№ 01 (January)

Currently, there are many problems in the teaching of mathematics associated with a decrease in students' motivation, many of them do not understand the studied material properly. One of the main reasons for this situation is the reliance in teaching not on the natural features of the perception of mathematical knowledge by children of different ages, but most often on a purely logical sequence of the material. Soviet teaching methods, for ideological reasons, limited direction of attention toward the natural characteristics of students. This led to the fact that a high theoretical level of teaching mathematics at school was combined with the complication of educational programs, absolutization of theoretical thinking in comparison with figurative thinking, and neglect of visual learning tools. The purpose of the article is the development of new approaches to the methodology of teaching mathematics, based on the principle of nature conformity - one of the most famous pedagogical principles. This principle considers the attitude towards a person during training as a part of nature, provides for the reliance on his/her own talents and inclinations given to him/her from birth. For a subject such as mathematics, which is studied from the 1st to the 11th grade, and then also in higher school, the principle of nature-conformity is implemented primarily through the phasing, multi-stage gain of new mathematical knowledge by students. The necessity of preliminary stages, steps in the study of basic mathematical concepts is shown. The phasing of knowledge is examined on the example of the formation of the most important algebraic concept of a group and such a structure as scalar. These two concepts permeate the entire course of school mathematics and some university courses. A new approach to the study of the principle and method of mathematical induction is also considered on the basis of a minimum condition that is clearer for students to understand. Examples of applying this form of induction to solving tasks are given.

The article discusses the issues of raising a communicative culture in the course of professional foreign language training for students of technical universities. The relevance of the problem under study is due to the fact that society needs specialists whose competences (professional, general professional and universal) meet the requirements of national and international labor markets and contribute to the subsequent successful employment of a technical university graduates. An analysis of the pedagogical literature allows us to conclude that in modern conditions the formation of universal (general cultural) competences plays an important role, since the main goal of the educational process is not only the preparation of competitive specialists, but also the formation of a system of values and moral qualities in them. In this regard, a pedagogical experiment was conducted at the Foreign Languages Chair of the Nizhny Novgorod State University of Architecture and Civil Engineering, the purpose of which was to increase the level of communication culture among students of non-linguistic specialties. To achieve this goal, the following theoretical methods were used: systematic study and analysis of psychological, pedagogical, scientific and methodological literature, materials of international scientific and practical conferences, generalization, comparison; empirical methods: observation, questionnaire, interview, assessment and self-assessment, analysis of the pedagogical experiment results, their psychological and pedagogical interpretation. A number of measures have been worked out (and partially implemented) aimed at improving the general culture of students and the culture of speech in particular. The main results of the work: students express their thoughts in the classroom and in conversations with the teacher more competently (in accordance with the norms of literary Russian language), which has a positive effect on the process of professional foreign language training of students; the number of students who have a negative attitude to using foul language in public places has increased, actively defending their point of view in discussions; the general cultural level of students increased thanks to extracurricular activities that stimulated a growing interest of students in the history, culture of our country and countries of the world. The materials of the study may be used in the educational work of universities that train engineering specialists.

The relevance of the study is determined by: insufficient research of theoretical issues related to teaching communicative grammar to students of non-linguistic universities in the domestic methodology; the need to develop methods for intensifying teaching of communicative English grammar and creating an appropriate model, taking into account the systematization of teaching methods and tools. The aim of the study is the theoretical and practical justification of the methodology of intensification of teaching communicative English grammar in a non-linguistic university. To achieve the goal of the study, the following methods were used: cognitive-generalizing methods; analysis of linguistic-didactic requirements for the content of the program for teaching a foreign language students of non-linguistic universities; diagnostic methods (questioning, interviewing students, group and individual conversations); prognostic methods; conducting experimental training in order to verify the effectiveness of the proposed complex of communicative grammar tasks; mathematical methods (student testing, qualitative and quantitative analysis of the data obtained). According to the results of the study, the article presents the theoretical and practical justification of the need and significance of developing a methodology for intensifying teaching communicative English grammar in a non-linguistic university. The theoretical significance of the study lies in the scientific and practical justification of the interactive model of teaching students communicative English grammar. The pedagogical model includes: the stages of the formation and development of communicative grammatical skills and abilities; functionally systematized teaching methods; criteria for the selection and organization of educational grammatical material, taking into account the specifics of the learning environment; criteria for assessing the level of formation of communicative grammatical skills. The practical value of the study lies in the creation of an interactive model for teaching communicative grammar using the algorithm for the formation of communicative grammar skills and abilities based on a set of grammatical tasks that implement the research methodology.

