The article discusses the history of the development of the problem of using artificial intelligence systems in education and pedagogic. Two directions of its development are shown: “Computational Pedagogic” and “Educational Data Mining”, in which poorly studied aspects of the internal mechanisms of functioning of artificial intelligence systems in this field of activity are revealed. The main task is a problem of interface of a kernel of the system with blocks of pedagogical and thematic databases, as well as with the blocks of pedagogical diagnostics of a student and a teacher. The role of the pedagogical diagnosis as evident reflection of the complex influence of factors and reasons is shown. It provides the intelligent system with operative and reliable information on how various reasons intertwine in the interaction, which of them are dangerous at present, where recession of characteristics of efficiency is planned. All components of the teaching and educational system are subject to diagnosis; without it, it is impossible to own any pedagogical situation optimum. The means in obtaining information about students, as well as the “mechanisms” of work of intelligent systems based on innovative ideas of advanced pedagogical experience in diagnostics of the professionalism of a teacher, are considered. Ways of realization of skill of the teacher on the basis of the ideas developed by the American scientists are shown. Among them, the approaches of researchers D. Rajonz and U. Bronfenbrenner who put at the forefront the teacher’s attitude towards students, their views, intellectual and emotional characteristics are allocated. An assessment of the teacher’s work according to N. Flanders’s system, in the form of the so-called “The Interaction Analysis”, through the mechanism of fixing such elements as: the verbal behavior of the teacher, events at the lesson and their sequence is also proposed. A system for assessing the professionalism of a teacher according to B. O. Smith and M. O. Meux is examined — through the study of the logic of teaching, using logical operations at the lesson. Samples of forms of external communication of the intellectual system with the learning environment are given. It is indicated that the conclusion of the found productive solutions can have the most acceptable and comfortable form both for students and for the teacher in the form of three approaches. The first shows that artificial intelligence in this area can be represented in the form of robotized being in the shape of a person; the second indicates that it is enough to confine oneself only to specially organized input-output systems for targeted transmission of effective methodological recommendations and instructions to both students and teachers; the third demonstrates that life will force one to come up with completely new hybrid forms of interaction between both sides in the form of interactive educational environments, to some extent resembling the educational spaces of virtual reality.