This article sets out some of the rationale and arguments for making major changes to the teaching and learning of statistical inference in introductory courses at our universities by changing from a norm-based, mathematical approach to more conceptually accessible computer-based approaches. The core problem of the inferential argument with its hypothetical probabilistic reasoning process is examined in some depth. We argue that the revolution in the teaching of inference must begin. We also discuss some perplexing issues, problematic areas and some new insights into language conundrums associated with introducing the logic of inference through randomization methods. (Contains 2 figures.)