Logic and mathematics are used to gain some insight into the effective and efficient application of instruction. A pupil's state of knowledge is represented by the degree of confidence he possesses in the subject matter. A cost, gain, and return from instruction are associated with each possible initial degree of confidence and each instructional sequence. Two group strategies, two individualized strategies, and a precisely-tailored instructional strategy are compared on the basis of expected return from instruction per individual strategy for seven distributions of initial knowledge. The relative effectiveness of instruction is found to depend critically upon the distribution of initial knowledge for the class of pupils. (Author)