Estimating time-related decline from mathematics platform logs: rapid repetition, learner variation, and model-implied review intervals

Introduction Digital mathematics platforms record repeated encounters with previously practiced knowledge, but these records combine rapid repetitions with retrieval after longer delays. This study examined how different revisit intervals affect estimates of time-related decline in response correctness and the review intervals derived from these estimates. Methods We analyzed repeated learner–knowledge component (KC) encounters in the public Junyi Academy Online Learning Activity Dataset. Exponential, power-law, and hyperbolic retention curves were compared using revisits separated by at least 1 h. A generalized linear model estimated the association between elapsed time and response correctness while adjusting for prior encounters, previous correctness, and KC differences. Learner-level decay estimates were used to calculate model-implied review intervals. A sensitivity analysis further examined learner-specific time slopes after accounting for practice history, previous correctness, KC effects, and learner baselines, with predictive performance evaluated on later responses. Results When all positive revisit delays were included, each additional day was associated with almost no change in the odds of a correct response (odds ratio = 0.9973). The estimated decline became more pronounced after rapid repetitions were excluded, reaching an odds ratio of 0.9706 for intervals of at least 1 day. Exponential and hyperbolic curves showed nearly equivalent fits for revisits separated by at least 1 h. Unadjusted learner-level estimates yielded a median model-implied review interval of 6.21 days, with an interquartile range of 2.12-16.66 days. After adjustment, learner-specific time slopes were weakly associated with the unadjusted decay estimates and did not improve prediction of subsequent responses. Discussion Rapid repetitions substantially influence estimates of time-related decline derived from mathematics platform logs. Although learner-level retention curves can be used to calculate review intervals, these intervals remain model-derived estimates rather than validated scheduling recommendations. Further learner–KC-level estimation and prospective validation are needed to determine whether the proposed intervals can reliably support personalized review scheduling.