This paper introduces a new approach for machine teaching that partly addresses the (unavoidable) mismatch between what the teacher assumes about the learning process of the student and the actual process. We analyze several situations in which such mismatch takes place, including when the student?s learning algorithm is known but the corresponding parameters are not, and when the learning algorithm itself is not known. Our analysis is focused on the case of a Bayesian Gaussian learner, and we show that, even in this simple case, the lack of knowledge regarding the student?s learning process significantly deteriorates the performance of machine teaching: while perfect knowledge of the student ensures that the target is learned after a finite number of samples, lack of knowledge thereof implies that the student will only learn asymptotically (i.e., after an infinite number of samples). We introduce interactivity as a means to mitigate the impact of imperfect knowledge and show that, by using interactivity, we are able to recover finite learning time, in the best case, or significantly faster convergence, in the worst case. Finally, we discuss the extension of our analysis to a classification problem using linear discriminant analysis, and discuss the implications of our results in single- and multi-student settings.