1. 1 Learning to Lead Mathematics Professional Development

2. 2 Reflecting on Last Time Thinking back to the September seminar and the “Amy’s Method” videocase…  What did the video and discussions about facilitating mathematics PD have you thinking about in terms of your work with teachers? Pairs

3. 3 Practices for Sharing Teacher Work ANTICIPATING teacher responses to mathematical tasks MONITORING teacher work on tasks Purposefully SELECTING teacher work for sharing Purposefully SEQUENCING teacher work to share CONNECTING teacher work

4. 4 Practices for Sharing Teacher Work How did you see/use the practices in math PD? What did you think about the paper? In particular, what did you find:  Interesting?  Confusing?  Enlightening?  Troubling? How might these practices impact teachers’ experiences in PD? Small/Whole Group

5. 5 Focus of Today’s Case Consider issues related to using classroom artifacts in PD, specifically the role of purpose in making decisions about what ideas to pursue Be thinking about: What insights might I gain from this snapshot of practice? How does this experience help me think about my role as a mathematics PD leader?

6. 6 Pairs What so you see as some challenges with regard to using classroom artifacts in mathematics professional development?

7. 7 Working with Videocases

8. 8 Productive Engagement with Videocases Try to understand other people’s ideas (those shared by leaders in this group and those of teachers in the video) to expand your own understanding of the mathematical ideas Provide evidence and reasoning to support your ideas and claims Treat different perspectives respectfully and use them to compare ideas and to consider the affordances and drawbacks of various alternatives Contribute to a mathematical community where questions are raised that push on mathematical thinking and reasoning

9. 9 The Task 4 tiles 3 tiles 2 tiles perimeter = 10 1 tile perimeter = 6 Take a few minutes to work on the task individually, then share your solution approaches in your group. Maria has some hexagonal tiles. Each side of her tiles measures 1 inch. She arranges her tiles in rows, then she finds the perimeter of each row of tiles.  What would the perimeter be for arrangements of 5,10 and 25 tiles?  What would be a rule or formula for finding the perimeter of a row of n hexagonal tiles?  If the perimeter of a row of tiles is 66 inches, how many tiles are in the row?

10. 10 Considering the Task What are some approaches to this task? What are some possible rules or formulas? 4 tiles 3 tiles 2 tiles perimeter = 10 1 tile perimeter = 6 Whole Group

11. 11 Considering Student A’s Work What does Student A seem to understand? What does Student A seem to be struggling with? What issues might teachers raise around this piece of student work? Small Group

12. 12 LUNCH We will start again promptly at 12:15

13. 13 We are looking at this We are here

14. 14 Context 32 middle school teachers and coaches All-day assessment workshop, part of an ongoing series for a consortium of school districts Teachers have worked in groups to analyze several pieces of student work on Hexagons Linda, the PD leader, asks the group about Student A’s misconceptions/confusions We drop in here

15. 15 A Caveat Linda and the teachers are offering us a gift of allowing us to carefully examine a real instance of practice. We are examining their practice, not critiquing them.

16. Linda

17. 17 Viewing the Case We will watch the video two times:  First viewing with a focus on the mathematics and teacher engagement with it  Second viewing with a focus on facilitation

18. 18 Frame for Viewing What mathematical ideas are at play? Suggestion: Use transcript to think about issues after viewing the video

19. What mathematical ideas are at play?

20. 20 Pairs Questions to Consider Take a few minutes to individually review the transcript. Then discuss:  How do you think the various teachers view what Student A understands/doesn’t understand?  What perspectives do teachers seem to have regarding the use of variables in the task? Be sure to cite your evidence! Using line numbers in the transcript and other tools can help. Small Group

21. 21 Whole Group Discussion How were teachers viewing the mathematics here?

22. 22 Frame for Viewing What is the PD leader doing? Suggestion: Use transcript to think about issues after viewing the video

23. What is the PD leader doing?

24. 24 Pairs Questions to Consider How was the PD leader using this piece of student work? What did you notice about her facilitation moves? What might have been her purpose for using Student A’s paper? Be sure to cite your evidence! Using line numbers in the transcript and other tools can help. Small Group

25. 25 Whole group Whole Group Discussion What were some key facilitation moves or non- moves? How might Linda’s actions have been related to her purpose(s)? Link

26. 26 Connecting to Practice What are some possible purposes for using student work in professional development? Whole Group

27. 27 Some Kinds of Classroom Artifacts Student assessments Other student written work Transcript of students talking about task Video showing students working on task Video or audiotape of student interview Teacher notes or reflections from observations of individuals or groups …

28. 28 Some Purposes for Using Classroom Artifacts in PD Related to Student Thinking  Understanding student thinking  Understanding how students learn  Learning to anticipate what students might do with a task  Identifying common misconceptions students hold  Assessing student understanding  Recognizing that students can do this kind of work

29. 29 More Purposes for Using Classroom Artifacts in PD Related to Teacher’s Practice  Considering instructional implications  Recognizing what standards-level work looks like  Considering task design  Considering cognitive demand of tasks Related to Mathematics  Deepening teachers’ own mathematical understanding  Considering the mathematical issues in teaching the content  Considering how mathematical ideas are connected  Considering the development of mathematical ideas

30. 30 Connecting to Practice Two possible purposes for having teachers discuss Student A’s paper are:  Student Thinking: To assess the student’s understanding  Mathematics: To have teachers deepen their mathematical understanding, specifically the meaning of variable Given each of these purposes, what are some potential next moves for the PD leader?  In this session?  In future sessions with these teachers? Small Group

31. 31 Connecting to Practice Given each of these purposes, what are some potential next moves for the PD leader?  In this session?  In future sessions with these teachers? What are some potential affordances and drawbacks of these moves? Whole Group

32. 32 Mathematics Professional Development Principles Purpose--Goal-directed design and enactment Mathematics--Important and worthwhile mathematics Sociomathematical Norms--Robust ways for engaging in mathematical work Sense-making--Teachers think and reason Access & Equity--Use as a lens for considering issues in teaching and learning within PD and in classrooms

33. 33 Reflecting on the Experience In your journal write your reflections on the day: How have today’s cases helped you think about the role of classroom artifacts in mathematics PD? What do you want to be sure to remember from this seminar?