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

Why am I here?

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

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

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.

The Basics

Consent & Technology basics- documenting our work

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

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

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

TALK FRAME ROUTINE

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!

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

The Trees Problem

1. Consider trees A and B below. a. Which tree is taller? b. How would you describe how much taller?

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.

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 IdeaTalk Idea

We understand…

We Understand

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

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?

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

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

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

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 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.

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.

BREAK

Please return at _______________