The topicality of the problem studied is determined by the necessity to bridge the gap between the rapid growth of the industry of electronic educational tools and insufficient didactic grounds for their usage in teaching and learning. The objective of the article is to identify the parameters of a technological blended learning model to organize digitally enriched instruction. The work applies the systematic approach which considers the educational process as a complex dynamic multi-level system. The approaches of technological designing and modeling of educational systems are also used. The analysis of scientific papers and works done in many different countries including Russia showed that the available technological blended learning models are based on the ratio of online learning at home to face-to-face instruction at school, with the parameters being inflexibly tied to each other. Such model rigidity limits its didactic potential. The analysis of the essential features of blended learning allowed to develop a cyclic blended learning model based on a technological approach. The proposed cyclic blended learning model consists of three components: 1) the objective which progresses from (1) primary delivery of content, to (2) its practicing and (3) checking; 2) educational tools (electronic versus non- electronic); 3) learning place (at school versus out of school). These three model components comply with the logics of the educational process and make up one educational cycle. The cycles follow each other continuously in an ascending spiral. The constituents of the second and third components of the cyclic model can be combined with each other in any variants and used freely at any of the three stages of the cycle. The cyclic blended learning model is characterized by goal-directedness, consistency, variability and flexibility. It can be used as a basis for building different variants of blended learning for the whole class mixing the components depending on a certain didactic need, student group structure, availability of electronic tools and other educational conditions. Besides, the cyclic blended learning model can serve as a tool of developing individual learning trajectories for individual students. The cyclic blended learning model can be applied for instruction in any subject.

This article presents the results of a theoretical study of discursive competence formation problem among military personnel studying Russian as a foreign language. Modern methodological trends in teaching foreign languages comply with finding ways to increase the effectiveness of learning, one of which, in our opinion, is the need to form a discursive competence. The process of formation of discursive competence has been studied inadequately, in a disordered and fragmented way. We consider that the formation of discursive competence in the process of teaching foreign languages has fundamental importance and it is assumed to be one of the relevant directions for increasing the effectiveness of teaching. The formation of discursive competence should be professionally oriented and take into account the specifics of students in every detail. The purpose of the study is to develop a methodological system aimed at the formation of discursive competence at the Russian as a foreign language classes at a military university. As a result of the theoretical study, the fundamental concepts of designing a methodological system were characterized. The structure of a methodological system was developed based on these concepts, taking into account the methodological features of discursive competence formation in the educational environment of a military university. The methodological system pursues specific goals and solves the tasks of teaching in these conditions, taking into account the characteristics of students. It has been determined that narrowly targeted and thematically oriented teaching contributes to improving the effectiveness of teaching foreign students at military universities in Russia. The theoretical significance of the study lies in the development of a professionally-oriented methodological system for teaching a certain group of foreigners, the uniqueness of which lies in its narrow focus, thematic organization and variability, taking into account the social institution and the category of students. The narrow specificity of the developed system does not limit the scope of its application; the results of the methodological system development can be used for teaching any foreign languages. The practical significance lies in the fact that, as a result of the theoretical study described in this article, the methodological system was practically implemented at Russian as a foreign language classes at a military university.

