Using Animated Classroom Scenarios in Teacher Education

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Using Animated Classroom Scenarios in Teacher
Education

• Daniel Chazan, University of Maryland,
• substituting for Patricio Herbst, University of
  Michigan

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The logic of the project
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Step 3 What weve created

• Animations, comic strips, slideshows
• Animated figures, not video
• Invented dialogue (often based on real classroom
  interaction), sometimes 1 voice

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Created for Purposes of Research

• Based on models of situations (2) Solving
  equations, Introducing a theorem.
• Include breaches of models, intended as probes
  into the rationality of practice (1).
• Include some repairs of these breaches, or leave
  those repairs to viewers.

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Representing key classroom mathematical
situations

• Introductory Algebra and Geometry
• Solving equations
• Proving propositions
• Developing theorems
• Doing word problems

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Teachers responses (4) A window into the
rationality of practice

• When groups of algebra and geometry teachers
  convene around these representations
• Tell each other alternative stories what could
  have been done or what might have happened.
• Evaluate actions of teachers and students and
  argue about why it would or would not happen
• Confirmation/Disconfirmation of our Models (5)

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What are they? Representations of classroom
mathematical work

• Mathematical work is a fundamentally human
  experience, occurs in time, in language, in
  action.
• Our animations are representations of
  mathematical work, mathematical practices, as
  they could happen in classroom.

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An active, not static representation of
mathematics

• This is a circle

This is a circle
This is also a circle
The intersection of a cone with a
planeperpendicular to the cones height
This is a circle
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Stories, not factual records of a class, but
represent classroom practice

• Not demonstrations of idealized teaching
  practices, but
• Elements of a virtual space of conceivable
  stories
• Support viewers
• projection of their own classroom experiences,
  and
• elaboration of their own alternatives

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An unanticipated side-effect Interest in a
different use

• The probes created for a research project have
  generated interest as tools for teacher
  education.
• For the last two summers, we have run week-long
  workshops for teacher educators interested in
  using the materials.

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Considering Teacher Education Uses

• What algebraic understandings and mathematical
  knowledge for teaching do we wish future teachers
  might gain in college?
• Lets examine one short animation!

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A stimulus for conversation

• An imagined classroom
• With active students
• Asking mathematical questions
• About typical procedures for solving algebra
  equations
• Not exemplary teacher practice, but
  representative of what might happen

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Blues questions
Questions for today

• What did Red do?
• Why would you do that? Im not even sure what
  that means!
• If we subtracted 5 from both sides, we would
  subtract 5 from just the 5 and the 65. But here,
  didnt Red divide everything by 5?
• Im convinced Red got the correct solution in
  this case, but does that way always work?

• Are these important (juicy) mathematical
  questions?
• Choose a question, describe a response you would
  like a teacher to make to this question?
• What would a teacher need to know to make this
  response? How would they learn to do this?

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A Geometry Animation
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Mathematical practices in the story

• Looking at special cases
• Seeking conditions under which a particular
  conclusion holds
• Seeking conclusions that hold under particular
  conditions.
• Productive informality and imprecision
• Changing the problem
• Proving a lemma

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Using the story to develop MKT, an example

• The teacher does not attach labels to these
  practices.
• Future teachers can be challenged to identify
  mathematical practices in the story.

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Value as resources to teach mathematics

• Animated students sometimes ask questions that a
  real student withholds, and that triggers
  teachers mathematical thinking
• They materialize for a teacher what another
  class did thus supporting a culture of
  mathematical argument

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Value for professional development

• Less overhead, easier to follow.
• Not critiquing a real teacher.
• Discussion of problematic moments and creation of
  alternatives in these classroom situations
• Can orient teachers to the timely, tactical,
  subject-matter related decisions a teacher makes
  when managing classroom interaction

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Value when teaching methods to prospective
teachers

• Showcase ways in which a teacher might manage a
  task of teaching
• For example, the teaching of a new theorem with a
  problem
• With appropriate supports it can make such a task
  amenable to analysis and design

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Support projecting oneself into the situation

• There isnt a right answer about what happened.
• Can ask people to invent what came before.
  Alternatives have same ontological status.
• Can ask people to act out classroom interaction,
  (e.g. reading comics).
• Can bring out teacher conceptions.

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Further developments in exploring these virtual
spaces

• Creating guides for using animations in
  pre-service education and professional
  development.
• Support for editing and showing animations for
  teacher education.
• Turning video of practice into animations.
• Support for teacher-created animations, e.g. an
  animated lesson plan.
• Creating on-line animation supported surveys.

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Sample related research questions

• What theory of individual differences suggests
  resources for telling stories, while maintaining
  projection?
• Does materializing non-standard mathematical
  practices allow them to travel?
• Psychometrics of animation-supported surveys.
• How can large-scale surveys done individually
  give insight to the rationality of practice?
• Might rich media representations of teaching be a
  resource in sharing the wisdom of practice (e.g.,
  in new electronic teachers guides)?

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If you want to browse the animations!
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Register!
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Browse and annotate!
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Contact us

• pgherbst-at-umich.edu
• dchazan-at-umd.edu
• grip.umich.edu