The article dwells on the issues of teaching mathematics as a subject training organisational process. Historical principles and tendencies concerning subject-specialised school creation in particular as well as Russian and Soviet school practice are analysed in the article. The differentiation process experience on the high stage of school education in such countries as , and the has been investigated. The main functions of a subject matter mastering conception at high school have been pointed out. Mathematical education is considered to be the principal component of comprehensive education as well as the factor influencing the quality of education at a higher educational establishment on the whole run. The peculiarities of mathematical education content at a subject-specialised school in different directions of mathematical training have been illuminated in the article along with the deep consideration of succession problem of both secondary comprehensive and higher school educational processes correspondingly, which, in their turn, are regarded as the possible ways of education quality improvement in terms of higher educational establishment (HEE). The constructional principles of educational courses in various mathematical subjects are defined in the article.

a subject-specialised school, differentiating education, mathematical education, directions (vectors) in mathematics training, levels of mathematical education in high school, succession in education