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Intelligent Tutors for All:
the Constraint-based
Approach
Tanja Mitrovic
Intelligent Computer Tutoring Group
University of Canterbury
Intelligent Tutoring Systems
 Goal: one-to-one teaching without the expense of
human tutoring
 Simulate a human teacher
 Problem-solving environments (learning by doing)
 Based on Artificial Intelligence
 Student modeling
Student modeling
Data about user
System
Student
Model
Adaptation Effect
Architecture of ITSs
Domain
knowledge
Domain
module
Student
modeler
Pedagogical
module
Pedagogical
expertise
Student
Models
Interface
Communication
knowledge
Student
Learning from performance errors
 Ohlsson, 1992
 Declarative/procedural knowledge
 Constraints as a knowledge-representation formalism
 Constraints do not assert anything
 Constraints encode correctness for a domain
 “If the relevance condition R is true,
then the satisfaction condition S ought to be true,
otherwise something is wrong.”
 Constraints support judgment, not inference
Learning from performance errors
 Learning phases:
 Error detection
 Error correction
 How can we catch ourselves making errors?
 If the knowledge is there, then why the error?
 If not, then how is the error detected?
 CBM: domain and student modeling
Constraint-based Modeling
 The space of incorrect knowledge is vast
 Therefore: abstractions are needed
 Represent only basic domain principles
 Group the states into equivalence classes
according to their pedagogical importance
Constraint-Based Modeling
 Domain knowledge represented by a set of
constraints
 A constraint is a pattern of form <Cr, Cs>
 If a solution matches the Cr then it must also
match the Cs, else something is wrong
 “Innocent until proven guilty” approach
Example constraints
 If you are driving in New Zealand,
you better be on the left side of the road.
 If the current problem is a/b + c/d,
and the student’s solution is (a+c)/n,
then it had better be the case that n=b=d.
Advantages of CBM
 Very efficient computationally
 No need for a problem solver
 No need for a bug library
 Insensitive to the radical strategy variability
phenomenon
 Neutral with respect to pedagogy
Implications for ITS Design: CBM
 Represent the domain in terms of constraints
 Model the student in terms of constraints
 Pedagogy:
 Augment student’s constraint base
 When should the ITS take an initiative?
 What to instruction to deliver?
 Models of meta-cognitive skills
 Student’s meta-cognitive skills
CBM: Model the Student
 A violated constraint implies incomplete or
incorrect knowledge
 Short-term student model:
 the set of violated constraints
 the set of satisfied constraints
 No one-to-one mapping between problems and
constraints
 Long-term student model:
 Constraint histories (overlay/probabilistic)
CBM: Pedagogy
 Constraint-based tutors function by augmenting
the student’s own knowledge base
 Choose practice problems that exercise
constraints
 Interrupt when a constraint is violated
 Attach feedback messages to the constraints
 Tell the student which constraint he/she just
violated and how
History of ICTG
 SQL-Tutor
 Solaris (1997), Windows (1998), Web (1999)
 CAPIT (2000)
 KERMIT (2000)
 WETAS (2002)
 LBITS (2002)
 NORMIT (2002)
 ERM-Tutor (2003)
 COLLECT-UML (2005)
 ASPIRE, VIPER
 J-LATTE
 Thermo-Tutor
CAPIT
LBITS – elementary vocabulary
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Current work
 ASPIRE, VIPER
 Supporting meta-cognitive skills (selfexplanation, self-assessment …)
 Affective modeling and pedagogical agents
 Supporting multiple teaching strategies
 New ITSs