1. Magdalene Lampert, Univ of Michigan UCLA, UW, University of Michigan
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. Megan Kelley-Petersen
Elham Kazemi
Allison Hintz
Adrian Cunard
Helen Thouless
Becca Lewis
Teresa Dunleavy
Megan Kelley-Petersen
Megan Franke
Angela Chan
Magdalene Lampert
Amy Bacevich
Heather Beasley
Hala Ghoussieni
Melissa Stull
Orrin Murray

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. Routine instructional activities
Bounded activities that contain within them high-leverage mathematics teaching practices
central to supporting the development of mathematical understanding
generative in nature
productive starting places for novice teachers
common focus for teacher learning across K-5 placements and compatible with range of elementary curriculum

5. 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

6. 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

7. 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

8. Participating in oral counting

9. Watching a range of teachers counting

10. Plan for rehearsal
Math comes up here. They ask each other why a pattern works – what patterns will come up if we write it this way and not another way.

11. Rehearse with colleagues

12. Debrief rehearsal

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

14. Hoon bought two packages of paper
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?

15. 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?

17. Count by 15, start at 15 Count by 1, start 180, count to 230

18. Choral counting

19. 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

20. 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

21. 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
[their initial tendency represents long standing ideas about teaching - one question can shift]

22. 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
Asking why questions, looking at and listening to students, use the markers to support student learning not confuse - +10

23. 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

24. Theoretical roots Cognitive science Sociolinguistics
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)
Theory has been very important to us in developing our framework. We don’t think about the theory/practice divide in conventional ways.
Instead we see that the problems we have have supporting novices points to both insufficient theories and practices that enact them.

25. 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)