Authoring Model-Tracing Tutors
For almost ten years, Carnegie Mellon University and now Carnegie Learning have been producing software and curriculum focused on high school mathematics. Our products are called Cognitive Tutors®, to reflect their basis in cognitive science research and their use of intelligent tutoring systems to guide student problem solving. We believe that the Cognitive Tutor products represent a unique approach to the use of technology in mathematics education. These products include Cognitive Tutor Algebra I (Koedinger, Anderson, Hadley, & Mark, 1997), Cognitive Tutor Geometry (Aleven, Koedinger, Sinclair, & Snyder, 1998) and Cognitive Tutor Algebra II (Corbett, Trask, Scarpinatto and Hadley, 1998), in addition to variants appropriate for integrated math and intermediate college algebra. Each of these products consists of software, print materials (equivalent to a textbook, homework assignments, teacher’s guide, etc.) and teacher training. Our intent is that each of these products provide teachers with all the materials and support they need to teach an entire mathematics course. Typically, students in the Cognitive Tutor courses spend 40% of their time in the computer lab. This represents a significant proportion of the students’ time in the course, and reflects the belief that students’ use of this software is essential to their success. The software automatically tracks the progress of student understanding over time and controls pacing through the software curriculum. This allows students entering the lab to begin working where they had left off at the end of their previous session and proceed through the materials at their own pace. Because the software comes to “know” the student over the course of a full year, it can effectively drive the pace and focus of the classroom implementation.
In this paper, I discuss the basic approach to instruction embodied in the Cognitive Tutor software, describe ways in which practical requirements of the software have resulted in deviations from the intended model and
then talk about approaches to authoring model-tracing tutors.