Learning About Student Mathematical Discourse: Case Study of a Middle-School Lesson Study Group

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Learning About Student Mathematical Discourse
Case Study of a Middle-School Lesson Study Group
Betsy Elizabeth King eking_at_mills.edu Mills College Aki Murata amurata_at_mills.edu Mills College
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Participants and Setting

• Washington Middle School (SF Area)
• 5 Mathematics Teachers
• Lesson Study during school year
• (2003-2004 meeting 2 - 3 times a month)
• Research lesson - 3 lesson study cycles.

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Research Question

• How does the teachers' thinking (beliefs, goals,
  knowledge) about student mathematical
  conversations evolve over the course of their
  participation in lesson study?

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Research Framework

• Students learn to communicate mathematically
• (NCTM, 1989, 1991 2000).

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Research Framework

• Students learn to communicate mathematically
• (NCTM, 1989, 1991 2000).
• Classroom social processes for mathematics
  reasoning (Cobb, et al., 1997).

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Research Framework

• Students learn to communicate mathematically
• (NCTM, 1989, 1991 2000).
• Classroom social processes for mathematics
  reasoning (Cobb, et al., 1997).
• Orchestrating classroom discourse, model for
  instructional practice (Sherin, 2002).

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Research Framework

• Students learn to communicate mathematically
• (NCTM, 1989, 1991 2000).
• Classroom social processes for mathematics
  reasoning (Cobb, et al., 1997).
• Orchestrating classroom discourse, model for
  instructional practice (Sherin, 2002).
• Lesson Study process to support teacher learning

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Teachers Lesson Study GoalTo promote student
mathematical conversations
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Research Methods Data Collected

• Lesson study meetings, lessons and debriefings
  were video/audio-taped
• Lesson artifacts
• Teacher interviews were audiotaped

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Research Methods Data Analysis

• Transcribed meetings, lessons, interviews
• Coded dialogue
• identified themes
• clustered into components
• Traced learning threads,
• shifts in teachers thinking

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Components of Teacher Learning

• Facilitation of Student Mathematics Conversation
• Use of Representations and Tools to Guide Student
  Mathematics Conversation

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Components of Teacher Learning

• Facilitation of Student Mathematics Conversation
• Classroom Norms and Culture

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Components of Teacher Learning

• Facilitation of Student Mathematics Conversation
• Classroom Norms and Culture
• Making On-the-Spot Decisions

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Components of Teacher Learning

• Facilitation of Student Mathematics Conversation
• Classroom Norms and Culture
• Making On-the-Spot Decisions
• Time and Pacing of the Lesson

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Components of Teacher Learning

• Facilitation of Student Mathematics
• Use of Representations and Tools to Guide Student
  Mathematics Conversation
• Representation Use
• Scaffolding

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Teacher QuestionsHow to make on-the-spot
decisions?

• How do you know which students questions to
  follow up?
• What if a student tells the answer early in
  lesson?
• How do you know when to move on?
• How do you know which students to call on and in
  what order?

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Research Lesson 1 Gauss Houses

1. Find apt when given bldg and floor.
2. Find floor for students apt .
3. Create algorithm for floor
4. Class generates formula or rule

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Anticipate Student Strategies

• Before the lesson
• Anticipate student strategies
• Decide sequence of strategies
• During the lesson
• Observe students strategies
• Students explain strategies in sequence

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Lesson 1

• Teachers anticipated student strategies for
  question 1
• Counting with drawing
• Multiply building x 6, subtract 1
• Strategies for other questions
• Divide by 6, interpret remainder
• Multiples
• No discussion about sequencing

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• How do you decide which students to call on,
• and in what order?

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Lesson 2 Planning

• Examined student strategies - lesson 1,
• anticipated strategies - lesson 2
• Planned sequence of students strategies
• Start with most accessible, more common, and
  build to more sophisticated

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Lesson 2 More Focus on Strategies

• Teacher facilitated students discussing their
  strategies.
• Strategies are named after student who suggests
  them.

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Lesson 3

• Common vocabulary and knowledge of student
  strategies and learning trajectory
• observe, easily record and discuss student
  strategies
• more visible student thinking and learning

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Lesson 3 Shift in Teachers Questions

• students engaging in mathematical
  conversations?
• successful studentshelping struggling
  students?
• evidence and proof in their arguments
• - 8th grade teacher

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Shifts in Teachers Thinking

• instead of intervening and saying, oh no, no,
  let me help you, I just tried to think about,
  Whats going on in this persons mind? So
  thats very different.
• -- 6th grade teacher

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Shifts in Teachers Thinkingit takes this
sort of very careful orchestration of the
conversation. And just saying, ok, talk about
this, solve this problem and talk about it while
youre solving it, isnt enough. - 8th
grade teacher
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Connecting Student Strategies

• Teacher makes connections between solutions
• pictorial to table representation
• table representation to numbers
• Students share solutions
• Kids main talkers in whole-class discussions
• Move from concrete operations
• towards formal operations
• -- 6th grade teacher

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Summary

• Student mathematical conversations need careful
  orchestration

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Summary

• Student mathematical conversations need careful
  orchestration
• Knowledge of student strategies
• facilitating discussions
• connections between strategies
• teachers observations/ student thinking

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Summary

• Student mathematical conversations need careful
  orchestration
• Knowledge of student strategies
• facilitating discussions
• connections between strategies
• teachers observations/ student thinking
• Shift in teachers questions
• from what teacher does
• to what students do

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Learning in Lesson Study

• Research lessons and debriefings
• visible
• Lesson study planning meetings
• largely invisible