1. From Answer Finding to Doing K–5 Mathematics Breakout Session Introduction to Professional Learning for New Teachers August 24–26, 2015 Office of Curriculum, Instruction & Professional Learning FACILITATOR NAMES

2. Welcome and Good Morning  Please find your table.  Take a moment to introduce yourselves to the other new teachers in your group: Your name The borough in which you will be working One topic in math that you are looking forward to exploring with students this year 2

3. Agenda  Introductions & Norms  Hexagon Task Lesson: Tables & Chairs  Hexagon Task Lesson: Planning Highlights  Engaging, Exploring & Sharing: Shifts in Mathematics  Case Study: Teacher Actions that Support Doing Mathematics  Closing & Reflection 3

4. Session Outcomes  Engage in a model lesson centering on a mathematics task that is intellectually engaging and enjoyable and analyze pedagogical techniques that support student learning.  Experience and analyze a mathematics lesson structure that promotes sense making and students as doers of mathematics.  Become familiar with the eight Mathematics Teaching Practices from NCTM and use them to analyze a case study of a classroom engaging with a mathematics task.  Gain insight into a lesson structure and pedagogical practices that promote deeper mathematical learning and discuss the impact on lesson planning. 4

5. Norms for Collaboration 1.Promoting a Spirit of Inquiry and Balancing Advocacy 2.Pausing 3.Paraphrasing 4.Probing 5.Putting Ideas on the Table 6.Paying Attention to Self and Others 7.Presuming Positive Intentions Adapted from CCE and the work of R. Garmston 5

6. Norms for Collaboration  Read the description for each norm.  Identify a norm that: supports you as a learner you sometimes struggle with and would like to work on  Turn and talk: Which norms did you choose and why? How can norms be useful in the classroom? 6

7. 7 Hexagon Task Lesson Tables & Chairs

8. Setting up for a banquet How many chairs could I set up around this table? How do you know? Could you fit more? Fewer? How so?

9. Setting up a single table

10. How about at two tables?

11. But I want my guests to talk to each other! How many chairs could I set up with two tables placed next to each other like this?

12. I am planning a big party! I want to know how many chairs could be set up if I keep adding tables next to each other, like this: And so on

13. 13 Explore  As you work on your own, consider: What mathematical ideas and strategies are you using? How might a student approach this problem?  Work with your table groups to create a poster Make sure your poster clearly illustrates your group’s thinking. Please be prepared to discuss your group’s poster and thinking with the entire group.

14. 14 Reflect & Table Talk  Take a few moments to reflect: 1.What stands out to you most about this classroom experience? 2.What teaching moves do you feel were effective in promoting student learning and understanding? 3.What features of the task itself helped to promote discussion?  Table Talk  Group Share

15. 15 Hexagon Task Lesson Planning Highlights

16. A few lesson planning considerations for: 16  Planning learning goals  Selecting a good task  Anticipating what students might say and do  Providing access to all students  Providing opportunities for students to think like mathematicians every day

17. Learning goals 17  Running out of time is a common challenge in the first year.  For each lesson, identify:  Need to know  Nice to know  How can learning goals be developed?  What are the standards?  What do they need for tomorrow’s lesson?

18. 18  Has multiple entry points and various solution pathways  “Low floor, high ceiling”  Requires exploration of a mathematical relationship  Students explore the task first and then formalize and connect solution methods Task that promotes “doing” mathematics For more info, see the characteristics of mathematical tasks at four “Levels of Cognitive Demand” from Smith and Stein, 1998.

19. Anticipating student responses 19  Anticipated likely solution paths and student misconceptions:  Prepared questions to:  Support students with misconceptions  Advance student thinking  Produce “student work” in advance containing errors and solution paths

20. Providing access for all students 20  How does this lesson provide multiple entry points for different learners?  In what ways can the classroom environment support various learners during the lesson?  How about the teacher?  Grouping?

21. Thinking like mathematicians 21  As defined by the Standards for Mathematical Practice  Table talk: Which Standards for Mathematical Practice were evident in the lesson or do you see opportunities for?  Planning Tip: Look for ways to design your lessons to regularly engage students in the Standards for Mathematical Practice.

