Metacognitive Control and Optimal Learning

The notion of optimality is often invoked informally in the literature on metacognitive control. We provide a precise formulation of the optimization problem and show that optimal time allocation strategies depend critically on certain characteristics of the learning environment, such as the extent of time pressure, and the nature of the uptake function. When the learning curve is concave, optimality requires that items at lower levels of initial competence be allocated greater time. On the other hand, with logistic learning curves, optimal allocations vary with time availability in complex and surprising ways. Hence there are conditions under which optimal strategies will be intuitive and easy to learn, and others in which they will be considerably more complicated. The model can therefore be used to address the question of whether and when learners should be able to exercise good metacognitive control in practice.