  Adaptive learning aims to provide customized educational activities (e.g.,
exercises) to address individual learning needs. However, manual construction
and delivery of such activities is a laborious process. Thus, in this paper, we
study a novel task of adaptive and personalized exercise generation for online
language learning. To this end, we combine a knowledge tracing model that
estimates each student's evolving knowledge states from their learning history
and a controlled text generation model that generates exercise sentences based
on the student's current estimated knowledge state and instructor requirements
of desired properties (e.g., domain knowledge and difficulty). We train and
evaluate our model on real-world learner interaction data from Duolingo and
demonstrate that LMs guided by student states can generate superior exercises.
Then, we discuss the potential use of our model in educational applications
using various simulations. These simulations show that our model can adapt to
students' individual abilities and can facilitate their learning efficiency by
personalizing learning sequences.
