Intelligent Tutoring systems (ITSs) and Intelligent Learning Environments (ILEs) have been developed and evaluated over the last 40 years. Recent meta-analyses show that they perform well enough to act as effective classroom assistants under the guidance of a human teacher. Despite this success, they have been criticised as embodying a retrograde behaviourist technology. They have also been caught up in broader controversies about the role of Artificial Intelligence in society and about the entry of big data companies into the education market and the harvesting of learner data. This paper concentrates on rebutting the criticisms of the pedagogy of ITSs and ILEs. It offers examples of how a much wider range of pedagogies are available than their critics claim. These wider pedagogies operate at both the screen level of individual systems, as well as at the classroom level within which the systems are orchestrated by the teacher. It argues that there are many ways that such systems can be integrated by the teacher into the overall experience of a class. Taken together, the screen-level and orchestration-level dramatically enlarge the range of pedagogies beyond what was possible with the "Skinner Box."