A review of cognitive modeling and intelligent tutors. Presentation based on three papers, summarized below. 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).

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

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