This article describes different and effective methods of finding modern solutions to modern problems of teaching mathematics in the school and higher education system. From these methods, the role and importance of modern methods and their rational use were given for monitoring and diagnosing the quality of students' mathematics education, improving the methodology of mathematics teaching, as an example of the topic of teaching sequences. During the lesson, Charkhpalak, Memory exercise, Basket, Contract methods were introduced, the correct use of mathematical programs such as MATLAB, Maple, GeoGebra, Minitab, Excel, and their importance and effectiveness in the educational process were discussed. Some suggestions are given for ending the degradation of mathematics, the interest of students in learning and the use of practice and prospective research.