Keyword: «methods of teaching mathematics»

Engineering education plays a key role in modern conditions of development of science and technology. It is necessary to implement a new technological breakthrough in the field of fundamental problems of engineering sciences, which in turn can be provided by preparation of highly qualified specialists in the field of engineering, capable to work out in professional sphere in the conditions of the development of new technologies and computerization; the development of new learning technologies based on fundamental basic knowledge and innovative approaches. The study, described and implemented by the authors, is development of new principles and methods of preparation of qualified engineers, with profound understanding of mathematics and its application opportunities in the engineering sciences: engineering, architecture and construction.

With the aim of mathematical training level raising among future students of mathematical and technical professions, we need to pay special attention to those math questions without solid knowledge of which successful learning in a University is impossible. In this article, on examples of solving tasks on the topic "Logarithmic inequalities", the author shows the possibility of differentiated approach to the training of future students of technical or mathematical higher schools who will have to learn a course of higher mathematics, particularly mathematical analysis. The development of skills using the traditional method based on the monotonicity of the logarithmic function, and a rationalization method to solving logarithmic inequalities is an important part of high school students training for passing the Unified State Examination in mathematics on advanced level. The content of the article may be interesting to teachers and students who want to enter Universities to study technical or mathematical areas.

The directions of digitalization of mathematics teacher training are highlighted: digitalization of knowledge, digitalization of teaching technologies, digitalization of methodical support. The ways of implementing educational trends are shown: the tendency to non-directive formats; time compression; knowledge management; personalized learning; blended learning; the ability to negotiate in horizontal interaction; micro-learning; gamification; lifelong learning; consumer+manufacturer.

In accordance with the Federal State Educational Standard of Basic general education, students' education should be aimed at cognitive activity. At the same time, interactive teaching methods are used. This article discusses the use of an interactive method in the form of online services for teaching students transfor-mations of graphs of functions. This topic is considered in order to improve the preparation of students for the main state exam in mathematics.