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 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 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 Cardetti Alvaro Lozano-Robledo Steve LeMay

AGENDA In general Pedagogy Argumentation Lunch Math Collaborative resource devel- opment (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 basics- documenting our work

Brief Introductions As you introduce yourself… Your name Your school/district Your birthday 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 –Purposes Provide 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 think To learn more math (connections); engage in productive struggle For fun!

Doing Problem Solving Tasks Together Ground Rules 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?

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

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 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, questions Consider: 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 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 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) 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 Argumentation Lunch Math – proportional reasoning Collaborative Protocol Collaborative Resource Development Please make sure your name is on your TREES handout and put it into your table folder.

BREAK Please return at _______________