In accordance with the Federal State Educational Standard of Secondary (Full) General Education, the development of creative thinking of high school students becomes one of the main tasks of school education. Most children have a predisposition to creativity from early age, but the traditional conditions of schooling do not provide for the development of this ability. One of the favorable age periods for the development of creativity is adolescence, since adolescents are characterized by increased emotionality; it is easier for them to operate with the acts of imagination, to establish new connections between objects, to rethink events and phenomena of reality. However, so far insufficient attention has been paid to the development of creative thinking of high school students in a comprehensive school. First of all, it is necessary to revise the traditional methodology of teaching school subjects with a focus on the “average” student, take into account the personal characteristics of each teenager development and include non-standard tasks aimed at developing students' creativity in the subject's content. Thus, the purpose of the article was to study the concept of creativity, to identify the conditions and characteristics of the development of creativity of high school students on the subject content of the school course in mathematics. The main methods in the study were theoretical and methodological analysis and generalization of the content of scientific works, as well as a pedagogical experiment to introduce the author’s complex of mathematical tasks aimed at developing creative thinking of students. As a result of the study, an analysis of approaches to the definition of “creativity” concept in relation to school education was made, the results of studies on the development of creativity among students were generalized, the conditions for the development of creativity on the subject content of the school mathematics course were identified. The analysis was the starting point for an in-depth study of this problem and the development of our own complex of creative tasks in mathematics. The tasks were drawn up reckoning upon visual-figurative thinking, independent cognitive search, creative self-expression, imagination, manifestation of individuality, internal motivation, interest, and self-purpose. During the pedagogical experiment on the basis of the Municipal Autonomous Educational Institution “Secondary School No. 31” (academic year 2018/2019) in the city of Ishim, Tyumen Region, we made a comparative analysis of the ascertaining and control stages results. The experiment confirmed that the systematic use of tasks requiring non-standard approaches to solving, imagination, picturing, divergent thinking from students contributes to the development of students' creativity. The results of the study complement the theory of creativity development among students of secondary schools. The article may be interesting to practicing educators, teachers of mathematics, students of pedagogical universities - mathematics majors.

The issues of training a competitive specialist have always been relevant, but they have been especially critical recently in connection with technological and economic changes in the industry. Mining is one of the most difficult areas. Mining companies have faced a number of problems over the past decades that have to be solved immediately. One of the global issues for all the leading Russian mining companies is the so-called “personnel shortage”. The relevance of the article is due to the discrepancy between the level of training of specialists in the field of mining in professional educational institutions and the requirements of production. The purpose of this work is to identify the main problems in the implementation of continuity for the preparation of a competitive specialist in the field of mining. In this article, the author shares her personal experience in the training of technicians and mining engineers (specialists) at the Zheleznogorsk Mining and Metallurgical College, specializing in the areas of training 21. 02.18 “Mineral Processing” and 21. 05.04 “Mining” (South-West State University). Leading research methods are empirical (observation, questioning, conversation, etc.). The author presents the experience of forming a system of continuity between educational institutions of different levels and the employer in the process of training a specialist in the field of mining. As a result of the study, the author identified the main problems of continuity in the training of specialists in the field of mining. First of all, this is the lack of an integrated educational environment between graduates of secondary vocational education (SVE) - higher education institutions - and the employer; unpreparedness of educational institutions graduates to the requirements of employers, and a decrease in the motivational component of SVE system graduates to continue their studies at universities. The article emphasizes: in solving the above mentioned problems, we must remember that the training of mining specialists is a part of the training course at colleges and universities, and this determines the requirements for training specialists and providing continuity between educational institutions of different levels. It is worth mentioning about the results of employers’ questioning, which allowed the author to formulate the requirements for graduates of colleges and universities in the field of mining. This, in turn, will make it possible to continue research on this problem in future and most accurately formulate professional competences necessary for a specialist in the field of mining. The article may be interesting to teachers and heads of educational institutions that train specialists in the field of mining, as well as scientists conducting research work in the field of professional training continuity.

