We consider the concept classes of DNF formulas and unions of discretized, axis-parallel d-dimensional boxes in discretized d-dimensional space with respect to several different learning models. In the model of learning with queries we present an algorithm to learn unions of boxes. We introduce a model of teaching that prevents illicit communication between the teacher and the leaner but that captures the intuitive aspect of teaching: a learner should perform at least as well with a cooperative teacher as with an adversarial teacher. We propose the study of teaching of DNF formulas and unions of boxes in this model. We also propose a study of a teaching model in which the learner may be randomized. It is currently unclear if randomization of the learner allows teaching of classes that are unteachable in the current teaching model
