The article discusses the concept of mathematical education of pupils of a school and the results of pedagogical research. Being trained to solve the simplest tasks without a deep (thorough) understanding of the meaning of mathematical relationships is not conducive to the development of intellectual abilities and is quickly lost after completing the topic. It is experimentally confirmed that a student aspiring to attain a higher technical education, in addition to computational skills, needs to have an idea about mathematics and its methods, possess logical development, a graphic culture, develop a spatial imagination, independent work skills, the ability, if necessary, to use the appropriate directory to restore specific facts and obtain the necessary information. The research also looks into ways of solving problems with designing the learning environment and elaborating variable models of studying the natural and mathematical sciences with application of certain components of a computer-oriented learning system with the aim of upgrading pupils’ performance (a mass model, the main model and the creative model – an advanced level). The structuring of knowledge and the correct correlation of the selected types of knowledge develop the content of profile education, taking into account significant differentiation and the possibility of building an individual educational curriculum for schoolchildren, and also contributes to the filling of the three most important components of the content of profile training: basic invariant, profile variational and additional ones.