Nowadays, the attitude of modern high school students to the poetry of Russian symbolism is of a discognitive nature. This is due to a number of sociocultural contradictions, as well as problems associated with the information polysemy. In modern conditions, a language arts teacher faces a global task – to search and to select the necessary information using a synthesis of arts at literature lessons. The relevance of our study is determined primarily by the requirements to a language arts teacher in the conditions of constant informatization, and by the need to clarify the problem in the methodological aspect. It is necessary to use integrative and differentiated approaches studying the poetry of Russian symbolism at literature lessons in high school. Depending on the level of training of high school students, a teacher, in order to uncover the figurative system of a work that acts as a correlate to a symbol, can rely on anticipatory tools and an emotive complex, which will not work effectively in classes with a low level of training. In a specialized class, the core of the “symbol” concept can be presented by a work of Russian symbolism poetry representative, and its formation will be carried out through anticipation of the cultural and historical context of the era. The psychological characteristics of students' perception of Russian symbolists’ poetry play an important role. The purpose of the study is to work out a methodology for studying the poetry of Russian symbolism, and for the analysis of the works by I.F. Annensky in particular. This article highlights the experience of studying the poetry of Russian symbolism using the example of the analysis of I.F. Annensky’s works within the framework of methodological and literary traditions with the aim of expanding the interpretative potential of secondary and high schools students both at extracurricular reading lessons and in the context of the Federal State Educational Standard implementation. According to the author of the scientific article, the present development stage of the literature teaching methodology requires an additional theoretical and literary substantiation of problems that reflects the status of the era that continues the present and makes not only researchers but also modern school students to look into the past, which undoubtedly indicates what kind of vector was set by I.F. Annensky in a fairly short period of time, given the influence of the "last Tsarskoye Selo poet" on the formation of the philosophical concept of modernism. The theoretical significance of the article lies in the fact that the segmentation of universal features that serve to build a methodological system was performed at the compositional, interpretational, ideological-figurative levels. The practical significance of the article is due to the creation of objective methodological guidelines for the study of Russian symbolism poetry in the context of the spiritual and moral quests of the era.

The article emphasizes the relevance of studying the characteristics of interpersonal relationships of people with disabilities in the professional field within the framework of the federal program "Accessible Environment". The purpose of the article is to identify the essence of interpersonal relationships as a process of communication, which is a communicative activity in the social field of subjects’ interaction. An empirical study revealed the main features of interpersonal interaction disharmony in the process of communication among people with disabilities in the business sphere.

The problem of deviant behavior of adolescents is rather relevant now. It is noteworthy that over the past two years there has been an increase in cases of deviant behavior, for example bullying (unfair treatment) in the student collective, from verbal to physical forms of aggression. The purpose of the study is to offer effective methods of psychological, pedagogical and educational correction by means of additional education – circle activities. The authors examine the main methods and results of the of deviant behavior correction, and propose the most appropriate methods from the point of view of age and personal characteristics.

The article discusses the main economic indicators of the modern technologies market dynamics over the past five years, as well as tools for consuming information in the modern media environment. The relevance of the topic is determined by the accelerated development of the market of “smart” gadgets for children and the reflection of this trend on the general consumer basket of the population in Russia. The purpose of the study is to identify the main directions and dynamics of the use of modern technologies by children in the economic and social aspect. The conclusion is drawn about the positive dynamics of the development of the market of “smart” things for children and their influence on the socio-psychological portrait of the child.

The purpose of the article is to conduct a study of the variability (volatility) of non-current assets of PJSC Gazprom based on the method of variance analysis for the period from 1998 to 2018. The authors describe in detail the method of variance analysis and estimate the absolute and relative volatility of non-current assets elements on the basis of corporate financial reporting. Based on the results of the methodology testing, the most volatile and least volatile elements of non-current assets are identified. Hence, the authors draw conclusions about the financial policy of managing non-current assets of the company.

The current socio-economic situation in the Arkhangelsk region aggravates the problem of the lack of prospects for young people, which indicates the relevance of the study. The purpose of the article is to analyze migration processes among young people in the Arkhangelsk region, as well as factors that increase migration trends. As a result of the study, it was found that the migration of the population in general and young people in particular in the Arkhangelsk region is mainly of an economic nature. Inattention to the problems of youth in the studied region increases the motivation of this group to migrate.