The paper presents an analysis of directions of development of cognitive information technologies for mathematical education. Two aspects of the problem are highlighted, they are a simulation of mental processes of a student and a modeling of a subject area. The proposed concept of development of cognitive informational technologies is confirmed by a retrospective analysis of information technologies applications for learning mathematics in schools on the example of dynamic geometry. We present our results in the field of verification and generation of mathematical problems and in the usage of models of subject areas. We also present directions of the future work on development of proposed directions.