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The base paper reports on an experiment of intelligent tutoring in three urban high schools in Pittsburgh. An intelligent tutor has been made a part of 9th grade algebra, accompanying a new algebra curriculum focused on mathematical analysis of real world situations and the use of computations tools. The 470 students in experimental classes outperformed students in comparison classes by 15% on standardized tests and 100% on tests targeting the PUMP objectives. The first auxiliary paper by Anderson describes the cognitive basis for intelligent tutors, from theory to model-tracing methodology, to issues that arise in implementation. The second auxiliary paper by VanLehn describes the lessons learned in developing and testing a cognitive tutor for physics at the U.S. Naval Academy. In particular, this system was designed to run as part of a course with minimal invasion of curricular design. Interestingly, the intelligent tutors for both algebra and physics, based on different models and designed for different educational contexts, had almost identical results.

It was amazing to see the long history of work on intelligent tutors, the scientific progress and implementation in schools across the country. The cognitive basis for such models is fascinating, tracing students' cognitive states in real time and modeling their knowledge as they learn new material. Yet, interaction with the tutor is simple: the tutor silently observes the students strategy, until the student asks for help or makes a mistake, and provides immediate feedback. This helps increase the quality and speed of learning as well as positively reinforce the joy (rather than the struggle) involved, keeping students motivated and moving in the right direction as they develop their problem-solving skills. However, its clear that there is a lot of work still remaining. Despite having a long history, the number of researchers in this area remains relatively small and the challenges ahead of them are large (including technical and political/social challenges).

