Problems and some aspects of training foreign citizens in the process of teaching mathematics in higher education institutions

Some of features, aspects and problems of teaching mathematics to foreign students in higher education institutions of Ukraine. The main issues on the structure of the organization of the educational process, the process of monitoring the acquired skills.

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PROBLEMS AND SOME ASPECTS OF TRAINING FOREIGN CITIZENS IN THE PROCESS OF TEACHING MATHEMATICS IN HIGHER EDUCATION INSTITUTIONS

Elina Zhelezniakova Simon Kuznets Kharkiv national university of economics

Tetiana Silichova Simon Kuznets Kharkiv national university of economics

Annotation

In the article presents some features, aspects and problems of teaching mathematics to foreign students in higher education institutions of Ukraine are considered. It is pointed out that the international character of education at the international level is the main and characteristic feature of the development of the modern higher school, which requires from the educational system relevant changes, primarily related to the consideration of all world laws and requirements in this direction. The authors present the main issues on the structure of the organization of the educational process, the process of monitoring and evaluating the acquired knowledge and skills, adjusting curricula and programs for teaching foreign students both at the preparatory department and at the first courses of education institutions respectively. Analysis of psychological and pedagogical literature, dissertational research in this direction and experience gained in working with foreign students in the process of teaching the disciplines of the mathematical cycle at the S. Kuznets Kharkiv National Economic University showed the expediency of using the forms and methods given in this article. Considering the further entry of higher education of Ukraine into the European space, the problem of preparing foreign students is very urgent, multifaceted, and requires further study and further scientific-pedagogical research.

Key words: higher education institution, foreign students, mathematical disciplines, teaching methods, training, adaptation problems, educational process.

У статті розглянуті деякі особливості, аспекти і проблеми навчання іноземних студентів математиці у вищих навчальних закладах України. Зазначено, що саме інтернаціональність освіти на міжнародному рівні є основною й характерною рисою розвитку сучасної вищої школи, що і вимагає від освітньої системи відповідних перетворень, перш за все, пов'язаних із урахуванням усіх світових закономірностей та вимог у цьому напрямі. Авторами окреслено коло основних питань щодо структурі організації навчального процесу, процесу контролю й оцінки набутих знань, умінь та навичок, коригування навчальних планів і програм з навчання іноземних студентів як на підготовчому відділенні, так і на перших курсах навчальних закладів відповідно.

Ключові слова: вищий навчальний заклад, іноземні студенти, математичні дисципліни, методика викладання, навчання, проблеми адаптації, навчальний процес.

В статье рассмотрены некоторые особенности, аспекты и проблемы обучения иностранных студентов математике в высших учебных заведениях Украины. Отмечено, что именно интернациональность образования на международном уровне является основной и характерной чертой развития современной высшей школы, что и требует от образовательной системы соответственных преобразований, прежде всего, связанных с учетом всех мировых закономерностей и требований в этом направлении.

Авторами очерчен круг основных вопросов по структуре организации учебного процесса, процесса контроля и оценки приобретенных знаний, умений и навыков, корректировки учебных планов и программ по обучению иностранных студентов, как на подготовительном отделении, так и на первых курсах учебных заведений соответственно.

Ключевые слова: высшее учебное заведение, иностранные студенты, математические дисциплины, методика преподавания, обучение, проблемы адаптации, учебный процесс.

higher education teaching mathematics

Introduction

One of the aspects of inclusion of the university in the international educational space is attraction of the foreign students to study at the university. Despite the political situation that has developed in Ukraine, there is an increase in international academic exchanges, which indicates the openness of our higher education, objectively contributes to improving the quality of educational services provided and strengthens the authority of domestic universities abroad. In this regard, the actual task for education institutions is organization of an effective process of teaching foreign students, which would ensure high quality of the educational services and would allow the effective implementation of modern professional and general professional competencies in the specialties chosen by students. The purpose of teaching foreign students is development of professional competence in Russian. The tool is formation of the information and educational environment for mastering the language of the specialty, methods, techniques and practical skills of applying information technologies. For foreign students, individual educational plans have been drawn up, which fully correspond to university training programs, but their peculiarity is to take into account the national specifics, the need for social adaptation, and learning of a foreign language in parallel with the acquisition of professional skills. At the same time, the main problem of the initial stage of training for foreign students is different level of preparation of students in the natural sciences and mathematics disciplines. The problem of teaching mathematics to foreign students is insufficiently illuminated and studied.

