This paper discusses a range of teaching styles possible for use in Intelligent Computer Aided Instruction (ICAI) and suggests that they may usefully be thought of as points within a framework of guided discovery teaching methods. The nature of guidance in tutoring and possible ways of providing guidance are discussed in the context of teacher-student relationships and the teaching interaction that occurs during an educational exchange. The use of Bounded User modelling within a guided discovery framework is introduced, and an application of the technique in a Lisp teaching system is described. Also mentioned are various instructional programmed tutoring systems including GUIDON, WHY, WEST, and IMPART. Extensions to the system to support more flexibility of teaching styles in conjunction with the user-modelling method are outlined. A complete list of CITE reports is included. (20 references) (Author/DB)