Bridging Practices Among CT
Mathematics Educators
MSP Grant – Summer Workshop
June 23, 2014
WELCOME!!
Please look at the hanging chart for your table
number.
The big questions
Responding to the question
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Pedagogies that focus on sense making,
justifying, and building on students’ thinking
Deep knowledge of mathematics, specifically
proportional reasoning, algebraic reasoning
and argumentation
Collaborating with others to develop tasks,
tools and other resources to support strong
math instruction
We also hope to advance productive schooluniversity collaborations to benefit all
involved
UConn Bridging Project Personnel
Dorothea Anagnostopoulos,
Director of Teacher Education
Megan Staples, Mary Truxaw, Tutita
Casa, Paul Steller, Maddie Williams,
Math Ed
Fabiana Cardetti
Alvaro Lozano-Robledo
Steve LeMay
AGENDA
In general
 Pedagogy
 Argumentation
 Lunch
 Math
 Collaborative
resource development (CRD)
Today
 Pedagogy – Talk Frame
 Argumentation
 Lunch - Sandwiches
 Math – All things proportional
 Collaborative resource
development – modeling a
protocol
As you arrive each day, you will be given handouts for the day. These
handouts will also be available on the Bridging Math Practices website.
The Basics
Consent & Technology basicsdocumenting our work
Brief Introductions
As you introduce yourself…
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Your name
Your school/district
Your birthday
Any chance we
share a
birthday?
http://blog.minitab.com/blog/fun-with-statistics/any-chance-we-share-a-birthday
Let’s jump in…
PEDAGOGY: DAY 1
GOALS:
 Introduce a general model for organizing
classroom discussions that centralize
mathematical reasoning
 Introduce a specific routine experientially–
Talk Frame – that is an example of this model
Getting our minds in gear
What’s the value of
having mathematical
discussions in class that
centralize your students’
thinking and reasoning?
What’s challenging about
doing that work?
One model: A pedagogy of
mathematical reasoning
Two routines:
Talk Frame
Conjectures Routine
New question(s)
Solidify and/or
refine new
meanings
Press on and
develop ideas
collaboratively
Generate ideas
Elicit and
Publicize ideas
TALK FRAME ROUTINE
Doing Problem Solving Tasks
Together –Purposes
Provide a common math-teaching-andlearning experience for reflection and
discussion
 Opportunity to discuss tasks and task
implementation
 Exposure to/discussion of some teaching
strategies
 Opportunities to see how others think
 To learn more math (connections); engage in
productive struggle
 For fun! 
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Doing Problem Solving Tasks
Together
Ground Rules
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You have the right to be share
your thinking, the right to be
listened to; you have an obligation
to explain to others
The Trees Problem
1. Consider trees A and B below.
a. Which tree is taller?
b. How would you describe how much
taller?
Think
2. Before, tree A was 8’ tall and tree B
was 10’ tall. Now, tree A is 14’ tall and
tree B is 16’ tall.
Which tree grew more?
Explain your reasoning.
Your Reasoning
Please (re)introduce
yourself to your
colleague!
Use the sentence frame:
I think tree _____ because _____
Sharing Ideas with Whole Group
Talk Idea
Talk Idea
Talk Idea
We understand…
We
Understand
Think
Talk Idea
Question worded using student accessible phrasing
Talk Idea
Talk Idea
Notes representing students’ ideas
(These include correct ideas as well as misconceptions. Also, the number of “talk idea” sections
used will vary according to the lesson, student contributions, and teacher’s decisions about how to
group ideas. The teacher can also choose to add in a particular “talk idea.”)
We
Understand
Summary of the mathematically valid conclusion agreed
upon by the class
Exploring Shape Games: Geometry with Imi and Zani, by M. K. Gavin, T.
M. Casa, S. H. Chapin, and L. J. Sheffield. Copyright © 2012, by
Kendall Hunt Publishing Company
Reflect – The Trees and the Talk
Frame
What did we just accomplish?
 Where was our/your productive struggle?
 What role did the Talk Frame play in
supporting our work?
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Reflecting on the Talk Frame
Think
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Talk Idea
We
Understand
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A framework (routine) for organizing
classroom discussions, big or small.
Allows for generation of ideas; bringing
them to public space; discussion, further
development; and solidifying
understandings, new meanings, or new
questions (start the cycle again)
Flexible routine
Choice of task has a large impact on type of
mathematics elicited
One model: A pedagogy of
mathematical reasoning
New question(s)
Solidify and/or
refine new
meanings
Press on and
develop ideas
collaboratively
Generate ideas
Elicit and
Publicize ideas
Reflecting on the Talk Frame
Think
Thoughts, comments, questions
Talk Idea
We
Understand
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Consider: What might the Talk Frame,
or a similar routine, help you do?
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What questions do you have?
Standards of Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of
others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Some resources (in blue = in packet)
TALK FRAME
 Casa, T. M. (2013). Capturing Thinking on the Talk
Frame. Teaching Children Mathematics, 19(8).
 Williams, M. M. & T. M. Casa (2012). Connecting
Class Talk with Individual Student Writing. Teaching
Children Mathematics. 314-321.
5-PRACTICES ROUTINE
 Smith, M.S., E. K. Hughes, R.A. Engle, & M. K. Stein.
(2009) Orchestrating discussions. Mathematics
Teaching in the Middle School 14(9). 549-556.
 Smith, M. S., & M. K. Stein (2011). 5 Practices for
Orchestrating Productive Mathematics Discussions.
Reston, VA: National Council of Teachers of
Mathematics.
Coming up next…
Tomorrow (in the morning)
 Talk Frame
 Connecting Classroom Discourse & Student
Reasoning
Rest of the today Please make sure your name is
on your TREES handout and
 Argumentation
put it into your table folder.
 Lunch
 Math – proportional reasoning
 Collaborative Protocol
 Collaborative Resource Development
Please return at _______________