FacetBased Learning

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Facet-Based Learning

• David Madigan, Department of Statistics
• (joint with Earl Hunt and Jim Minstrell)

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Whats the problem?

• Undergraduate Science and Math Education
• Major long-term concern for US economy
• The Education President/Governor etc.
• An act of unthinking, unilateral educational
  disarmament
• Solutions typically focus on
• Curricular reform
• Standardized testing
• Site-based management
• Accountability
• etc.

National Committee on Excellence in Education
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Better Learning Through Science

• Learning Sciences A Theoretical Foundation for
  Learning
• Decades of research on how the human mind works
  and how students learn
• Facet-Based Learning (FBL)
• Classroom
• Intelligent Tutoring System
• World Wide Web

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Facet-Based Learning

• Starts from prior understandings
• Identify students pre-existing and
  context-specific pieces of knowledge
• Weave them into a coherent whole
• Persuasive rather than Memorable
• Sense-Making in the context of Communal Enquiry
• Focus on Learning rather than Teaching

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Facets

• Knowledge in Pieces
• A facet is a convenient unit of thought, an
  understanding or reasoning, a piece of content
  knowledge or a strategy seemingly used by a
  student in a particular situation
• Facets are context specific
• Facets can be expert-like or novice-like

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Facets from Introductory Physics

• Zero pounds Without air, there would be no
  weight, like in space
• A little less than 10 pounds Air is very light,
  so it doesnt press down very hard, but it does
  press down some
• 10 pounds The air has no effect either becuase
  the medium doesnt exert any forces, or it exerts
  equal forces in all directions
• A little more than 10 pounds A slight buoyant
  force is exerted by the air
• A lot more than 10 pounds A large buoyant force
  is exerted by the air

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Facets from Statistics

• The probability of a repeatable event is the
  frequency with which it occurs in the long run
  (44/47)
• If the probability of wining is 0.25 and if you
  played four times, then it would be surprising if
  you didnt win exactly once (5/37)
• If the probability is 1/n then there has to be n
  outcomes (18/49)
• No comparisons are possible if the sample sizes
  are different (9/49)
• If the observed difference is small, it could be
  due to chance (42/47)
• (Nisbett, Tversky, etc.)

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From Where do the Facets Come?

• Syllabus Pretest
  Interviews Protocol Analysis

Use Facets to Track Development of Understanding
Pre-Instruction Diagnoser
In-Class Benchmark Lesson
Elaboration and Diagnoser
Post-instruction Virtual Benchmark Lesson
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Diagnoser Evaluation
P-value 0.03
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Diagnoser I

• Here is some information about the freshman class
  at UW
• 50 Male
• 25 Have a car
• 60 of those with a car drive to school
• 40 are blonde
• 80 are from the state of Washington
• 10 are from Oregon
• 5 are from California
• If I pick a student at random, what is the chance
  that he/she is blonde and from Washington?
• 20
• 120
• 40
• 32
• 60
• I cant tell from the information given

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Diagnoser II

• What reasoning best explains your answer
• I added the chance of being blonde and being from
  Washington
• I multiplied the chance of being blonde and being
  from Washington
• I dont know the chance of a person being blonde,
  given that they are from Washington
• The chance is the smaller of the two chances
• I added the chance of being blonde and being from
  Washington and subtracted 100 since my answer
  was bigger than 100
• I averaged the chances of being blonde and being
  from Washington

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Diagnoser III

• Think about a difference example. Suppose I have
  a 50 of going to the grocery store today and a
  0 chance of going to the gym (my membership has
  expired). What is the chance I go to both the
  grocery store and the gym today?
• Is it the average of the two probabilities? If
  that is the case, the probability that I go to
  the grocery store and go to the gym is (500)/2
  25. But that couldnt be correct, could it?
• etc.

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Benchmark Lessons

• Teacher-instigated, Facet-directed, Full-class
  Discussions
• The Big Ideas
• Focus on Phenomena and Ideas rather than
  Correctness
• Large Classes???

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Blood Alcohol Content

• Suppose a person who is suspected of driving
  while under the influence of alcohol (DWI) has
  blood withdrawn for purposes of doing a blood
  alcohol content (BAC) test. Five people
  independently run the BAC test from portions of
  the same original sample and acquire the
  following results as a trained assistant, you
  get a reading of 0.12 BAC, while a nurse gets
  0.09, a resident intern gets 0.0913, a laboratory
  technician obtains a reading of 0.08, and the
  head MD (doctor) gets 0.19.
• 1. What would you report as the BAC for the
  individual being tested?
• 2. Give several reasons why five trained
  individuals might come up with different
  readings?
• 3. Should the individual be presumed to be under
  the influence of alcohol under Washington State's
  RCW?

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Web-based Benchmarks

• Answer the question and post to the website
  (blinded)
• Blind lifted
• Post a critique (or two or more) to the website
• Post a summary to the website

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Web-based Benchmarks
Advantages

• Familiar Software
• Outsiders can participate
• Instructor Intervention

Disadvantages

• Editing and Privacy
• Multimedia
• Newsgroup Administration

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Intelligent Tutoring Systems
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Future Work

• Facet Identification
• Bayesian Student Modeling
• Mainstream?