The number of foreign students in a higher education institution depends on the numerous factors: the value of the contract, the territorial location of the higher academic institution, and so on. But the main and inalienable condition is the very quality of the educational services of the higher education institution, the possibility of obtaining after the university an actual and demanded profession, further career growth and formation of a number of professional competencies.

Analysis of relevant research. A thorough analysis of research and publications that deal with the main problematic aspects of teaching foreign citizens in Russian universities showed that in most cases the methodology and content of courses taught for domestic and foreign students are significantly different.

General issues of teaching foreign students in higher education institutions were examined in the works of T. Dementieva, N. Bulhakova, T. Kapesina, N. Semennikova, V. Chuhaieva, A. Madiarov, H. Shmarova, H. Kutuzova, N. Huzarova and others. So, according to T. Blinova, A. Novikova and N. Rudnova, it is the lack of a habit of working independently, to study, which is observed among the majority of foreign students, considerably complicates the educational process [2]. A. I. Hrebennikova, N. Semennikova, T. Medvedkina in their works draw attention to the difficulties in adapting foreign students to the sociocultural conditions of life, which are practically new for them [9]. All this, indeed, is very relevant in a situation where the main contingent of foreign students is represented by immigrants from non-European countries.

Low level of motivation of foreign students to study is noted by O. Hanych and V. Chuhaieva. In their view, the main reason for this phenomenon is low level of language training [3]. N. Huzarova also believes that in recent years the level of training of students at the preparatory departments has dropped substantially, which, in turn, is the reason for the sharp lag in the studies of such students in the first courses.

The results of the basic statistical data show that about 150 different countries annually send their students to Ukraine. Only in 36 Kharkov universities, 19.6 thousand foreign students are studying. Basically, these are citizens from Azerbaidzhan, Turkmenistan, Morocco, India, Nigeria, Uzbekistan, Jordan and Iraq. Of course, compared with the world leaders in providing educational services (Germany, Great Britain, USA, Australia, etc.), where the share of the total income obtained from the training of foreign students is about 25-26 % of income, Ukraine clearly loses out. In our country, this figure barely reaches 5 %. However, Ukrainian education has an indisputable advantage: at a relatively low cost of education and residence (compared to other countries), a sufficiently high level of training in various specialties (especially medical and natural-technical professions) is offered.

Aim of the study is to analyze the peculiarities of organization of training of the foreign students of the preparatory department and students of junior courses on the example of S. Kuznets Kharkov National Economic University and identify the main problems in teaching subjects of the mathematical cycle among foreign students in higher education institutions and find the best ways to resolve them.

Research Methods: scientific analysis of philosophical, psychological- pedagogical and methodological literature, pedagogical observations, analysis of the pedagogical experience of teachers of higher education institutions for work with foreign students.

Results

The process of adaptation of a foreign student in a Ukrainian university cannot proceed in isolation from an external socio-cultural environment. The process of adaptation of foreign citizens coming to Ukraine to receive education is influenced by climatic, personal-psychological, social and domestic factors. The student's ability to adapt to the pedagogical system of the institution directly depends on the ability of the pedagogical system itself to take flexibly into account the interests and needs of foreign students who come to study at the university. Adaptation of a foreign student to a new socio-cultural environment is facilitated by two groups of factors: dependent on the student and dependent on the teacher. On the part of the student, important are: sufficient level of basic training, the level of knowledge of the Russian language, individual ability to learn, the peculiarities of the national mentality. The teacher, in turn, should be competent in the subject, have a good command of the language of communication and have certain personal qualities. So the knowledge and ability to take into account the personal characteristics of students in practice contribute to reducing the timing of successful adaptation of foreign students. And this, in turn, has a direct impact on the effectiveness of the learning process. Taking into account that it is the first years of education that are the years of adaptation of a foreign student to new conditions, it can be asserted that the subjects of the fundamental cycle that are studied by students at the first courses and are the basis of the professional formation of a specialist require increased attention.

Of course, we agree with the idea that the language problems that arise while studying subjects of the mathematical cycle are much less than the problems that arise in the study of the cycle of humanitarian subjects, but we cannot also assume that, in this case, the problem is simpler.

The main problem of the initial stage of training of foreign students is different level of the preparation of students in the natural sciences and mathematics disciplines. This is due to the differences in national programs and textbooks on mathematics in different countries and different educational institutions.

An important role in the solution of this issue is given to the work of the preparatory department. This idea is reflected in the works of L. Belskaia and V. Kuzminov, who also draw attention to the need to enhance the role of the preparatory department [1, 6]. Indeed, the use of the preparatory department is the best way out in this situation, but the realities of life are different. Most foreign students want to study at a university without prior training, thus saving time and money. In conditions of the modern struggle for each student, those universities that "offer everything at once" win.

