Integration of the subject and semantic approaches to the developing education and teaching the fundamentals of analysis to the high school students

The article presents activity and semantic approach conception in the context of developing education and teaching mathematical analysis essentials to the high school students. This conception is based on the idea of integration of subject and semantic activity regulation subsystems in the course of formation of abstract mathematical notions. The implementation of integration approach allows to accentuate the understanding of the study material by every student and to overcome the formalism of its mastering.