Modernization of the educational systems can be understood as a conscious solvation of the discrepancy between the increasing demands of the society on education, and the limits of learning capacities of the man and the educational institutions. Modernization of a university subject has certain specifications if compared with that at basic and secondary schools which were centrally and methodologically catered for, and moreover provided with relevant text-books and teaching aids.
As for the future it will not be possible to be at peace with arbitrariness and spontaneity with which both the modernization of mathematical subject at technical universities and colleges, and the evaluation of the phenomena concerning education and the teaching have been so far approached.
Some of the contemporary global analyses indicate that the educational system needs fundamental changes. Experiences have revealed that radical and strictly controlled modernization might bring about a considerable damage. For that reason we claim a process of modernization that would be gradual, applied in checked steps and stages. We solve problems such as the Weltanschauung in mathematics, the students’ transition from secondary schools to universities, the exploitation of up-to-date didactic and calculation technologies which shlould suport the teaching. In mathematics at universities and colleges we struggle for the development of of the theory of the teaching of this subject and its more consequentional applying in the practice.
Also some results of our researches are briefly presented in the article. The direction of the further modernization are marked here out. Fundamental qualitative changes can be expected, especially in a broader exploitation of the calculation technology in the educational process.