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- 1. Cognitive Modeling and Intelligent Tutors Cody A. Ray Base slides adopted from Ken Koedinger’s presentation for 2011 Franklin Award for John R. Anderson
- 2. Goals of Intelligent Tutoring <ul><li>Automate education. Private tutors=$$$ </li></ul><ul><li>Explore epistemological issues related to the knowledge being tutored and how it can be learned.* </li></ul>Anderson, Boyle, Corbett, & Lewis. Cognitive modeling and intelligent tutoring. Artificial Intelligence . 42 (1990) 7-49 * Intelligent tutoring is used to test cognitive theories, such as ACT-R
- 3. Cognitive Modeling <ul><li>Performance models of executing skills </li></ul><ul><ul><li>Correct & incorrect rules to perform skills </li></ul></ul><ul><ul><li>Model tracing : follow in real-time the cognitive states the student goes through in solving the problem </li></ul></ul><ul><li>Learning models of how skills acquired </li></ul><ul><ul><li>Assumptions about how knowledge state changes after each step in solving problem </li></ul></ul><ul><ul><li>Knowledge tracing : track changes in student’s knowledge across problems </li></ul></ul>
- 4. Real World Impact of Cognitive Science (PAT) <ul><li>Algebra Cognitive Tutor </li></ul><ul><li>Based on computer model of student learning </li></ul><ul><li>Used in 2600 schools 500,000 students </li></ul><ul><li>Spin-off: </li></ul>Koedinger, Anderson, Hadley, & Mark (1997). Intelligent tutoring goes to school in the big city.
- 5. Cognitive Tutor Algebra: Problems that engage intuition & interest Health Care Extinction Smoking Risks Importance of Math Education
- 6. Algebra Cognitive Tutor Sample Analyze real world problem scenarios Tracked by knowledge tracing Model tracing to provide context-sensitive Instruction Use graphs, graphics calculator Use table, spreadsheet Use equations, symbolic calculator
- 7. ACT-R: A Cognitive Theory of Learning and Performance <ul><li>Big theory … key tenets: </li></ul><ul><ul><li>Learning by doing in addition to watching & listening </li></ul></ul><ul><ul><li>Production rules represent performance knowledge: </li></ul></ul><ul><ul><li>These units are: Instruction implications: </li></ul></ul><ul><ul><ul><li>modular </li></ul></ul></ul><ul><ul><ul><li>context specific </li></ul></ul></ul>isolate skills, concepts, strategies address "when" as well as "how" Anderson, J.R., & Lebiere, C. (1998). Atomic Components of Thought . Erlbaum.
- 8. Learning in ACT-R <ul><li>Declarative Knowledge and Productions </li></ul><ul><li>Productions </li></ul><ul><ul><li>by-product of interpretive use of declarative knowledge. Highly efficient, use-specific </li></ul></ul><ul><li>Knowledge Compilation </li></ul><ul><ul><li>learning process which creates productions </li></ul></ul><ul><li>Tutoring </li></ul><ul><ul><li>create experiences to acquire production rules of a competent problem solver </li></ul></ul>
- 9. <ul><li>Cognitive Model : A system that can solve problems in the various ways students can </li></ul><ul><ul><li>Strategy 1: IF the goal is to solve a(bx+c) = d </li></ul></ul><ul><ul><li> THEN rewrite this as abx + ac = d </li></ul></ul><ul><ul><li>Strategy 2: IF the goal is to solve a(bx+c) = d </li></ul></ul><ul><ul><ul><li>THEN rewrite this as bx + c = d/a </li></ul></ul></ul><ul><ul><li>Misconception: IF the goal is to solve a(bx+c) = d </li></ul></ul><ul><ul><li>THEN rewrite this as abx + c = d </li></ul></ul>Cognitive Tutor Technology Apply ACT-R to individualize instruction Anderson, J. R., Corbett, A. T., Koedinger, K. R., & Pelletier, R. (1995). Cognitive tutors: Lessons learned. The Journal of the Learning Sciences , 4 (2) 167-207
- 10. Cognitive Tutor Technology Use cognitive model to individualize instruction <ul><li>Cognitive Model : A system that can solve problems in the various ways students can </li></ul>3(2x - 5) = 9 6x - 15 = 9 2x - 5 = 3 6x - 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 <ul><li>Model Tracing : Follows student through their individual approach to a problem -> context-sensitive instruction </li></ul>Anderson, J. R., Corbett, A. T., Koedinger, K. R., & Pelletier, R. (1995). Cognitive tutors: Lessons learned. The Journal of the Learning Sciences , 4 (2) 167-207
- 11. Cognitive Tutor Technology Use cognitive model to individualize instruction <ul><li>Cognitive Model : A system that can solve problems in the various ways students can </li></ul>3(2x - 5) = 9 6x - 15 = 9 2x - 5 = 3 6x - 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 <ul><li>Model Tracing : Follows student through their individual approach to a problem -> context-sensitive instruction </li></ul><ul><li>Knowledge Tracing : Assesses student's knowledge growth -> individualized activity selection and pacing </li></ul>Anderson, J. R., Corbett, A. T., Koedinger, K. R., & Pelletier, R. (1995). Cognitive tutors: Lessons learned. The Journal of the Learning Sciences , 4 (2) 167-207 Hint message: “Distribute a across the parentheses.” Bug message: “You need to multiply c by a also.” Known? = 85% chance Known? = 45%
- 12. Cognitive Tutor Algebra course yields significantly better learning <ul><li>Course includes text, tutor, teacher professional development </li></ul><ul><li>8 of 10 full-year controlled studies demonstrate significantly better student learning </li></ul>Koedinger, Anderson, Hadley, & Mark (1997). Intelligent tutoring goes to school in the big city.
- 13. Andes Physics Tutoring <ul><li>Upgrading homework support only </li></ul><ul><ul><li>Same problems, exams, lectures, etc. </li></ul></ul><ul><ul><li>other existing physics courses can use it </li></ul></ul><ul><ul><li>Different cognitive models, tutoring system, and context </li></ul></ul><ul><ul><li>same results! </li></ul></ul>
- 14. Koedinger vs Andes <ul><li>Conceptual understanding * </li></ul><ul><li>Multiple-choice standardized tests * </li></ul><ul><li>* effect size </li></ul><ul><li>Yet Koedinger changed curriculum and tutoring, while Andes only changed the way students completed homework. </li></ul>Koedinger 1.2 0.7 Andes 1.21 0.69 Koedinger 0.3 0.3 Andes 0.25 -
- 15. Summary <ul><li>Intelligent tutors provide evidence for underlying cognitive theory (eg, ACT-R) </li></ul><ul><li>Personalized tutors enhance learning </li></ul><ul><ul><li>Examples: Algebra Tutor, Physics Tutor </li></ul></ul><ul><li>Cognitive tutoring might help independently of curricular reform </li></ul><ul><ul><li>Can be used more widely, helping students in both reformed and traditional courses </li></ul></ul>
- 16. Thank you! <ul><li>Acknowledgements </li></ul><ul><li>Koedinger, Anderson, Hadley, & Mark (1997). Intelligent tutoring goes to school in the big city. Artificial Intelligence in Education. 8 (1997) 30-43 </li></ul><ul><li>Anderson, Boyle, Corbett, & Lewis. Cognitive modeling and intelligent tutoring. Artificial Intelligence . 42 (1990) 7-49 </li></ul><ul><li>VanLehn, Lynch, Schulze, Shapiro, Shelby, Taylor, Treacy, Weinstein, & Wintersgill. The Andes Physics Tutoring System: Lessons Learned. Artificial Intelligence in Education . 15 (2005) 147-204 </li></ul>

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