Abstract: Along with the general subject, in the content of the logical-conceptual competence, the methodical and mathematical foundations of its formation are also singled out. In the object-mathematical plan, the methodical-mathematical adaptation of the psychological-didactic regularities of the formation of the system of subject-based subject knowledge is presented as a basic method. It is supplemented by specific methodical and mathematical patterns: the formation of abstract mathematical thinking and its components; structural formation of spatial and theoretical-spatial types of thinking; analysis of the system of mathematical knowledge in the content of the educational mathematical theory; integration of mathematical language, mathematical speech and mathematical thinking; conceptual-categorial integration of educational mathematical theories.