Thus, the problem of teaching mathematics to foreign students and the disciplines of the mathematical cycle can be considered in two aspects. Namely, training of an international student at the preparatory department and already directly in the process of studying at the university. With regard to mathematics, it can be said that the main result of teaching mathematics should not be a system of knowledge and skills in itself, but a set of mathematical competencies, and a student with mathematical competencies can correctly apply mathematics to solve problems arising in everyday life.

Of course, the system of preparing foreign students in mathematics is based on the methodology of teaching mathematics to Ukrainian applicants and schoolchildren. However, the available methodological and didactic material is not intended for training of foreign students and requires special processing and adaptation.

Based on the experience of working with foreign students, mathematics teachers of S. Kuznets Kharkiv National Economic University is actively working on the creation of a teaching and methodological complex: written training programs, teaching aids, methodological recommendations for practical classes, developed exercises for students' independent work. A set of test tasks was developed to assess the mathematical preparation of foreign students entering the preparatory department, which allows them to evaluate their knowledge of mathematics regardless of their knowledge of Russian. The orientation of the limited vocabulary of foreign students studying mathematics in Russian causes the need for careful selection of the formats of presentation, terms, variants of formulations of definitions, theorems, properties in the process of preparing teaching materials for this contingent of students. At the same time, one has to find a compromise between the desire to unify and simplify the lexical forms of presentation of materials relating to different sections of the course and the desire to ensure their logical completeness. Tasks for an independent decision on each topic play an important role in mastering the theoretical material. The student can perform them in the process of preparing for the lesson, directly in the class itself, under the guidance of the teacher or as a homework assignment to consolidate the teaching material. While working with foreign students, it was revealed that the combination of various forms of training, the implementation of flexible forms of using electronic resources in the teaching process, contribute to a more complete mastering of professional skills in Russian, which is realized in optimizing the selection of educational material, improving the methods of information delivery, the effectiveness of analyzing the degree of assimilation of the studied material.

It is practically impossible to present a regular lecture in its entirety for foreign students. Problems also arise during seminars and laboratory sessions. One of the ways to solve this problem can be a significant simplification of the material. But, it is not always possible and not always expedient. So, for example, if foreigners are included in a regular group or are in the general flow among domestic students, then this is simply impossible. If it is a separate stream of foreign students, then there can be a "permanent lag syndrome" and the level of training will be different. Taking into account the fact that in most cases foreign students return home after 5 years of schooling, and the level of the university preparation may simply be "understated", which in the future will lead to the outflow of foreign students or can cause serious problems with the nostrification of diplomas. Unfortunately, it is not always possible to single out a separate group of foreign students. There are specialties in which recruitment is carried out in the amount of 20-30 people and no more. Another, no less important factor, as mentioned above, is the level of mathematical preparation. On this basis, the composition of students in the group can also be completely different. So, students from Vietnam and China have a much higher level of training than students from other countries that have a low level of mathematical training but do not experience difficulties in communication. Almost all these shortcomings can be, if not completely eliminated, and then significantly reduced by training students in the preparatory department.

At the preparatory department at S. Kuznets Kharkiv national economic university, if possible, take into account all these features. Students study in small groups, where the main task of the teacher is not only to teach them mathematics, to restore or correct the existing amount of knowledge, but also to teach the complexities of mathematical terminology, the features of writing words and names.

The mathematical text intended for foreign students has its own design features. So the volume of the text should be relatively small; texts should have a fairly transparent structure; language design of the text should help to isolate the key information on the topic.

It was noted that it is the descriptive process that causes the greatest difficulty in solving problems. This, for example, is the use of such introductory words as "let, suppose, follows, ...". In addition, some words and whole expressions due to linguistic features can be perceived absolutely differently. The expression "the number is divided" can be perceived as "the child shares candy". There are significant differences in mathematical terminology. So, the "tangent" of function tgx often is written in foreign literature as tan x, a natural logarithm lnx as logx. There are also some peculiarities in the recording of roots, fractions, degrees, which are found out together with the teacher at the first lessons. The emergence of such situations, on the one hand, places high demands on training of the teacher, but, on the other hand, knowledge of the various variants of names promotes development of the skills of a foreign student to freely navigate in the reference literature, acquire new technical knowledge using modern educational and information technologies. Teachers of mathematical disciplines are assisted to some extent by the symbolic language, which in its general basis is the international language and partly assumes the functions of the mediating language.

For example, one of the tasks on the topic: "Arithmetic operations on numbers" is as follows:

45+24=69 - this is the addition.

