
Purposeful Questioning Math Practices
Effective teaching of mathematics facilitates discourse
among students to build shared understanding of
mathematical ideas by analyzing and comparing
student approaches and arguments.
Review pages 29-41…
What was one thought that resonated with you from
either practice?
Share out your thoughts in a small group.
Facilitating Discourse
Simply having students talk does not necessarily
advance the mathematical goals of a lesson.
oHow can the Five Practices identified on page 30, as
described by Smith and Stein (2011), support and
facilitate the purposeful exchange of ideas in the
mathematics classroom?
oNow consider Mr. Donnelly’s lesson and how he
incorporated the Five Practices to facilitate classroom
discussion. (p. 34)
Five Practices to Support
Facilitating Discourse
1. Anticipating student response prior to the lesson
2. Monitoring students’ work on and engagement with
the tasks
3. Selecting particular students to present their
mathematical work
4. Sequencing students’ responses in a specific order
for discussion
5. Connecting different students’ responses and
connecting the responses to key mathematical ideas
Facilitating Meaningful Discourse
Considering the Levels of Student Discourse:
oWhich of these practices are under utilized in
oHow can we help teachers become more
intentional incorporating these practices?
Mathematics Teaching Practice
Pose Purposeful Questions
oGathering Information
oProbing Thinking
oMaking the Mathematics Visible
oEncouraging Reflection and Justification
Pose Purposeful Questions
Consider the math task for your Grade Band from Digging
for Dinosaurs
1. Review the standards associated with the task you
2. Do the math
3. Anticipate likely student responses and misconceptions
(see Smith & Stein’s practice 1, p. 30)
4. Create a list of related questions using the framework
in figure 14 (pp. 36–37)
5. Create a poster with your questions
Review Levels of Discourse
Review Chart from Principles to Actions (p. 32)
oWhat do you see as next steps to see you move
along the continuum?
oHow does this continuum help you think about
your work with teachers?
The Center for Strengthening
the Teaching Profession (CSTP)
Module 4 – Case Story
Apply your developing understanding of the
Teacher Leadership Framework and your skills as a
Teacher Leader to Case Stories.
Reflect on your growth as a teacher leader in your
role as a Fellow this year.
Review your results from the Teacher
Leadership Framework Self-Assessment:
◦ Do these results reflect where you are now? Why
or why not?
◦ What has gotten more challenging? What has
gotten easier?
◦ How do you deal with dilemmas that come up
and still focus on building capacity?
Learning Through Case Stories
Read the Case Story “Overwhelmed and
As you read, consider what you know from
the Teacher Leadership Framework that
might connect to the Case Story – either in
evidence provided or lack thereof. Annotate
your thoughts within the article or on
scratch paper.
Learning Through Case Stories
How do you and don’t you see yourself in this dilemma?
Where does this dilemma ‘live’ in terms of the five areas in
the Teacher Leadership Framework (could be multiple
Where do you see evidence of the teacher leader
employing specific knowledge, skills and dispositions from
the Teacher Leadership Framework?
What from the Teacher Leadership Framework might assist
this teacher leader in managing this dilemma?
Set-Up: Circle of Viewpoints
Brainstorm a list of players in this dilemma – in
other words, who is part of the system described in
the Case Story?
Each person in your group takes on the role of one
of the players identified in your brainstorm
Circle of Viewpoints
Use the Circle of Viewpoints Routine to re-examine and discuss the Case
Going one at a time, each group member contributes to the following
three prompts:
◦ I am thinking of this Case Story from the point of view of…
◦ I think…
◦ A question I have is…
Repeat with the next group member until you’ve gone all the way
around the whole group.
Reflections & Next Steps
After using the Circle of Viewpoints routine, what
new ideas do you have that you didn’t have
What implications or realizations did you have for
your own work as a fellow in reading this Case
What are your next steps?
I used to think…Now I think…
Fellows 2015-16
Applications are now open..
Returning Fellows
New Fellows
Lunch-Meet back with your fellows group at 12:30
Math Fellows Next Steps…
Fellows Student Task Data SurveyFellows Self-Assessment Pre/PostSubmit Fellows Plans
Video Questions-
OPSI Clock Hours/Evaluations
Date: April 21, 2015
Title: Washington State
Math Fellows
Professional Development
Hours: 6
The Language of Mathematics for All
Children (CCSS to ELP and Beyond)
Helping all students communicate mathematical
Session Goals…
 Promote student engagement through
interactive math tasks
 Provide strategies and tools to support
student discourse
 Updates/Assessment Resources
What do you know about English
Language Learners in Washington State?
