Elham Kazemi, UW Megan Franke, UCLA Magdalene Lampert, Univ of Michigan Research Teams at

1. Teaching Elementary Mathematics Ambitiously: Supporting Novice Teachers to Actually do the Work of Teaching Elham Kazemi, UW Megan Franke, UCLA Magdalene Lampert, Univ of Michigan Research Teams at UCLA, UW, University of Michigan

2. Magdalene Lampert • Amy Bacevich • Heather Beasley • Hala Ghoussieni • Melissa Stull • Orrin Murray Megan Franke Angela Chan Elham Kazemi Allison Hintz Adrian Cunard Helen Thouless Becca Lewis Teresa Dunleavy Megan Kelley-Petersen

3. Identifying productive IAs… • Core to teaching and Core to the subject matter • Makes explicit aspects of differentiation and equity • Accessible to novices • Can be used across K-5 grade levels, with any curriculum • Can be used repeatedly in the classroom • Lots of ways to get better at this practice—many entry points, many ways to develop it • Provides a foundation for further development of teaching practice

4. Instructional Activities • Choral Counting & other counting activities • Strategy Sharing (computational methods) • Sequencing problems strategically and purposefully • Problem Solving • Problem posing • Monitoring student work time • Sharing strategies • Class discussion • Closure

5. In any of the IAs, learn dimensions of the work of teaching as they relate to one another Considering your mathematical goal… Pose a task Elicit student thinking Manage discussion Closure/highlight mathematical idea Manage student participation Engage with meanings of equity in instruction Deal with incorrect responses Use representations Ask follow-up questions

6. Detailing practice (a) unpacking articulate the parameters of the activity, connect it to other practices, see it in relation students’ participation in the practice (b) supports conversations about meaning (c) helps us be explicit

7. Participating in oral counting

8. Watching a range of teachers counting

9. Plan for rehearsal

10. Rehearse with colleagues

11. Debrief rehearsal

12. FIELD Experiences & Studio Days Plan and rehearse with students

13. Hoon bought two packages of paper. Each package has the same number of sheets. He used 16 sheets of paper from one package, leaving 1/3 of that package. How many sheets of paper did Hoon buy in all?

14. Launching the Problem • Read problem to self. Remove a key number • Read chorally • Pretend you’re watching this as a movie. • What is going on in this problem – tell me what the story is about. • What questions do you have? • I wonder if we need a picture to help us think about what is happening? • Do you have ideas about how to get started? • What is your answer going to sound like?

16. Count by 15, start at 15 • Count by 1, start 180, count to 230 • Count by 7/8 • Count by .004 start at 53.280 • Count by 10 start 66, count to 266 • Count by .99, start at 1 • Count by 2, start at 0 • Count by 11, start at -77

17. Choral counting

18. What this approach is buying us • Talking about aspects of practice not typical for us • how do you end it • what do you do if only 5 or 6 students are with you • what if I write it this way • Sequence matters • there are some practices that are easier for them to get a handle on and help them later

19. What we learn as teacher educators • what the practice entails • how to help them differentiate moves within instructional activities across grade levels • what novices struggle with when they first start practices and what they need to work on after they have a little practice • knowing how to prioritize when to intervene with coaching

20. Challenges leading to change • helping students explicitly see relevance of instructional activities, the practices inside them with their classroom teaching • connecting practices to what they perceive as "regular teaching” • helping them challenge competing notions of how to engage with students • make many assumptions which keep them from realizing how they are not listening to or supporting student participation

21. What teachers are learning • Documenting differences in their stance towards teaching mathematics • More specific, more confident, see they can get better • Documenting their ability to unpack and detail practice • More specific, ask different questions • Deal with error • Documenting “improvement” in their use of the instructional activity

22. What we are learning • Identity, knowledge, questions Ts take as they enter classrooms about content, pedagogy and participation. What and how they experiment. • Planning for rehearsal brings out the mathematics • We are learning which aspects of the IAs they can do first and which take time to develop and how to support • We are learning about feedback and how and when it matters (Grossman’s work) • Organizational constraints and supports across teacher education sites

23. Theoretical roots Cognitive science • Routines help novices cope with “overload.” (Dreyfus and Dreyfus, 1986) • Routines can be used to maintain a high level of mathematical exchange in classrooms. (eg. Leinhardt & Greeno, 1986; Leinhardt & Steele, 2005) Sociolinguistics • Discourse routines structure interaction and make it predictable, allowing participants to maintain common ground. (Schegloff 1968, Chapin, O’Connor, and Anderson, 2003)

24. Organizational Studies • Routines have two parts, ostensive and performative. (Feldman & Pentland, 2003 following Latour, Giddens) • In complex interactive practice, structure and agency interact. (March & Simon, 1958; M. Cohen, 1991) • Routines enable coordination of action. (Nelson & Winter, 1982) Professional Education • Practices can be decomposed into their constituent parts for purposes of teaching and learning them. (Grossman, et al., 2005) Research on teaching • Professional practice involves disciplined, structured improvisation. (Yinger, 1980; Sawyer, 2004)