AbstractThe main task of an educational system is to generate instructional situations which induce students to learn knowledge and problem solving abilities as applied to a cognitive domain.To this end, an instructional dialogue must be seen as a process aimed at making student and teacher learn from each other: the student has to learn the subject matter from the teacher, while the teacher has in turn to learn from the student how to regulate instructional interaction. The process relies on different kinds of expert knowledge: experience of the domain, about the actual student, and of teaching methods and objectives. This means that an instructional dialogue cannot be realised without an explicit representation of all the kinds of knowledge involved.Research has established that Knowledge Based Educational Systems (KBESs) can be the keystone in building effective learning tools, but because of the difficulty in realising a system of this kind, most existing systems are prototypes and are intended only as workbenches for the computational analysis of educational processes.This paper analyses the main problems which underlie the realisation of such systems, with reference to research into knowledge based systems intended for use with teaching/learning mathematics.