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In the context of new requirements for the specialist’s personality

In the context of new requirements for the specialist’s personality, the general cultural and professional competencies existing in the modern educational space acquire special urgency. Without mastering it, the math students teaching of the English language does not guarantee success in productive foreign language communication in their future professional activities. Considering these requirements to the level of the English language competence of a specialist in the conditions of market relations, the modern university students’ teaching should be carried out using the language, methods, and principles aimed at mastering vocational vocabulary, developing information and communication skills, improving abilities and skills of professional experienced text translation, etc. Outlined from the general set of competences of a mathematics student, the English language competence makes an invaluable contribution to the general cultural, personal and professional development of the future specialist.

2. Problem Statement
Developing English language competence occurs mainly in the process of studying the discipline “Foreign Language” during the first two years of study at the university. The teachers of the university face a problem, the solution of which will contribute to the formation of a higher level of foreign-language knowledge of students.
At the scientific and theoretical level, the urgency of the problem is determined by an art oriented educational paradigm. However, pedagogical theory and practice have not sufficiently developed models for teaching the students with a scientific style of thinking that would be consistent with this paradigm and were adequate to the contemporary conditions of an opened educational space. These models should take into account in the pedagogical process the diversity of individual characteristics of students with a scientific style of thinking, but the features should not limit the depth of understanding of knowledge and not reduce the result of instruction to the level of reproductive reproduction.
At the methodological level, the following circumstance must be taken into account. If the student has chosen a scientific direction in accordance with his inclinations, then, most likely, the features of his thinking are more in line with the work in a scientific field of knowledge. The requirements for thinking in the exact and natural sciences do not correspond to the art style of thinking. At the same time, it is obvious that the number of academic hours for studying the art sciences in the classes is small. It becomes urgent to methodologically substantiate and organize the educational process so that the students with scientific state of mind in a situation of severe time constraints could master the knowledge that requires an unusual style of thinking.

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3. Research Questions
The research questions for this study are to consider the psychological features of math students by developing English language competence.

4. Purpose of the Study
This study aims to identify effective approaches by developing English language competence of math students.

5. Research Methods
This study is based on the personal experience of teaching English at the first-degree math students. To determine the person types all necessary tests were conducted.

6. Findings
The Concept of Long-Term Social and Economic Development of the Russian Federation for the Period to 2020 presents the leading goal of higher professional education as “the preparation of 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 activity, ready for permanent professional growth, social and professional mobility “(2020).
Knowledge of a foreign language makes a professional portrait of a modern specialist harmonious and complete, bringing into it such personal and professional qualities as interpersonal skills, curiosity, erudition, ability to think creatively, timely and adequately respond to change, work in a team, make independent non-standard decisions, generate new ones original ideas, solve creative problems.
Foreign language competence is included in the list of mandatory requirements for mastering the basic educational programs presented in the new federal state educational standards for higher professional education in all areas of training, including natural sciences. As a compulsory course, a foreign language in integration with basic disciplines improves the quality of professional training of students, has a significant impact on the content and formation of the conceptual foundations of many special courses, and contributes to the acquisition of necessary professional qualities. Through a foreign language, the conceptual and terminological differentiations, the scientific conceptual and conceptual content of professionally relevant disciplines are clarified, which contributes to the expansion of professional intelligence, the formation of skills for effective professional communication. A professionally oriented approach to the content of the teaching material, and the system of practical exercises helps to increase the level of communicative abilities, cognitive interests and intercultural competencies in the context of future specialization, motivation to study the English language professionally, develop a creative approach to the cognitive process and develop research skills.
In the conditions of modern innovative processes with all their extraordinary phenomena, the problem of developing profile-oriented teaching of a foreign language is especially acute in accordance with the educational standards of the new generation. Such a strategic course should be aimed at active, conscious, creative and initiative participation of students in the educational process of the educational organization. Therefore, to motivate students to take a valuable attitude toward the study of a foreign language, the teacher should develop specific skills to operate on the already learned linguistic materials (to produce and restructure transformations, to consider various options, alternative solutions, new links, associations, etc.) They should approach the problematic issue creatively: in the conditions of the multivariance of the solution, to seek, find and argue their answer, relying on the received knowledge, skills and skills, while using creative thinking imagination, emotions, etc.
Formation of professional foreign-language competence requires changing the content, structure, and technology of teaching a foreign language for special professional purposes. A necessary condition for the effective formation of a professional foreign language competence of the specialist is an interdisciplinary integration of educational activity of students in a foreign language and special courses in which foreign language it is a means of solving the simulated vocational subject and challenges professional activities. The methodology of integrative teaching can be implemented as a scientific basis of formation of professional competence of the specialist natural science, which is the theoretical significance of the proposed teaching methods. The practical significance of the use of interdisciplinary integration is that this foreign language teaching technology increases the incentive and educational interest of students, as a special natural sciences and to the mastery of a foreign language for professional purposes.
While preparing and conducting classes for students of different specialties, it is important to remember that extroverts (usually students of art) and introverts (students of science) differ in the ways they fill their energy resources: introverts in communication deplete their energy, extroverts are replenished.
The big role by developing English language competence is given to speaking, that is to communicate with other people, extroverts and introverts have different attitudes to these kinds of tasks: some feel inspired, others – exhausted. Attempts to force introverts to talk more, and extroverts – more to read only lead to rejection of studies.
Of course, there are almost no pure introverts and extroverts; however, often the qualities of introverts and extroverts are combined in people in different proportions. In foreign language lessons, extroverts and introverts are different from each other and need exercises of different types.
In the lessons of a foreign language, extroverts and introverts behave differently:

Table 01. Differences in teaching extroverts and introverts
Extroverted students Introverted students
They communicate without invitation, comment on the words of the teacher, answer questions shouting from the spot They raise their hands and wait for them to be asked; prefer not to shout out of place
They don’t like writing exercises, often don’t finish them Well perform written assignments, with pleasure perform tests
Drafts are not used, they answer questions spontaneously They always try to write down the answer on the leaflet first and only then answer the question
They do not note teacher’s words Trying to write down everything, especially what seemed interesting, that they will ask in the future
After learning a new word and expression, they immediately try to use it New words and expressions are first tried to “pass” through, analyse and only then used
New words, concepts and grammatical constructions are studied intuitively by these students Everyone tries to comprehend, analyse, find logic and understand the new material completely
They do not like and cannot work on the same tasks, they need to change their activities and change their roles frequently Conservative, prefer to perform those tasks that they already know and understand
They work at a high pace, are mobile, active, talkative, emotional, quickly grasp material and try to apply it The pace of work is quite low, emotions barely manifest, prefer to sit quietly at the desk and not to be “touched”
They like exercises and questions about themselves They don’t like to talk about themselves, are afraid to reveal their inner world and are afraid of questions and topics about themselves
They are not afraid of mistakes: they easily give answers without even being sure of them. Wrong answers do not upset them, teacher’s remarks are quickly forgotten They are afraid to make mistakes, remember the teacher’s remarks and their mistakes. Respond only in case of confidence in the answer, and the more painful to hear that the answer was wrong
Bad knowledge of grammar they know grammar better than extroverts,
They have a large active dictionary, easily enter into communication, use gestures and facial expressions Their active dictionary is good enough, and sometimes unexpectedly good is a passive vocabulary. Many understand, but cannot answer, get lost

Proceeding from these tasks, let us consider what teaching methods can be used in foreign language classes, working with math students:
• When playing dialogs: give clear roles which are familiar for introvert, do not force inventing something, suggest templates, phrases, etc.
• When studying topics about yourself, allow (at least for the first time) to talk not only about yourself, but also about a fictional hero.
• As an example, refer less to the personality of the student, and if necessary, refer, for example, to the same fictional character.
• Let them work in small groups (for example, in pairs), exclude the need for public speaking, be forced to play roles (especially those unknown to them), perform publicly, etc.
• Let the introverts after the dialogues and communication with the group stay 1-2 minutes alone for recovering
• In conversation clubs, allow the introvert to sit silently on the sidelines (at least for the first time), let him look around and assess the situation
• Encourage self-study of the language by introverts. For them are highly effective:
? reading in a foreign language with exercises;
? performance of tests and exercises in workbooks;
? training on special sites with tests and exercises;
? interactive games, tests, presentations;
• If the introvert is embarrassed to talk with the group, encourage them to communicate with you or simply communicate with themselves: playing scenes, retelling read texts
• Create a situation of success, try to avoid criticism, because Introverts react sharply to it, remember well and are afraid to be active in the future.

7. Conclusion
The knowledge of the English language is an indispensable condition for becoming a professionally mobile specialist. The task of a foreign language as an object with numerous interdisciplinary opportunities in the formation of knowledge in related fields of subjects and sciences is to help active implementation of the process of forming professional mobility of students at a modern university. By developing English language, competence of math students is highly important to take into account their peculiarities and organize the classes according to their features.

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