Introduction. The article discusses the problem of improving the quality of mathematical education in secondary schools. The purpose of the study is to build school mathematics course based on the competence approach developed and refined by the author, to demonstrate what has been said using the example of the first three basic competencies of the ‘Divisibility of integers’ topic.
Materials and Methods. The basis of the methodology is the integration of the author’s consistent theory and technology about the competence approach and long-term practice in teaching this topic.
Results. Many students trained using this technology have become worthy citizens of Russia, doctors of sciences and professors. The expediency of choosing this topic is due to the following circumstances: it causes great difficulties for teachers (not only Russian ones), students of pedagogical universities and, as a result, for high school students who lose points on the Unified State Exam; there are almost no textbooks capable of solving this problem.
Conclusions. The introduction of a competence-based approach into the process of studying school mathematics will help improve the quality of mathematical education and personal development of students, thereby contributing to preparing future professionals to solve the significant problem posed by the President of the country: to develop the Russian economy ahead of the foreign ones.