Elham Kazemi, UW

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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

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• 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
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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 practicemany
  entry points, many ways to develop it
• Provides a foundation for further development of
  teaching practice

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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

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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

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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

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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

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Participating in oral counting
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Watching a range of teachers counting
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Plan for rehearsal
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Rehearse with colleagues
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Debrief rehearsal
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FIELD Experiences Studio Days Plan and rehearse
with students
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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?
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Launching the Problem

• Read problem to self. Remove a key number
• Read chorally
• Pretend youre 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?

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(No Transcript)
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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

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Choral counting
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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

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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

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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

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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

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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 (Grossmans work)
• Organizational constraints and supports across
  teacher education sites

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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, OConnor,
  and Anderson, 2003)

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• 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)