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

2. 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

3. 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

4. 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

5. 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....

6. Algebra Cognitive Tutor Use graphs, graphics calculator Analyze real world problem scenarios Use table, spreadsheet Use equations, symbolic calculator Tracked by knowledge tracing Model tracing to provide context-sensitive Instruction

7. 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

8. Replicated Field Studies Controlled, full year classroom experiments Replicated over 3 years in urban schools In 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.

9. 300+ Schools in 2000-01 700+ 2001-02 1080? 2002-03

10. Combining Theory & Practice

11. A Simple Instructional Design Principle Instruction is most effective when it builds on what students already know Sequence instruction from easy to hard

12. 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

13. Typical textbook strategy

14. Informal Strategies

15. Students are still learning the foreign language of algebra!

16. Expert Blindspot: Expertise can impair judgment of student difficulties 0 10 20 30 40 50 60 70 80 90 100 Elementary Teachers Middle School Teachers High School Teachers % making correct ranking (equations hardest)

17. Expert Blindspot Experts’ 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

18. 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

19. Combining Theory & Practice

20. 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.

21. 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 = d Strategy 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

22. 3(2x - 5) = 9 6x - 15 = 92x - 5 = 36x - 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) = 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 Model Tracing: Follows student through their individual approach to a problem -> context-sensitive instruction

23. 3(2x - 5) = 9 6x - 15 = 92x - 5 = 36x - 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) = d Then rewrite as abx + ac = d If goal is solve a(bx+c) = d Then 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 to multiply c by a also.” Knowledge Tracing: Assesses student's knowledge growth -> individualized activity selection and pacing Known? = 85% chanceKnown? = 45%

24. The Rules of Mathematics Thinking ≠ The Rules of Mathematics Leads to order of operations error: “x * 3 + 4” is rewritten as “x * 7” Works for “2x + 3x” but not for “x + 3x” 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” Production rules are not textbook rules, but “theorems in action” that characterize common thinking patterns

25. 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