Because interaction is the only observable information people have about teaching processes, it follows that the primary aspect of intelligent tutoring systems (ITS) is interaction, and that future work on domains or student models should be driven by the needs identified in the study of interaction. This paper begins by examining the idea of teaching styles in terms of the implications that they have for types of interaction between student and machine. The second and third sections describe the teaching knowledge of two existing ITS systems, IMPART and Dominie, which are models of interaction. It is noted that the interaction in IMPART is based on cognitive models of dialogue in humans, while the interaction in Dominie is based on cognitive models of thinking. Subsequent sections relate these systems to current studies of dialogue, and a set of components is proposed that must exist in a tutoring system if it is to support the kinds of interaction described. It is concluded that the proposed model requires approaching interaction as a planning process in which multiple plans are created simultaneously at a variety of levels of abstraction and completeness. (27 references) (DB)