This level of mathematical training of entrants makes it almost impossible to train engineers, which are extremely necessary for the implementation of plans for innovative development of Ukraine.

Thus, society faces the problem of finding a mechanism of self-organization that will direct the most talented students and their parents, relatives to the systematic mastery of certain disciplines, and not just to successful testing within the EIE.

According to the author, it is possible to fulfill the task of training high-level specialists in priority specialties for Ukraine only if the problems of the state procurement system and the rules of admission to the HEI are solved.

Therefore, it is necessary to create such objective conditions that would guide learners and their parents from high school to the maximum use of the child’s natural abilities in certain areas of knowledge. It is critical to form in parents and students during their studies at school the desire to make the most of existing skills in the field of exact or humanities in the process of choosing a future specialty when entering the HEI.

Thus, it is necessary to start the mechanism of self-organization in the system «parents, students, schools». To this end, it is necessary to create such an atmosphere in the country that parents send their children to schools that provide systematic knowledge; they turned to tutors who form children’s ability to think systematically in general, and especially in those areas of knowledge that meet the strategic interests of the state.

To create such an atmosphere, it is necessary to transform public opinion. Today, it is strategically important to prepare the most capable students in the field of mathematics and natural sciences to work in certain areas of knowledge, recognized as a strategic priority in Ukraine.

We must also take into account that in our society the so-called «impression economy» prevails, in which the principle of «price – quality» ceases to play a decisive role in the process of choosing a specialty for a child when entering the HEI. Very often, entrants prefer not those specialties that have more government orders and lower tuition fees, and not those that are most in demand in the labor market, but those specialties that are considered prestigious from the public point of view. Examples are given in the previous section of this monograph.