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Bridging Practices Among CT Mathematics Educators MSP Grant – Summer Workshop June 23, 2014...
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Transcript of Bridging Practices Among CT Mathematics Educators MSP Grant – Summer Workshop June 23, 2014...
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Bridging Practices Among CT Mathematics Educators
MSP Grant – Summer Workshop
June 23, 2014
WELCOME!!Please look at the hanging chart for
your table number.
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The big questions
Why am I here?
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Responding to the questionPedagogies 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 school-university collaborations to benefit all involved
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UConn Bridging Project Personnel
Dorothea Anagnostopoulos, Director of Teacher Education
Megan Staples, Mary Truxaw, Tutita Casa, Paul Steller, Maddie Williams, Math Ed
Fabiana CardettiAlvaro Lozano-RobledoSteve LeMay
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AGENDA
In generalPedagogyArgumentationLunchMathCollaborative
resource devel-opment (CRD)
TodayPedagogy – Talk FrameArgumentationLunch - SandwichesMath – 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.
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Consent & Technology basics- documenting our work
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Brief IntroductionsAs you introduce yourself…Your nameYour school/districtYour birthday
Any chance we share a birthday?
http://blog.minitab.com/blog/fun-with-statistics/any-chance-we-share-a-birthday
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Let’s jump in…
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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
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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?
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One model: A pedagogy of mathematical reasoning
New question(s)
Generate ideas
Elicit and Publicize ideas
Press on and develop ideas collaboratively
Solidify and/or refine new meanings
Two routines: Talk Frame Conjectures Routine
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TALK FRAME ROUTINE
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Doing Problem Solving Tasks Together –PurposesProvide a common math-teaching-and-
learning experience for reflection and discussion
Opportunity to discuss tasks and task implementation
Exposure to/discussion of some teaching strategies
Opportunities to see how others thinkTo learn more math (connections);
engage in productive struggle For fun!
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Doing Problem Solving Tasks Together
Ground RulesYou have the right to be
share your thinking, the right to be listened to; you have an obligation to explain to others
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The Trees Problem
1. Consider trees A and B below. a. Which tree is taller? b. How would you describe how much taller?
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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. Think
Which tree grew more? Explain your reasoning.
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Your Reasoning
Please (re)introduce yourself to your colleague!
Use the sentence frame:I think tree _____ because _____
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Sharing Ideas with Whole Group
Talk Idea Talk IdeaTalk Idea
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We understand…
We Understand
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Question worded using student accessible phrasing
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.”)
Summary of the mathematically valid conclusion agreed upon by the class
We Understand
Think
Talk Idea Talk IdeaTalk Idea
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
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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
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
Talk Idea
Think
We Understand
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One model: A pedagogy of mathematical reasoning
New question(s)
Generate ideas
Elicit and Publicize ideas
Press on and develop ideas collaboratively
Solidify and/or refine new meanings
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Reflecting on the Talk Frame
Thoughts, comments, questionsConsider: What might the Talk
Frame, or a similar routine, help you do?
What questions do you have?
Talk Idea
Think
We Understand
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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.
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Some resources (in blue = in packet)TALK FRAMECasa, 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 ROUTINESmith, 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.
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Coming up next…
Tomorrow (in the morning)Talk FrameConnecting Classroom Discourse &
Student ReasoningRest of the todayArgumentationLunch Math – proportional reasoning Collaborative ProtocolCollaborative Resource Development
Please make sure your name is on your TREES handout and put it into your table folder.
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BREAK
Please return at _______________