+ What Should I Expect to See During Mathematics Instruction? Helping Elementary Principals Recognize and Support Mathematical Thinking and Reasoning

+ Boston Public Schools: A Snapshot

+ Goals  Consider strategies for helping principals understand the expectations of the CCSSM;  Reflect on how we can help prepare principals to look for mathematical thinking and reasoning in classrooms; and  Identify next steps with principals that can help prepare them to be instructional leaders in mathematics in their buildings.

+ Agenda Welcome and Overview What does mathematical thinking and reasoning feel like, look like, and sound like? What kinds of classrooms support mathematical thinking and reasoning? What are implications for planning and teaching? Where are connections to your own work with principals? What might be some useful next steps?

+ At your table… Introduce yourselves. a) Name b) District/School c) Role Also make appointments with a “salt” and “pepper” partner who is not at your table for later conversations.

+ BPS Core Actions for K-12 Mathematics

+ Read through the indicators for Core Actions 1, 2, and 3. What do you think principals would be able to imagine? Where do you think principals might need support? Turn and talk to a partner about your thoughts.

+ Slab of Soap Problem

+ A slab of soap on one pan of a scale balances ¾ of a slab of soap and a ¾ pound weight on the other pan. How much does the full slab of soap weigh? Use some “private think time” to explore the problem. Talk with a partner about your strategies and approaches. Articulate each other’s approaches to each other.

+ Now consider how principals might engage with this problem. Now turn and talk with another partner at your table to discuss your thoughts.

+ Slab of Soap Video Clip: Looking for Evidence of Core Action Indicators Use the “Go Around” protocol to share what you saw. 1. Each person shares his or her thoughts for 1 minute. 2. Listeners jot down any questions or comments or additional thoughts. 3. After everyone has shared, take 4-5 minutes for group discussion to find common themes.

+ Find your Salt Partner. Have a brief conversation about these questions. What would principals see in this clip? What questions might they have?

+ What are the students doing? What is the teacher doing? Joey’s Run: Where do you see evidence of the Core Actions in this classroom?

+ Mathematics Teaching Practices: Pose purposeful questions Read the material. Think about the following questions: 1. How would you define purposeful questions? 2. What insights do you now have about the kinds of questions and the patterns of questions that support student thinking? 3. What are implications for planning and teaching?

+ Joey’s Run Revisited: Where do you see examples of purposeful questions? Consider questions that 1. gather information 2. probe thinking 3. make the mathematics visible, and 4. encourage reflection and justification. Add to your evidence.

+ Joey’s Run Video Clip: Looking for Evidence of Core Action Indicators Use the “Go Around” protocol again to share what you saw. 1. Each person shares his or her thoughts for 1 minute. 2. Listeners jot down any questions or comments or additional thoughts. 3. After everyone has shared, take 4-5 minutes for group discussion to find common themes.

+ Find your Pepper Partner. Have a brief conversation about these questions. What would principals see in this clip? What questions might they have?

+ What can you do as a school team to get these Core Actions “off the page” for principals?

+ Review the list of suggested resources. Think about what might be useful in your school or district. What resources are available for working with principals? Identify a resource to explore.

+ Possible Next Steps for Principals Principal collaborations with math coaches and teachers in schools. Principal visits to classrooms that include supportive conversations and questions. Principal support for participation in professional development designed to strengthen mathematics teaching practices. Principals putting in place structures that support teacher collaboration and learning. Other possibilities...

+ THANK YOU!

+ Contact Information Linda Ruiz Davenport BPS Director of K-12 Mathematics Anurupa Ganguly BPS Assistant Director of K-12 Mathematics