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

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

+ Boston Public Schools: A Snapshot

+ District Context Curriculum materials currently in place in the district; Instructional approaches currently in place in secondary mathematics classrooms; Opportunities for communication with principals; and Current capacity of the Mathematics Office.

+ Goals  Consider strategies and experiences to help 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.

+ BPS Core Actions for K-12 Mathematics

+ Read through the indicators for Core Actions 1, 2, and 3. Highlight words and/or statements that you believe principals would struggle to visualize. Turn and talk to a partner about your thoughts.

+ CORE ACTION 1: Ensure the work of the lesson reflects the content shifts required by the CCSS for Mathematics. A.The lesson focuses on the depth of course-level cluster(s), course-level content standard(s) or part(s) thereof. A.The lesson intentionally relates new concepts to students’ prior skills and knowledge. A.The lesson intentionally targets the aspect(s) of rigor ( conceptual understanding, Procedural Fluency, Application) called for by the standard(s) being addressed. Starting points

+ CORE ACTION 2: Employ instructional practices that provide opportunities for all students to master the content of the lesson. A.The teacher makes the mathematics of the lesson explicit by using explanations, representations, and/or examples. A.The teacher provides time for students to work with and practice course-level problems and exercises. A.The teacher strengthens all students’ understanding of the content by sharing a variety of in students’ representations and solution methods. B.The teacher deliberately checks for understanding throughout the lesson and adapts the lesson according to student understanding. C.The teacher summarizes the mathematics with references to student work and discussion in order to reinforce the focus of the lesson.

+ CORE ACTION 3: Provide all students opportunities to exhibit mathematical practices in connection with the content of the lesson. C. The teacher establishes a classroom culture in which students explain their thinking. Students elaborate with a second sentence (spontaneously or prompted by the teacher or another student) to explain their thinking and connect it to their first sentence D. The teacher creates the conditions for student conversations where students talk about each other’s thinking. Students talk about and ask questions about each other’s thinking, in order to clarify or improve their own mathematical understanding.

+ 20 x 20

+ How much would a 100 x 100 burger cost? How much would an N x N burger cost? A 2 x 2 has 2 slices of meat, and 2 slices of cheese.

+ Structure of the Activity ① Principals worked on the problem in groups of 3. ② We selected 3 solution pathways while monitoring their progress. ③ We explored connections and ultimately established equivalence among the approaches. ④ We elicited their justifications and thinking as they explained their solutions.  Implications for Planning? “Thinking Through a Lesson Protocol”

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+ In’n’Out Activity/Thinking Through a Lesson Protocol In your table groups, discuss: 1 What important ideas emerged for you as you went through the activity and read through the planning framework? 2 How will this impact your work with principals?

+ What does it look like, sound like, feel like when students are reasoning through a problem? Please read the 2 student dialogues: Fitting a Polynomial and Rational Exponents

+ Find your Salt Partner. Have a brief conversation about these questions. What was helpful about the student dialogues? What questions might principals have?

+ What are multiple representations? Do you think there are more lines or points? Or are the number of each equal? Provide evidence for your claim.

+ Did this activity help expand your understanding of multiple representations? Why or why not? How would principals engage with this activity?

+ Conceptual Understanding and making meaning

+ What is Pi, Anyway? Use the “Go Around” protocol again to share what you read. 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 case? What questions might they have?

+ Possible Next Steps with Principals Principal collaborations with math coaches and teachers leaders 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 sharing evidence or and artifacts from thoughtful mathematics instruction in their buildings. Principals creating regular and consistent collaborative planning structures for teachers Other possibilities...

+ THANK YOU!

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