Tuteurs cognitifs: La théorie ACT-R et les systèmes de production Roger Nkambou.

Tuteurs cognitifs: La théorie ACT-R et les systèmes de production

Roger Nkambou

What is a “Cognitive Model”?

A simulation of human thinking & resulting behaviorUsually 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 softwareUses 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 CaseCognitive 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 EdMost cited Journal of AI-ED paper

Koedinger, Anderson, Hadley, & Mark (1997). Intelligent tutoring goes to school in the big city.

. . .

Algebra Cognitive Tutor

Use graphs, graphics calculatorUse graphs, graphics calculator

Analyze real world Analyze real world problem scenariosproblem scenarios

Use table, Use table, spreadsheetspreadsheet

Use equations, Use equations, symbolic symbolic calculatorcalculator

Tracked by Tracked by knowledge tracingknowledge tracing

Model tracing to provide Model tracing to provide context-sensitive context-sensitive InstructionInstruction

Cognitive Tutor AlgebraCourse

Integrated tutor, text, and teacher trainingIn computer lab 2 days/week, classroom 3 days/weekLearn by doing:

Project-based Student-centered Cooperative learning Teacher as facilitator

Replicated Field StudiesControlled, full year classroom experimentsReplicated over 3 years in urban schoolsIn Pittsburgh & Milwaukee

Results:50-100% better on problem solving & representation use.

15-25% better on standardized tests.

Koedinger, Anderson, Hadley, & Mark (1997). Intelligent tutoring goes to school in the big city. International Journal of Artificial Intelligence in Education, 8.

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Iowa SAT subset ProblemSolving

Represent-ations

Traditional Algebra Course

Cognitive Tutor Algebra

300+ Schools in 2000-01700+ 2001-02

1080? 2002-03

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CognitiveTutorTechnology

Algebra I GeometryEquationSolver

Algebra II

Cognitive Tutors

ArtificialIntelligence

CognitivePsychology

Research base

Math InstructorsMath EducatorsNCTM Standards

Curriculum Content

Combining Theory & Practice

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

x * 6 + 66 = 81.90

Typical textbook strategy

Informal Strategies

Students are still learning the foreign language of algebra!

Expert Blindspot:Expertise can impair judgment of student difficulties

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ElementaryTeachers

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% makingcorrectranking

(equations hardest)

Nathan, M. J. & Koedinger, K. R. (2000). An investigation of teachers' beliefs ofstudents' algebra development. Cognition and Instruction, 18(2), 207-235

Expert BlindspotExperts’ judgments are biased by self-assessing 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

CognitiveTutorTechnology

Algebra I GeometryEquationSolver

Algebra II

Cognitive Tutors

ArtificialIntelligence

CognitivePsychology

Research base

Math InstructorsMath EducatorsNCTM Standards

Curriculum Content

Combining Theory & Practice

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, strategiesaddress "when" as well as "how"

Anderson, J.R., & Lebiere, C. (1998). Atomic Components of Thought. Erlbaum.

Cognitive Model: A system that can solve problems in the various ways students can

Strategy 1: IF the goal is to solve a(bx+c) = d THEN rewrite this as abx + ac = dStrategy 2: IF the goal is to solve a(bx+c) = d

THEN rewrite this as bx + c = d/a

Misconception: IF the goal is to solve a(bx+c) = d THEN rewrite this as abx + c = d

Cognitive Tutor Technology:Use ACT-R theory to individualize instruction

ACT-R production rules are not textbook rules, but “theorems in action” that characterize common thinking patterns

3(2x - 5) = 9

6x - 15 = 9 2x - 5 = 3 6x - 5 = 9

Cognitive Tutor Technology:Use ACT-R theory to individualize instruction

Cognitive Model: A system that can solve problems in the various ways students can

If goal is solve a(bx+c) = dThen rewrite as abx + ac = d

If goal is solve a(bx+c) = dThen rewrite as abx + c = d

If goal is solve a(bx+c) = dThen rewrite as bx+c = d/a

Model Tracing: Follows student through their individual approach to a problem -> context-sensitive instruction

3(2x - 5) = 9

6x - 15 = 9 2x - 5 = 3 6x - 5 = 9

Cognitive Tutor Technology:Use ACT-R theory to individualize instruction

Cognitive Model: A system that can solve problems in the various ways students can

If goal is solve a(bx+c) = dThen rewrite as abx + ac = d

If goal is solve a(bx+c) = dThen rewrite as abx + c = d

Model Tracing: Follows student through their individual approach to a problem -> context-sensitive instruction

Hint message: “Distribute a across the parentheses.”

Bug message: “You need tomultiply c by a also.”

Knowledge Tracing: Assesses student's knowledge growth -> individualized activity selection and pacing

Known? = 85% chance Known? = 45%

The Rules of Mathematics Thinking≠The Rules of Mathematics

Leads to order of operationserror:“x * 3 + 4” is rewritten as “x * 7”

Works for “2x + 3x” but not for “x + 3x”

Overly general productionIF “Num1 + Num2” appears

in an expressionTHEN

replace it with the sum

Overly specific productionIF “ax + bx” appears in an

expression and c = a + bTHEN

replace it with “cx”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