Learning games typically employ adaptation rules such as increasing the difficulty of the learning tasks after correct answers and decreasing it after incorrect answers so as to maintain a certain prescribed success rate. However, even though a success rate within certain bounds may be necessary, the ad hoc adaptation rules are in fact not very efficient for reaching it, and any success rate by itself cannot guarantee good learning results. Thus, a more general principle for adaptation is called for. In this work, we approach the problem from the mathematically solid foundation of Bayesian adaptive estimation. Our key hypothesis is that the contents for learning tasks that yield the most *new* information about the skills of the child, while being desirable for measurement in their own right, would also be among those that are effective for learning. Indeed, optimization of the informativity appears to naturally avoid tasks that are exceedingly difficult or exceedingly easy as the model can predict the results of such tasks to be correct or incorrect, respectively, and so the actual answers would yield little new information. However, as failures can easily lower motivation, we propose the more child friendly objective of optimizing the expected information gain divided by the expected failure rate, i.e., the cost of the information is measured as the number of failures. |