| Abstract: | A mathematical model for computer-aided instruction is developed. It is assumed that the course is divided into a hierarchy of levels of difficulty. These levels are such that if a student is able to perform successfully at a given level of difficulty, he can also perform successfully at all levels of lesser difficulty. Furthermore, if student performs successfully at one level, it increases his probability of being able to perform successfully at the next higher level of difficulty. Given the initial vector of probabilities for successful performance at each level, the vector describing how these probabilities change with successful performances at each level, and the expected times it takes to attempt a successful performance at each level, this model computes an instructional sequence that minimizes the expected time required for the student to complete the course by performing successfully at the highest level of difficulty. Dynamic programming is used to find this sequence. |
