Gifted students' individual differences in distance-learning computer-based calculus and linear algebra

We examine student performance in computer-based calculus and linear algebra courses offered by Stanford University to pre-college students of high mathematical ability. Our analysis puts special emphasis on modeling student performance over time and on capturing long-term trend effects. The sequential nature of students' responses to course exercises is characterized through the use of stochastic and nonlinear models. We find that student performance varies widely within this group for a variety of different measures, including error rates, times to completion, progress rates, and latency of response. In addition, we measure the informational efficiency of the courses through a Markov order analysis of student response sequences. For the performance measures studied, the 75th and the 25th percentile of sampled values differ by a factor of approximately two. We also find that there is little correlation among the performance measures, which suggests that student performance in this ability range may not be well characterized by any single performance measure or ability parameter.