Classroom Discussions

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Classroom Discussions

• Using Math Talk to
• Help Students Learn

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Using Math Talk as An Instructional Tool

• Cognitive Goals
• Make mathematical conjectures
• Present evidence support their position
• Voice agreement/disagreement
• Learning of core mathematical concepts and
  procedures
• Social Goals
• Listen to one another respectfully
• Cooperate
• Building on one anothers ideas

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Cognitive Aspects of Math Talks

• Enables students to understand mathematical
  concepts, procedures, and problem solving deeper
  and with greater clarity
• Promotes reasoning skills
• Provides students practice in reflecting on their
  own thinking processes

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Social Aspects of Math Talks

• Teaches students to communicate clearly and
  precisely
• Builds students confidence about their own
  abilities

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Five Math Talk Strategies

• Revoicing
• Asking students to restate someone elses
  reasoning
• Asking students to apply their own reasoning to
  someone elses reasoning
• Prompting students for further participation
• Using wait time

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Incorporating Math TalksInto Daily Instruction

• Ms. Davies has given her third grade students a
  series of numbers, and in a whole-group
  discussion has asked them to say whether the
  numbers are even or odd. They have established
  that if you can divide a number by two evenly,
  then it is an even number.

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Revoicing(So youre saying that its an odd
number?)

• Philipe is working the number 24.
• Philipe Well, if we could use 3, then it could
  go into that, but 3 is odd. So then if it
  wasbut3 is even. I mean odd. So if its odd,
  then its not even.
• Ms. Davies OK, let me see if I understand. So
  youre saying the 24 is an odd number?
• Philipe Yeah. Because 3 goes into it, because
  24 divided by 3 is 8.

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Asking Students to Restate Someone Elses
Reasoning(Can you repeat what he just said in
your own words?)

• The classroom conversation continues
• Ms. Davies Can anyone repeat what Philipe just
  said in his or her own words? Miranda?
• Miranda Um, I think I can. I think he said that
  24 is odd, because it can be divided by 3.
• Ms. Davies Is that right, Philipe? Is that what
  you said?
• Philipe Yes.

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Asking Students to Apply Their Own Reasoning to
Someone Elses Reasoning(Do you agree or
disagree and why?)

• The classroom conversation continues
• Ms. Davies Miranda, do you agree or disagree
  with what Philipe said?
• Miranda Well, I sort oflike, I disagree?
• Ms. Davies Can you tell us why you disagree with
  what he said? Whats your reasoning?
• Miranda Because I thought that we said yesterday
  that you could divide even numbers by 2. And I
  think you can divide 24 by 2. And its 12. So
  isnt that even?

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Prompting Students for Further
Participation(Would someone like to add on?)

• The classroom conversation continues
• Ms. Davies So we have two different ideas here
  about the number 24. Philipe, youre saying that
  24 is odd because you can divide it by 3?
• Philipe Uh-huh.
• Ms. Davies And Miranda, youre saying that its
  even because you can divide it by 2? Is that
  correct?
• Miranda Yes.
• Ms. Davies OK, so what about other people? Who
  would like to add to this discussion? Do you
  agree or disagree with Mirandas or Philipes
  ideas? Tell us what you think, or add on other
  comments or insights.

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Using Wait Time(Take your timewell wait)

• The classroom conversation continues
• Eduardo Yes, I agree with Mirandas idea,
  because the only way you told us to find out if
  something is even is to divide by 2. And if we
  divide 24 by 3, we can also divide it by 4. And
  we can divide it by 6, too. So I think we should
  stick with 2 only.

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Three Productive Talk Formats

• Whole Class Discussion
• Small Group Discussion
• Partner Talk

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Whole Class Discussion

• Teachers role is to get students to share their
  thinking, explain the steps in their reasoning,
  and build on one anothers contributions
• Provides students with practice in mathematical
  reasoning that will further their mathematical
  learning

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Small Group Discussion

• Groups of 3-6 students discuss a question among
  themselves that the teacher has assigned
• Teacher circulates as groups discuss the question

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Partner Talk

• Teacher asks a question and then gives students a
  short time to put their thoughts into words with
  their nearest neighbor

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The Mathematics What Do We Talk About?

• Mathematical Concepts
• Computational Procedures
• Solution Methods Problem-Solving Strategies
• Mathematical Reasoning
• Mathematical Terminology, Symbols, Definitions
• Forms of Representation

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Conceptual vs. Procedural Knowledge

• Conceptual Knowledge
• Well-defined concepts
• Relationships among ideas, concepts, skills
• Procedural Knowledge
• Knowledge of facts, symbols, rules, procedures