Revisiting the Regularity of Student Learning Rate: Sensitivity to Which Observations Are Included
In student learning data, the number of practice opportunities a student accumulates on a given skill varies substantially and is rarely independent of the learning process itself. Despite a well-established statistical literature on the consequences of such imbalance for longitudinal parameter estimation, this structural feature of learning data has not been examined as a threat to inference in student models. Using the 26 datasets and modeling framework from Koedinger et al. (2023)---who reported an ``astonishing regularity'' in student learning rates---we show that estimated learning-rate variability is sensitive to practice sequence length structure in ways that are substantial and systematic. Progressive truncation analysis reveals that estimated heterogeneity declines as observation windows expand across the vast majority of datasets. A closer examination shows that shorter and extended sequences differ meaningfully in their estimated learning trajectories, and that excluding sequences longer than ten opportunities increases median estimated learning-rate variability by 75\%, while excluding sequences longer than five increases it by 205\%. These findings identify unbalanced practice depth as an unexamined but consequential feature of student learning data, and raise important questions about the validity of learning-rate estimates from observational data more broadly.
Authors
Hansol Lee, Guilherme Lichand, Cristina Barnard, Lucas Klotz, Candace Thille, Yunsung Kim, Benjamin W. Domingue