Logistic Knowledge Tracing: A Constrained Framework for Learner Modeling

Adaptive learning technology solutions often use a learner model to trace learning and make pedagogical decisions. The present research introduces a formalized methodology for specifying learner models, Logistic Knowledge Tracing (LKT), that consolidates many extant learner modeling methods. The strength of LKT is the specification of a symbolic notation system for alternative logistic regression models that is powerful enough to specify many extant models in the literature and many new models. To demonstrate the generality of LKT, we fit 12 models, some variants of well-known models and some newly devised, to 6 learning technology datasets. The results indicated that no single learner model was best in all cases, further justifying a broad approach that considers multiple learner model features and the learning context. The models presented here avoid student-level fixed parameters to increase generalizability. We also introduce features to stand in for these intercepts. We argue that to be maximally applicable, a learner model needs to adapt to student differences, rather than needing to be pre-parameterized with the level of each student's ability.