Reducing the Knowledge Tracing Space

In Cognitive Tutors, student skill is represented by estimates of student knowledge on various knowledge components. The estimate for each knowledge component is based on a four-parameter model developed by Corbett and Anderson [Nb]. In this paper, we investigate the nature of the parameter space defined by these four parameters by modeling data from over 8000 students in four Cognitive Tutor courses. We conclude that we can drastically reduce the parameter space used to model students without compromising the behavior of the system. Reduction of the parameter space provides great efficiency gains and also assists us in interpreting specific learning and performance parameters.