22. 22 Engaging, Exploring & Sharing Shifts in Math Instruction

23. CCLS-M One Key Shift Answer FindersDoers of Mathematics Most of the mathematical thinking happens before finding the answer. Success is identifying the proper procedure and applying it to solve a problem. Tasks are tools to assess student understanding. Tasks are tools to help students discover underlying mathematics in situations. Multiple approaches are essential for this discovery. Key mathematical work exists in connecting students’ ideas to one another and generalizing discoveries. The solution is one key step, but not the main purpose. 23 from Answer Finders to Doers of Mathematics

24. CCLS-M One Key Shift from Answer Finders to Doers of Mathematics Doing Mathematics 24 Finding the Answer

25. The Butterfly Effect 25 “Mechanical execution of procedures without understanding their mathematical basis often leads to bizarre results” - Gary W Martin (2009) What other mathematical “butterflies” have you experienced?

26. Traditional Lesson Structure for Mathematics 26 Homework Review Students put answers on the board Teachers show solution paths on request Lecture Concept explained in abstract Teacher shows several examples Students ask questions Practice Students assigned 1-20 odd for HW 17 and 19 are tricky word problems Answers in the back of the book Assess Chapter Test Final Exam Key Features Teacher and text book disseminate knowledge Application happens after basic skills

27. Metacognitive Modeling (I Do, We do, You do) 27 Do Now / Routines Activates prior knowledge May be topical or review Mini-Lesson Teacher models new content Teacher thinking made explicit (think aloud) Whole Class Students try it with support from teacher and one another Whole class discussion All voices heard Independent Practice Either in class or for HW Key Features Teacher thinking is central and explicit Gradual Release Assessment happens throughout

28. Lesson Structure for Doing Mathematics (You Do, Ya’ll Do, We Do) 28 Engage – Whole Class Develop enthusiasm Access prior knowledge Clarify conditions Explore – Small Group May begin independently Develop solution path Articulate thinking Share – Whole Class Share and connect solution paths Identify and analyze errors Concretize learning Apply, Connect, Extend – Independent Key Features Sense-making and assessment happen throughout Relatable, but not necessarily real world Focusing not funneling

29. Teacher and Student Roles TraditionalMeta-CognitiveDoers Role of Teacher Role of Student 29 Convey Content Make Teacher Thinking Explicit Make Student Thinking Explicit Connect Student Thinking Solve Problem Sets Learn to Think Like Teacher Participate in a Community of Mathematicians

30. Connecting to the Hexagon Task Lesson 30  How did the Hexagon Task lesson reflect the “Doing Mathematics” lesson structure?  At your tables: What are students and the teacher doing during each phase?  Note-taking tool to capture thoughts  Group Share

31. 31 Case Study Teacher Actions that Support Doing Mathematics

32. Case Study 32 Exploring Linear Functions: The Case of Ms. Peterson Note that the hexagon task used earlier was modified from the version in this text.  As you read, consider:  What does the teacher do to support student learning?  How does this lesson support students doing mathematics?  Take a few minutes to share thoughts at your tables.  Group Share

33. Teaching Practices that support students in doing mathematics 33  “Mathematics Teaching Practices” from NCTM’s Principles to Actions  Read the Overview page  Turn and talk:  Which Mathematics Teaching Practices stand out to you most and why?  Which practices are you most curious about?

34. Teaching Practices and the Case Study 34 1.Read the “Teacher and Student Actions” table for your table’s specific Mathematics Teaching Practice 2.Re-read the Case Study through the lens of that single Mathematics Teaching Practice  Capture any evidence of your Teaching Practice in the Case Study as you re-read; please document line numbers. 3.In your table groups, discuss and chart the evidence that you discovered. 4.Group Share

35. 35 Closing & Reflection

36. Reflection – Compass Points “We don’t learn from experience, we learn from reflecting on experience” – John Dewey 36 N S EW Something I am excited about doing in my classroom this year… Something that I will share with my colleagues… Something I am still wondering about… Something new and/or noteworthy that I don’t want to forget…

37. Additional Resources  See the “Supplemental Resources” document for websites that have math tasks, classroom videos, lesson plans, professional learning materials, and other resources for implementing the Common Core in your classroom. 37

38. 38 Thank You!