Languages Spoken in
Washington State Schools
219 Different Home Languages
Most identified language is Spanish, spoken by
67.4% of students
Next were Russian, Vietnamese, Somali, Chinese,
Ukrainian, Arabic, Tagalog, Korean, Marshallese,
spoken by 19% of Students
ELL’s in Washington State
Around 110,000 Bilingual Student a 5.3% increase
from the previous year
Comprises 9.7% of the statewide student
population - 0.6% points higher than the previous
Since 2005–06, the number of ELLs served by TBIP
in the state has increased by 32.6%
ELL’s in Washington State
Twenty-seven districts had an ELL headcount of
at least 25% of their total student population.
Thirty districts enrolled more than 1,000 ELLs.
These districts collectively served 72% of all
ELL’s statewide.
Forty-seven districts enrolled 500 or more ELL
Thirteen districts reported an increase of 10–
ELL’s in Washington State
Fifty-six districts enrolled fewer than 50 ELL
Fifteen districts reported fewer than 10 ELLs.
55.9% served by the TBIP were enrolled in grades
25% are newly eligible students
ELL’s in Washington State
42 districts have more than 20 languages
19 of these districts had more than 50 languages.
Of the 219 languages, 103 of these languages have
less than 10 students
The largest language increase is in Spanish
The greatest decrease is in Korean
Classroom Level
Discuss the language supports in your
Focused Mathematical
“In linguistically diverse classrooms, unstructured small
group and partnering activities continually fail to
produce substantive L2 oral language growth. Merely
increasing student interaction without explicit, coached
language instruction and accountability for application
leads to discussions with minimal cognitive or linguistic
challenge and negligible academic content.”
Gersten & Baker, 2001
Saunders and Goldenberg, 2010
Preparing ELL’s
To meet both content and language standards
 Talk
Build on prior knowledge about new ideas
 Read
Introduce new content
 Talk
Integrate new content into schema
 Write
Informally show what you know and ask
questions you still have
 Talk
Refine thinking and deepen learning
“Reading and writing float on a sea of talk.” James Britton
Graphic Organizers…
What do you know about
A Race
Amy and Rebecca are running in a road race.
The map, drawn to scale, shows the route of the race:
It takes Amy 8 minutes to run a mile.
Rebecca takes 12 minutes to run a mile.
The race consists of four laps of the route and Amy and
Rebecca run clockwise along the route at a constant speed.
Sharing Individual
1. Take turns to share your individual work with
your partner(s).
2. Share the notes you made on how you might
improve your work.
3. Listen carefully to each other, asking
questions if you don’t understand.
4. Use the Present an Idea Card and Pose a
Question to guide your conversation.
Joint Solution: Making
Posters-Talk Through
1. In your group, agree on the best method for completing the
2. Produce a poster that shows a joint solution to the A Race
task, that is better than your individual work.
3. State on your poster any assumptions you have made.
4. Give clear reasons for your choice of method.
Sharing Posters- Talk Through
1. One person from each group get up and visit a different
2. If you are staying with your poster, explain your work to the
visitor, giving reasons for your choice of method.
3. If you are the visitor, look carefully at the work, asking
clarifying questions to help you to understand the method
4. Discuss whether or not the method described on the poster
is similar to the visitor’s method.
5. The visitor is to write on a post-it note, suggestions on how
the work could be improved.
Sample Responses to
Discuss: Sally
Sample Responses to
Read each piece of sample student work carefully.
Use the E.L. Achieve Discussion Cards (Build on and Idea and Challenge
and Idea) to understand what Sally, Diane and George’s mathematical
Take turns explaining your thinking to your partner.
Listen carefully and ask clarifying questions. Use the Pose a Question
Card to frame your questions.
Provide feedback to each of the three responses using the discussion
E.L. Achieve Discussion Cards
Support Your Thinking-Secondary Math
Simple Academic Language
•The solution is reasonable because…
•Look at the pattern. I see…
•My method for solving this problem can
also work for …
E.L. Achieve Discussion Cards
Support Your Thinking-Secondary Math
Solid Academic Language
The solution demonstrates that … because
Based on the data, I see that…
My strategy for solving this problem can
also be used for ….
E.L. Achieve Discussion Cards
Support Your Thinking-Secondary Math
Sophisticated Academic Language
Although I estimated …., my solution is
reasonable because…
Based on the rule … I can justify that …
Because …, I can generalize the that the
strategy for solving this problem applies to …
Rich Math Tasks
Rich Math Tasks:
Digging for Dinosaurs
Exploration and Extensions…
Having quality Math Task leads to discussion.
