Student masters skills by interacting with and adaptive spacing system. This system chooses each exercise per each iteration in a manner that it will optimize utility function l which in turn rewards long-term mastery of Knowledge Components(KCs). After getting students answer, corresponding updates are made.

As the authors claim: "In a nutshell, our present research goal is to maximize mastery and memory of a fixed set of skills among students during a given time interval while minimizing the time spent studying."

This assumptions are made:

1. information to learn and remember consists in a set of skills $k\in [1, K]$
2. skill mastery and memorization of student s at time t is measured by the ability of s to answer an (unseen) item involving that skill, i.e. by their ability to generalize to unseen material
3. students first have access to some theoretical knowledge about skills, but learning happens with retrieval practice
4. items are tagged with one or multiple skills and this information is synthesized inside a binary q-matrix
5. students forget: skill mastery decreases as time goes by since last practice of that skill