45 - is the term, 24 - is the term, 69 - is the sum.

56-23=33 - this is the difference.

56 - is a minuend, 23 - is a subtrahend, 33 - is the difference.

25x6=150 - this is multiplication.

25 - is a multiplier, 6 - is a multiplier, 150 - is a product.

98:14=7 - this is division.

98 - is a numerator, 14 - is a denominator, 7 - is a quotient .

Thus, when studying each topic, emphasis is placed on mathematical vocabulary, the correctness of reading numbers, letter expressions. Home assignments are specified in the form of tests, tables, and ordinary tasks. Students need not only to solve the problem, but also correctly sign, name and designate.

For example, the topic "Decimals" also contains theoretical material. Let's give an example:

How to read decimals?

0.3 - zero point three tenths;

0.06 - zero point six hundredths;

2.035 - two point thirty-five thousandths.

An important component of working with foreign students is the systematic repetition of the material that has been passed, which is provided by a system of individual tasks for homework. Before beginning the study of the section, each student receives an individual assignment containing tasks of different levels of complexity (both reproductive and creative). In the process of working on such assignments, students' personal interest in the results of work is manifested; individual consultations of the teacher allow answering all the questions of interest, overcome misconceptions that may have arisen in the course of group classroom studies, independent work on the assignment.

The drawbacks of training students at the preparatory department should be attributed to the fact that the classes are conducted in a short time and for the qualitative mastery of the material there is just not enough time. Although in general the mathematics course at the preparatory department of S. Kuznets Kharkiv national economic university is designed for 252 hours, students study mathematical terminology in Russian, systematize knowledge acquired in their homeland, eliminate gaps, acquire skills of listening to the material, writing notes, and independent work with literature.

The next stage is training of the foreign students at the first courses of higher education institutions. Here, the learning process can be divided into two parts: the learning process itself, as the process of gaining knowledge, and the process of monitoring the received knowledge.

If the learning process is aimed at a direct process of gaining knowledge, then the purpose of monitoring is to identify "weak" places, gaps with a view to their further elimination. As for the learning process, it should be noted that the teachers of the Department of Higher Mathematics and Economic and Mathematical Methods of S. Kuznets Kharkiv national economic university wrote and published a sufficient number of methodological recommendations and teaching aids for foreign students in all disciplines that are taught at the department. All the teaching materials, written in an accessible language, do not contain cumbersome proofs, and complex mathematical formulations, the language of writing is Russian. One of the best ways to improve the quality of training for foreign students in mathematical disciplines is the extensive use of electronic teaching aids. Some aspects of teaching of the disciplines of the mathematical cycle have been examined in numerous research papers and articles. Thus, the problems of teaching mathematics in economic studies were dealt with by A. Petrova, E. Loktionov [7, 10], N. Demidova, V. Kuzminov [4, 6]. Questions of the formation of mathematical concepts with visualization elements were dealt with by N. Vlasova, I. Livanov, O. Khachaturov, N. Zverev, V. Levin and others. These groups of researchers believe that it is precisely giving the mathematical courses more visibility through the use of electronic capabilities, which is one of the directions for solving the problem. Similar views are present in the works of T. Kuznetsova, who studies some issues of preparing foreign students, believes that the solution to this problem lies in the use of a single "verbal" basis, and most of the lecture classes should be reduced to formulas, graphs, equations, that can be unified and not depend on the country [5]. Lectures for foreigners are accompanied by slides, visual models. In the process of selfpreparation students widely use electronic textbooks and teaching materials developed by teachers of our university and placed in the system of distance learning in the Moodle system.

Special attention in the learning process deserves a site of personal training systems, where each teacher places educational material, methodological recommendations and manuals, gives recommendations on the use of additional literature for a more thorough study of a single topic or course as a whole. It should be noted that it is the use of the site of personal work systems that, above all, is the realization of such an important direction of learning as an independent work of students. The material presented on the site is diverse in its structure and content. On the site there are lectures, presentations of lectures, methodological materials for practical and laboratory sessions, tasks for independent work with numerous examples of solving problems. One of the main advantages of using the site of personal training systems is the lack of time binding. Everyone can choose for themselves a convenient schedule of work, the necessary amount of time, can simultaneously take advantage of the recommended literature on the site, and any other additional literature. These materials are available in electronic form through the local network of S. Kuznets KhNEU and the Internet resource http://pns.ingek.com/.