How did the use of the E.L. Achieve Cards an other
graphic organizers help support critiquing the
reasoning of others?
How might you utilize a teaching tool such as the
E.L. Achieve Cards and graphic organizers?
Smarter Balanced Assessment Consortium
Mathematics Content Specifications
How do we
ensure that our
student can
Structure of the Smarter Balanced Assessment
Consortium Mathematics Content Specifications
Introduction and Background
General Considerations
Claims and Assessment Targets
Rationale and Evidence for Each Claim
Cognitive Rigor Matrix / Depth of Knowledge
4 Claims for Mathematics
(a/o Round 1 – released 8/29/11)
Concepts and
“Students can explain and apply mathematical
concepts and carry out mathematical
procedures with precision and fluency.”
Problem Solving
“Students can frame and solve a range of
complex problems in pure and applied
“Students can clearly and precisely construct
viable arguments to support their own
reasoning and to critique the reasoning of
Data Analysis and
“Students can analyze complex, real-world
scenarios and can use mathematical models
to interpret and solve problems.”
Mathematics Claim #1
Concepts and Procedures
“This claim addresses procedural skills and the
conceptual understanding on which developing
skills depend.”
◦ Selected Response
◦ Short Constructed Response
◦ Highly Scaffolded Tasks
◦ Extended Response
Claim #2
Problem Solving
“Assessment items and task focused on this claim
include well-posed problems in pure mathematics
and problems set in context.”
Single Step/Multistep Problems
Balanced types of problems that could include…
◦ Problems in Pure Math
◦ Design Problems
◦ Planning Problems
Claim #2
Problem Solving
Draw from knowledge
and skills within many
May draw on knowledge
and skills from lower
Provide evidence for
many assessment targets
Relevant verbs include:
Claim #3
Communicating Reasoning
“This claim refers to a
recurring theme in the
CCSSM content and
practice standards: the
ability to construct and
present a clear, logical
convincing argument.”
Relevant Verbs
◦ Understand
◦ Explain
◦ Justify
◦ Prove
◦ Derive
◦ Assess
◦ Illustrate
◦ Analyze
Claim #4
Modeling and Data Analysis
“Modeling is the process of choosing and
using appropriate mathematics and statistics
to analyze empirical situations, to
understand them better, and to improve
Math Practices in the Claims
Claim 1 – MP 5, 6, 7, 8
Claim 2 – MP 1, 5, 7, 8
Claim 3 – MP 3, 6
Claim 4 – MP 2, 4, 5
SBAC Cognitive Rigor Foundation
The Common Core State Standards
require high-level cognitive demand,
such as requiring students to
demonstrate deeper conceptual
understanding through the
application of content knowledge and
skills to new situations and sustained
SBAC Cognitive Rigor Foundation
For each Assessment Target in
English language arts and
mathematics, the depth(s) of
knowledge (DOK) that the
student needs to bring to the
item/task has been identified.
Content Specification
Math Content Specifications, p. 41
Webb’s Depth of Knowledge (DOK)
Depth of Knowledge measures the
degree to which the knowledge elicited
from students on an assessment
matches the complexity of what
students must know and do as part of
the standards.
Cognitive Rigor and Depth of Knowledge
The level of complexity of the cognitive demand.
Level 1: Recall and Reproduction
Requires eliciting information such as a fact, definition, term,
or a simple procedure, as well as performing a simple algorithm
or applying a formula.
Level 2: Basic Skills and Concepts
Requires the engagement of some mental processing beyond
a recall of information.
Level 3: Strategic Thinking and Reasoning
Requires reasoning, planning, using evidence, and explanations
of thinking.
Level 4: Extended Thinking
Requires complex reasoning, planning, developing, and
thinking most likely over an extended period of time.
Hess Cognitive Rigor Matrix
What type of thinking
(verbs) is needed to
complete a task?
How deeply do you
have to understand
the content to
successfully interact
with it?
How complex or
abstract is the
Hess Depth of knowledge…
Assessing your understanding of
the Mathematical Claims and DOK
Work in Small Groups or Partners
• Choose a grade band of Sample Test Items
• Decide on a Mathematical Claim for the Sample Item
• Decide on the DOK for the Sample Item
• Provide evidence for your answers
• Check answers with Answer Sheets
Fellows Next Steps…
Student Data Survey…
Teacher Survey…
Turn in Fellows Plans…
Fellows Application…
Topics for Next Year
Meeting Dates