The course of higher mathematics at technical universities is reduced annually due to the reduction of the time allotted for the development of its program. The use of more effective teaching methods can only partially compensate for these losses. Especially depressing is the loss of the opportunity to bring proofs of even the simplest statements and theorems in the course of mathematics. If, as R. Kronecker said, definitions are the soul of mathematics, then its beauty lies in the impeccable application of logic, and the driving forces and its very life are in the ideas of proofs.

The article substantiates the cognitive approach acceptability using digital resources in professional teaching of English word formation through such an organization of educational activities, which includes tasks and exercises aimed at the development of word-formation competence and creative abilities of students-methodologists.

The Content and Language Integrated Learning methodology, where content is taught by means of a foreign language, can become one of the options for solving the problem of reducing the hours allocated for teaching a foreign language in universities. However, the analysis of the psychological and pedagogical features of Content and Language Integrated learning indicates an increase in the cognitive load, both on students and teachers.

The article analyzes the modern practice of forming the managerial competence of cadets in the process of mastering the military and military equipment. The author considers the stages of training of cadets of the Higher Educational Institution of Higher Education, suggests the modernization of education in one didactic direction related to the formation of the managerial competence of cadets when they master military and special equipment.

The article considers to the problems of forming the subjective position of students from the point of view of psychology and pedagogy. The author of the article investigates the issues related to the theoretical foundations and practical aspects of the formation of a subjective position in the educational environment of a military university. Particular attention is paid to the role of the teacher in the formation of the cadet's subjective position.

The article reveals the author's view on the psychological problems of man connected with the formation of a personality of a child at an early age, when the Self-esteem of a child is violated by a personally immature mother. The aim of the study. The causes of the child-harmful upbringing in the family motivate the society to improve the psychological literacy of the population in terms of the problem under discussion, i.e. the early childhood and conscious motherhood relationship. Results of the study.

The article is devoted to polytechnic resources as one of the core components of chemical education. The authors analysed the school curriculum on the first Russian programs on chemistry for secondary schools to the unified traditional program used up to the end of the 1990s. The school course of chemistry is consistently provides system of polytechnic concepts, as well as describes technologies of production of the most important chemical products, including corresponding chemical experiments and didactic material.

The article presents the model of preparing future teachers for the implementation of the educational function within the program for children with disabilities. The relevance of the model structure focuses on the requirements of the quality of training future teachers that have significantly increased in the higher educational system. The Model covers the process of the formation of students as trained specialists for the activity program for children with limited health abilities.

The problem of both quantity and quality of research publications in English by Russian scientists in high-ranking journals is still relevant today. In the absence of specialized training in academic writing at technical universities, researchers have to rely on self-study or on the translator and language proofreaders help. However, the skills of independent analytical writing develop more slowly than all other skills, and in the process of translating a scientific text into a foreign language, both logic and content may be distorted or misinterpreted.

The aim of this research is to study the readiness of foreign language teachers to use Massive Open Online Courses (MOOCs) in the educational process of higher education institutions. To achieve this goal, a multi-level approach was used, including questionnaire analysis, conducting interviews with teachers, and critical analysis of educational documents. It was found that despite theteachers’ positive attitude and recognition of MOOCs`potential they face a number of difficulties that hinder the use of MOOCs in full, i.e.