Aspects of teaching higher mathematics in higher education institution

Currently, the processes of economic development, industry and technical education are characterized by an ever-increasing need for new generation of specialists - developers of highly efficient technologies that own the most advanced tools, including modern mathematical methods. Material production and society as a whole form a social order for the training of highly qualified specialists at the university, capable of working in the specialty at the level of world standards, ready for continuous professional growth, social and professional mobility.

The main goal of vocational education is to prepare a qualified employee of the appropriate level and profile, competitive in the labor market, competent, responsible, fluent in his profession and oriented in related fields of activity, capable of efficient work in his specialty at the level of world standards, ready for continuous professional growth, social and professional mobility. Higher mathematics is a special educational discipline studied at the university, it serves as the foundation for the study of other general educational, general engineering and special disciplines. She has a special role in the formation and development of the scientific worldview of students, the education of their intellect, and in the improvement of mental abilities. The search for effective methods of teaching a course in higher mathematics is one of the most important areas of work for university teachers.

Nowadays, higher mathematics as an educational discipline has firmly consolidated its position in the curricula of both technical, economic, and humanitarian specialties. However, despite the fact that mathematical postulates and laws have remained unchanged for many years, the problems in its teaching, unfortunately, do not disappear.

Teachers of higher education are well aware of the features of the modern stage in the formation of mathematical education and the position in which all participants in the educational process and methods of teaching mathematics are put: reducing the number of hours allocated to mathematics; the gap between the level of mathematical knowledge of school graduates and the requirements of universities; widening the gap between the level of mathematical knowledge of university graduates and the objective needs of modern science and technology. State educational standards propose reducing the number of lectures and classroom activities and increasing the time for independent study of a course in higher mathematics, which implies not self-education of the student at his own discretion, but a systematic student-led independent activity of the student. Even A.N. Krylov argued that the main task of the university is to “teach the ability to learn,” and no school can graduate from a completed specialist: a professional is formed by his own activity. “Learning Ability” is most fully developed by students during their independent work. Teaching complexes on higher mathematics are introduced into the educational process, containing lecture texts and practical exercises, on the basis of which a large number of tasks for independent solution and various materials for self-education and self-control, creative tasks are offered. These educational complexes can include special workbooks for self-study, which can be distributed electronically in the form of files. Moreover, there may be students who will be directly involved in the development of such manuals. Thanks to such methodological complexes, a lecture can turn into an active dialogue between the teacher and students, and will allow directing independent work in the right direction.

In the educational process, it is important to maintain and support the desire of students to learn, in order to increase the effectiveness of training, in addition to organizing independent work of students, the following methods can be used. At the beginning of the school year, students can be offered a math test that includes questions on different sections of school mathematics. The test results determine the level of students' training, identify gaps and areas of individual work with each student and individual groups. At the introductory lecture, students get acquainted with the structure of the course. All material is divided into blocks. The study of each block is carried out by a certain group of students, who further explain it to the rest of the students, using active forms of training and further monitoring the quality of assimilation of the material.

An individual approach to students helps to increase the effectiveness of training. Some of the students quickly learn new material and are able to solve more complex problems, while others require a longer period of time. Such students need to solve more basic tasks, since a quick transition to more complex tasks will lead them to lose interest in independent creativity. Solve the problem of an individual approach to help home independent work. Each student must solve such a number of tasks at a basic level that will provide him with quality knowledge in the future.

It should be noted that the presence of positive emotions is an important factor in the learning process, a necessary condition for successful cognitive and creative activity. Such emotions arise when a friendly atmosphere is created in the classroom and the student, not by coercion, but by his own will begin to solve the task. The task should be clearly formulated and shown the opportunities that may open up when solving this problem. For example, when studying partial derivatives, it can be explained that knowledge of the methods of differentiating a function will help in the future to solve problems of finding optimal solutions to economic or engineering problems. The existing basic knowledge and skills of students should also be taken into account. So, in the above example, if students have already formed the concept of a derivative function of one variable, and they can calculate derivatives of one-dimensional functions, then they will easily master the technique of differentiating functions of several variables.

The presence of an incentive in the implementation of mental activity is also an important factor in awakening the student's cognitive and creative activity. The point-rating system for assessing students' knowledge and skills contributes to the intensification of its cognitive activity. The essence of the point rating is that all tasks that students perform are assigned a certain number of points. Points are obtained for attending classes, speaking in the classroom, preparing reports or essays, completing homework, tests and tests, etc. The amount of points scored per semester are taken into account when issuing an examination grade. The point-rating system of ratings allows you to intensify the work of students, increase the effectiveness of training, since any success or failure is evaluated, which allows you to more objectively evaluate the activities of students.

I would also like to note that students need to be taught not only according to the traditional methodology, since a future engineer or economist, in addition to knowledge in the subjects of specialization, should have an information culture and knowledge in the field of using new information technologies in their future professional activities. Computer mathematical systems are an ideal way to provide conditions for the search process, since they lead to a sharp expansion of mathematical practice. Intensive improvement of computer algebra systems and the emergence of computer mathematical systems entails the expansion of their scope in scientific, engineering research and in education. At present, one can single out a successfully developing area of using the Mathematica computer mathematical system as a means of new educational information technologies and as a means for creating and using educational software products.

Thus, in the process of teaching higher mathematics, students should develop logical thinking, acquire such skills of mental activity as the ability to analyze, abstract, sketch, isolate particular cases. Such a result can be obtained if the above methods are used in the educational process using modern teaching methods to intensify cognitive activity.