Problem Order Implications for Learning Transfer
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Transcript of Problem Order Implications for Learning Transfer
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Problem Order Implications for Learning TransferNan Li, William Cohen, and Kenneth Koedinger
School of Computer ScienceCarnegie Mellon University
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Order of ProblemsOne of the most important variables that
affects learning effectivenessBlocked order vs. interleaved order
Interleaved is better! Why?
Type I Type II Type III
Type I Type II Type III Type I Type II Type III
Most existing textbooks
Numerous previous studies
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Need for Better Theory Studies
Contextual interference (CI) effect (Shea and Morgan, 1979)
Mixed results on complex tasks or novices
… Hypothesis
Elaboration hypothesis (Shea and Morgan, 1979)
Forgetting or reconstruction hypothesis (Lee and Magill, 1983)
… Proposed Approach
A controlled simulation study Using a machine-learning agent,
SimStudent Given problems of blocked orders or
interleaved orders
A precise implementation.
Easier to inspect SimStudent’s learning processes and
outcomes.
Lacks the precision of a computational theory.
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A Brief Review of SimStudent
• A learning agent that• Acquires production
rules• From examples and
problem-solving experience
• Given a perceptual representation, a set of feature predicates and operator functions
Matsuda et al., CogSci-09
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SimStudent Learns Production Rules
Skill divide (e.g. -3x = 6)
Retrieval path: Left side (-3x) Right side (6)
Precondition: Left side (-3x) does not
have a constant term
=> Function sequence:
Get-coefficient (-3) of left side (-3x)
Divide both sides by the coefficient
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Retrieval Path Learner A perceptual learner
Finding paths to identify useful information (percepts) in GUI E.g. <-3x, 6> <Cell 11, Cell 21> <4x, 12> <Cell 12, Cell 22>
Specific general E.g. Cell 21 Cell 2? Cell ??
The most specific path that covers all of the training percepts
Retrieval path:Left side (-3x)Right side (6)
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Precondition Learner A feature test learner
Acquiring the precondition of the production rule Given a set of feature predicates
A boolean function that describes relations among objects E.g. (has-coefficient -3x), (has-constant 2x+5)
Utilize FOIL (Quinlan, 1990) Input:
Positive and negative examples based on the percepts <percept1, percept2> E.g. positive: <-3x, 6>, negative: <2x+4, 8>
Output: A set of feature tests that
describe the desired situation to fire the production rule E.g. (not (has-constant ?percept1))
Different problem orders Different intermediate production rules Incorrect rule applications Different negative feedback
Precondition:Left side (-3x) does not have constant term
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Function Sequence Learner
An operator function sequence learner Acquires a sequence of operator functions to apply in
producing the next step Given a set of operator functions
E.g. (coefficient -3x), (add-term 5x-5 5)
Input: A set of records, Ri = <perceptsi, stepi>
E.g. <<-3x, 6>, (divide -3)>
Output: A sequence of operator functions, op = (op1, op2, … opk), that
explains all recordsE.g.
(bind ?coef (coefficient ?percepts1)), (bind ?step (divide ?coef))
Function sequence:Get-coefficient (-3) of left side (-3x)Divide both sides with the coefficient
(coefficient -3x)
(divide -3)<-3x,
6>
-3(divide -3)
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Problem Order StudyBlocked order vs. Interleaved orderThree domains
Fraction addition Equation solving Stoichiometry
Training and testing problems Solved by human students in classroom studies
SimStudent Tutored by automatic tutors that simulate the
automatic tutors used by human students
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Fraction AdditionProblem
TypesType Feature ExampleType I denominator1 =
denominator2
1/4 + 3/4
Type II One denominator is a multiple of the
other denominator
1/2 + 3/4
Type III No denominator is a multiple of the other
denominator
1/3 + 3/4
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Equation SolvingProblem
S1 + S2V = S3
TypesType Form ExampleType I S1 + S2V = S3 -2 + 5x = 7Type II V/S1 + S2 = S3 x/3 + 1 = 4Type III S1/V = S2 -6/x = 3
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Stoichiometry Problem
How many moles of atomic oxygen (O) are in 250 grams of P4O10? (Hint: the molecular weight of P4O10 is 283.88 g P4O10 / mol P4O10.)
Skills Unit conversion: 0.6 kg H2O = 600 g H2O Molecular weight: There are 2 moles of P4O10 in 283.88 * 2 g
P4O10
Composition stoichiometry: There are 10 moles of O in each mole of P4O10
Types Type Skills NeededType I Unit conversionType II Unit conversion + Molecular weight
Type III Unit conversion + Molecular weight + Composition stoichiometry
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Problem OrdersBlocked-Ordering
CurriculaInterleaved-Ordering
Curricula
Type I Type I Type II Type II Type III Type III Type I Type II Type III Type I Type II Type III
Type I Type I Type III Type III Type II Type II Type I Type III Type II Type I Type III Type II
Type II Type II Type I Type I Type III Type III Type II Type I Type III Type II Type I Type III
Type II Type II Type III Type III Type I Type I Type II Type III Type I Type II Type III Type I
Type III Type III Type I Type I Type II Type II Type III Type I Type II Type III Type I Type II
Type III Type III Type II Type II Type I Type I Type III Type II Type I Type III Type II Type I
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Speed of Learning
Fraction Addition Equation Solving Stoichiometry
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Cause of the EffectSimStudent vs. Human Student
More controllableMore observable
Conjecture: Interleaved order Receive feedback from all three
types
Blocked order Receive feedback from some types
Interleaved order More explicit negative feedback More effective learning
Type I Type II Type III
Type I Type II Type III Type I Type II Type III
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Explicit Negative Feedback
More negative feedback More effective precondition learning
Opportunities to expose to over-general preconditions
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ExampleE.g., S1+S2V=S3 (Type I)
Subtract both sides by S1
Subtract both sides by Si, if Si is a signed number &
there is a “+”
Negative feedback: Subtract both sides of S1/V=S2 by V or
S1 (Type III)
Subtract both sides by S1Subtract both sides by Si, if Si is a signed number
Negative feedback: Subtract both sides of S1V+S2=S3 by
S1V (Type I)
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SummaryInterleaved order More negative feedback
Better precondition learningSimStudent with limited memory
Blocked order More training examples Better function sequence learning
Future studiesGenerality across problem setsSimStudent with limited memoryA study on human students
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