Elham Kazemi, UWMegan Franke, UCLA
Magdalene Lampert, Univ of MichiganResearch Teams at
UCLA, UW, University of Michigan
Teaching Elementary Mathematics Ambitiously: Supporting Novice Teachers to Actually do the Work of Teaching
Megan FrankeAngela Chan
Magdalene LampertAmy Bacevich Heather Beasley Hala Ghoussieni Melissa StullOrrin Murray
Elham KazemiAllison HintzAdrian CunardHelen ThoulessBecca LewisTeresa DunleavyMegan Kelley-Petersen
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
Instructional Activities
Choral Counting & other counting activitiesStrategy Sharing (computational methods)Sequencing problems strategically and
purposefullyProblem Solving
Problem posing Monitoring student work time Sharing strategies Class discussion Closure
In any of the IAs, learn dimensions of the work of teaching as they relate to one another
Considering your mathematical goal…Pose a taskElicit student thinkingManage discussionClosure/highlight mathematical idea
Manage student participationEngage with meanings of equity in instructionDeal with incorrect responsesUse representationsAsk follow-up questions
Detailing practice
(a) unpackingarticulate 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
Participating in oral counting
Watching a range of teachers counting
Plan for rehearsal
Rehearse with colleagues
Debrief rehearsal
FIELD Experiences & Studio Days
Plan and rehearse with students
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?
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?
Count by 15, start at 15
Count by 1, start 180, count to 230Count by 7/8Count by .004 start at 53.280Count by 10 start 66, count to 266Count by .99, start at 1Count by 2, start at 0Count by 11, start at -77
Choral counting
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
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
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
What teachers are learning
Documenting differences in their stance towards teaching mathematics More specific, more confident, see they can get
betterDocumenting their ability to unpack and
detail practice More specific, ask different questions Deal with error
Documenting “improvement” in their use of the instructional activity
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
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)
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)
