Аннотация:The emphasis laid upon the skills of numerical calculations and algebraic transformations, which dominated the pre-computer era, is gradually losing its significance. Today mathematical education is viewed as aiming at the formation of scientific thinking skills. The paper suggests an approach to mathematical education based on the concept of object-oriented mediation. The characteristic feature of this approach consists in that the student is placed in conditions similar to those that historically led to the formation of new sections of mathematics.