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Tuteurs cognitifs: La théorie
ACT-R et les systèmes de
production
Roger Nkambou
What is a “Cognitive Model”?
A simulation of human thinking & resulting
behavior
Usually used to explain or predict data on
human behavior

Like error rates or solution time
Usually implemented as a computer program
that can behave like humans

Often using AI knowledge representations like
semantic nets, frames, schema, production rules
What are Cognitive Models
used for?
Output of basic research

Explain results of psychology experiments
Guide design of software systems

Have cognitive model “use” the system
 Model predicts people’s time & errors(VanLehn)
 Redesign system to reduce time or errors

Can derive predictions without full implementation
(e.g., Ethan)
As a component in an intelligent system


Player in a game or training simulation
Part of expert system or intelligent tutor
What is an “Intelligent
Tutoring System” (ITS)?
A kind of educational software
Uses artificial intelligence techniques to



Provide human tutor-like behavior
Be more flexible, diagnostic & adaptive
Write more general code to get more capabilities
with less effort
Components of an ITS:

Interface or problem solving environment, domain
knowledge, student model, pedagogical (tutoring)
knowledge
An ITS Success Case
Cognitive Tutor Algebra (aka Pump)
Most widely used ITS


1000+ schools across the country
Marketed by local spin-off company
Carnegie Learning
“Exemplary Curricula” by US Dept of Ed
Most cited Journal of AI-ED paper

Koedinger, Anderson, Hadley, & Mark (1997). Intelligent
tutoring goes to school in the big city.
...
Algebra Cognitive Tutor
Analyze real world
problem scenarios
Use graphs, graphics calculator
Use table, spreadsheet
Use equations,
symbolic calculator
Model tracing to provide
context-sensitive Instruction
Tracked by
knowledge tracing
Cognitive Tutor Algebra
Course
Integrated tutor, text, and teacher training
In computer lab 2 days/week, classroom 3
days/week
Learn by doing:




Project-based
Student-centered
Cooperative learning
Teacher as facilitator
Replicated Field Studies
Controlled, full year classroom experiments
Replicated over 3 years in urban schools
60
In Pittsburgh
Traditional Algebra Course
& Milwaukee
50
Results:
50-100% better on
problem solving &
representation use.
15-25% better on
standardized tests.
Cognitive Tutor Algebra
40
30
20
10
0
Iowa
SAT subset
Problem
Solving
Koedinger, Anderson, Hadley, & Mark (1997). Intelligent tutoring goes to school
in the big city. International Journal of Artificial Intelligence in Education, 8.
Representations
1080?
700+
2002-03
2001-02
300+ Schools in 2000-01
b
Combining Theory &
Practice
Research base
Cognitive
Psychology
Artificial
Intelligence
Cognitive
Tutor
Technology
Curriculum Content
Math Instructors
Math Educators
NCTM Standards
Cognitive Tutors
Algebra I
Equation
Solver
Geometry
Algebra II
A Simple Instructional
Design Principle
Instruction is most effective when it
builds on what students already know
Sequence instruction from easy to hard
Difficulty Factors Assessment:
Which Problem Type is Hardest?
Story Problem
As a waiter, Ted gets $6 per hour. One
night he made $66 in tips and earned a
total of $81.90. How many hours did Ted
work?
Word Problem
Starting with some number, if I multiply it by
6 and then add 66, I get 81.90. What
number did I start with?
Equation
Typical textbook strategy
Informal Strategies
Students are still
learning the
foreign language
of algebra!
Expert Blindspot:
Expertise can impair judgment of student
difficulties
100
90
80
% making
correct
ranking
(equations
hardest)
70
60
50
40
30
20
10
0
Elementary
Teachers
Middle
School
Teachers
High School
Teachers
Nathan , M. J. & Koedinge r, K. R. (2000). An inve stigation of teacher s' beliefs of
students' algebra deve lopment. Cognition and Instruction, 18(2), 207-235
Expert Blindspot
Experts’ judgments are biased by selfassessing their own performance
Sources of bias in expert judgment:


Under-estimate novice’s intuitive,
concrete modes of thinking
Over-estimate ease in acquiring formal, abstract
modes of thinking
Result: Inaccurate evaluations, poor design
choices
What is the Student Like?
To avoid your expert blindspot,
remember:
“The Student Is Not Like Me”
Use Cognitive & HCI methods to find
out what students are like
b
Combining Theory &
Practice
Research base
Cognitive
Psychology
Artificial
Intelligence
Cognitive
Tutor
Technology
Curriculum Content
Math Instructors
Math Educators
NCTM Standards
Cognitive Tutors
Algebra I
Equation
Solver
Geometry
Algebra II
ACT-R: A Cognitive Theory of
Learning and Performance
Big theory … key tenets:

Learning by doing, not by listening or watching

Production rules represent performance knowledge:
These units are:
Instruction implications:
 modular
 context specific
isolate skills, concepts, strategies
address "when" as well as "how"
Anderson, J.R., & Lebiere, C. (1998). Atomic Components of Thought. Erlbaum.
Cognitive Tutor Technology:
Use ACT-R theory to individualize instruction
Cognitive Model: A system that can solve problems
in the various ways students can
Strategy 1:
Strategy 2:
Misconception:
IF the goal is to solve a(bx+c) = d
THEN rewrite this as abx + ac = d
IF the goal is to solve a(bx+c) = d
THEN rewrite this as bx + c = d/a
IF the goal is to solve a(bx+c) = d
THEN rewrite this as abx + c = d
ACT-R production rules are not textbook rules,
but “theorems in action” that characterize
common thinking patterns
Cognitive Tutor Technology:
Use ACT-R theory to individualize instruction
Cognitive Model: A system that can solve problems
in the various ways students can
3(2x - 5) = 9
If goal is solve a(bx+c) = d
Then rewrite as abx + ac = d
If goal is solve a(bx+c) = d
Then rewrite as abx + c = d
If goal is solve a(bx+c) = d
Then rewrite as bx+c = d/a
6x - 15 = 9
2x - 5 = 3
6x - 5 = 9
Model Tracing: Follows student through their
individual approach to a problem -> context-sensitive
instruction
Cognitive Tutor Technology:
Use ACT-R theory to individualize instruction
Cognitive Model: A system that can solve problems
in the various ways students can
3(2x - 5) = 9
If goal is solve a(bx+c) = d
Then rewrite as abx + ac = d
If goal is solve a(bx+c) = d
Then rewrite as abx + c = d
Hint message: “Distribute a
across the parentheses.”
Known? = 85% chance
Bug message: “You need to
multiply c by a also.”
Known? = 45%
6x - 15 = 9
2x - 5 = 3
6x - 5 = 9
Model Tracing: Follows student through their
individual approach to a problem -> context-sensitive
instruction
Knowledge Tracing: Assesses student's knowledge
growth -> individualized activity selection and pacing
The Rules of Mathematics Thinking
≠
The Rules of Mathematics
Overly general production
IF “Num1 + Num2” appears in
an expression
THEN
replace it with the sum
Overly specific production
IF “ax + bx” appears in an
expression and c = a + b
THEN
replace it with “cx”
Leads to order of operations
error:
“x * 3 + 4” is rewritten as
“x * 7”
Works for “2x + 3x”
but not for “x + 3x”
Production rules are not textbook rules,
but “theorems in action” that characterize
common thinking patterns
Multiple Uses of Cognitive
Model
Summarizes results of analysis of data on
student thinking
Is the “intelligence” in the tutor
Most importantly, provides guidance for all
aspects of tutor development

Interface, tutorial assistance, problem selection
and curriculum sequencing