Bayesian Nets in Student
Modeling
ITS- Sept 30, 2004
Sources of Uncertainty
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Incomplete and/or incorrect knowledge
Slips and/or guesses
Multiple derivations
Invisible inferences
Not showing all work
Help messages
Self-explaining ahead
Andes student model
• Knowledge tracing
• Plan recognition
• 1st to use student’s domain knowledge
• Action prediction
• Andes first to support all three
Goals of Andes
• Students work as much as possible alone
• React to student’s incorrect action,
signal error, explain
• React to student’s impasse, provide
procedural help
• Assure student understands examples,
prompt self-explaining
Types of help
• Error help
• Procedural help (ask for hints)
• Unsolicited help (for non-physics
errors)
• Different levels of hints ‘til
“bottom-out hint”
Usage of student model
• Plan recognition: recognize and
support goals (requires prediction)
• Asses knowledge: help presentation
(reminder v. minilesson)
• Assess mastery level: prompt selfexplanation or not
Self-Explaining Coach
• Step correctness (domain)
• Rule Browser
• E.g.: using force or acceleration
• Step utility (role in solution plan)
• Plan Browser
• Recognize goals
Bayesian network
• Solution graph: map of all solutions
with no variables (propositional)
Types of nodes
• Domain-general: rules
• 2 values indicating mastery
• Task-specific:
• facts, goals, rule apps, strategy nodes
• Doable (done already or knows all
needed)
• Not-doable
Knowledge evolution
• Dynamic Bayesian network
• Analyze each exercise alone
• Roll-up: prior probabilities set to
marginal probabilities for previous
• Improvements: could model
dependencies & knowledge decay
Intention or ability?
• Probability that student can and IS
implementing a certain goal
• Decision-theoretic tutor keeps
probabilites of “focus of attention”
Problem creation
• Givens
• Goals
• Problem-solver applies rules,
generating subgoals until done
• Solution graph created
Andes assessor
• Dynamic belief network for domaingeneral nodes
• Rules - priors set by test scores
• Context-Rules
• P(CR=true|R=true)=1
• P(CR=true|R=false)=difficulty
• One context changes, adjust rest
Task-specific nodes
• Fact, goal, rule application, strategy
• Context-Rule nodes link task-specific
to domain-general rules
Fact & Goal Nodes
• A.k.a. Propositional Nodes
• 1 parent for each way to derive
• Leaky-OR: T if 1 parent T, also
sometimes true if not
• Reasons: guessing, analogy, etc
Rule-Application Nodes
• Connect CR,Strategy & Prop nodes to
new derived Prop nodes
• Doable or not-doable
• Parents: 1 CR, pre-condition Props,
sometimes one Strategy node
• Noisy-AND: T if ALL parents T, but
sometimes not, 1-alpha
Strategy Nodes
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Used when >1 way to reach a Goal
Paired with a Goal Node
Values are mutually exclusive
No parents in network
Priors=freq. students use this strat.
Compare Figures
• Figure 9 before observing A-is-body
• Figure 10 after observing A-is-body
Hints
• Add a new parent to a Prop node
• Accounts for guessing
SE-Coach
• Adds nodes for Read
• Link these to Prop nodes
• Longer read time, higher prob knows Prop (p
26)
• Adds nodes for plan selection
• Link these to Context-Rules
• Rule Application node prob T if knows CR
& all preconditions=Noisy-AND
Evaluation
• Simulated students, 65% correct for rule
mastery
• 95% if no “invis inferences” and has to
“show all work”
• Post-test shows significant learning
• Voluntary acceptance?
• Accuracy of plan recognition