How to improve learning

There is a learning technique pioneered in language studies by Pimsleur which makes sense: You learn a word (or some other thing) and over time forget it, and the "forgetting curve" is steep. But, if you re-encounter that same information while the curve is descending you learn it again and the descent into nothingness is shallower. Encounter it again and the line flattens out. This is why if you take a Pimsleur language course, they tell you to NOT study ahead; You are to use each module daily, not skipping a day and not doing two modules in one day. Very nice idea but not mathematically rigorous.

But now we have this:

A dilemma faced by teachers, and increasingly by designers of educational software, is the trade-off between teaching new material and reviewing what has already been taught. Complicating matters, review is useful only if it is neither too soon nor too late. Moreover, different students need to review at different rates. We present a mathematical model that captures these issues in idealized form. The student's needs are modeled as constraints on the schedule according to which educational material and review are spaced over time. Our results include algorithms to construct schedules that adhere to various spacing constraints, and bounds on the rate at which new material can be introduced under these schedules.

The paper is here