One of the ways to solve the problem of mathematical preparation of foreign students is to see modern scientists using a set of individual tasks [8]. However, the question arises of where to take the time and the teacher and student for such individual control and assistance to the student by the teacher. In this regard, the use of the site of personal training systems gives very good results. As a rule, the semester course is divided into two modules, each module contains a modular final evaluation, which consists of the current and final control. The teacher, at the beginning of the semester, gives two individual assignments, or one at the beginning of each module. The student performs an individual task for a certain time. Key points are always considered by the teacher in the classroom. A sample solution, task variants are on the site of personal training systems. Another important direction of work with foreign students is the use of various forms and methods of control.

Throughout the educational process, we can distinguish three main forms of control: current, periodic, and final with the corresponding scales of assessment. The existence of such a variety of methods of control is sufficiently justified, both on the part of the student and on the part of the teacher, and is achieved through the introduction of various methods of interaction between the teacher and the student.

Current control is carried out every lesson, and the student's knowledge is evaluated directly on the pair. The current control includes the direct work at the lesson, as well as small control works, within 20-30 minutes, short surveys on the theoretical material, the fulfillment of the calculation tasks in the appropriate software environments in the laboratory sessions. After checking such mini-works, the teacher and students make a review of typical mistakes, difficulties. In addition, taking into account the peculiarities of working with foreign students, the specifics of the subject, students are allowed to use abstracts in the process of performing such monitoring work, ask questions to the teacher, and turn to fellow students. The received estimate for this small work is added to the evaluation received for activity at the lesson. Individual tasks also relate to methods of monitoring. Of course, these tasks can not have a large estimated weight. They can not be many, since the teacher can not control the independence of the work. But in this method of working with foreign students in math classes there is a positive moment. So, if a student performs individual and homework, even with the help of outside assistance, at lessons, tries to perform the current training load, then he is provided with a positive evaluation of the subject.

The next stage of control is periodic monitoring. It is usually held at the end of each big topic, or a few small ones. Usually, for foreign students this type of control is carried out once per module or twice a semester. At the discretion of the teacher is assessing the practical skills: the ability to solve problems, perform laboratory work, may not be performed additionally if the student agrees with the final total assessment of the current monitoring. If the student wants to raise the ball, then the teacher issues a task that includes all the material of the topic, and it must be done during the lesson itself. In addition, periodic monitoring involves evaluating the theoretical knowledge of students. The material for theoretical control contains questions, the answers to which are not shown by how much the student memorized the theory, but how he can apply this or that knowledge in practice. Thus, language difficulties are eliminated in writing the main theorems and definitions, and the teacher can really assess the level of theoretical knowledge of students. The final control includes credits and examinations. In this case, the evaluation of the material takes place either throughout the entire training course or in a small part of it. This is the most important and difficult stage in assessing students. In this case, the tasks themselves and the atmosphere of their implementation are close to the situation of real professional life. The teacher selects tasks so that they have some economic sense, and not just contain a set of some mathematical operations. Tasks maximally cover all subjects of discipline and are differentiated in complexity level. The student's task in this case is to choose independently those forms and methods of solution that are directly suitable for the solution of a task. It should also be noted that in this case, the complexity and scope of assignments for foreign students do not differ from assignments for domestic students. The final grade for the entire training course consists of three evaluations: current, periodic and final control.

Conclusions

Analysis of psychological and pedagogical literature, thesis research in this direction and experience gained in working with foreign students in the process of teaching the disciplines of the mathematical cycle at S. Kuznets Kharkiv national economic university showed the expediency of using the forms and methods given in this article. Considering further entry of higher education of Ukraine into the European space, the problem of preparing foreign students is very urgent, multifaceted, and requires further study and further scientific and pedagogical research. Thus, when organizing work with foreign students, it is necessary to develop more carefully the training program, select training materials, literature, use electronic resources more actively, and take into account the national characteristics of the listeners.

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9. Сторчак, Л. В., Медведкина, Т. А. (2013). Об особенностях общения на этапе адаптации иностранных студентов. Актуальные проблемы обучения иностранных студентов в современных условиях: тезисы Всеукраинской научно-практической конференции ДонНУ, 34 (Storchak, L. V., Medvedkina, T. A. (2013). On the peculiarities of communication at the stage of adaptation of foreign students. Actual problems of teaching foreign students in modern conditions: abstracts of the All-Ukrainian Scientific and Practical Conference of DonNU, 34).

10. Петрова, А. В. (2006). Структурні компоненти професійної компетентності менеджера зовнішньоекономічної діяльності. Педагогіка і психологія професійної освіти, 4, 51-59 (Petrova, A. V. (2006). Structural components of professional competence of the manager of foreign economic activity. Pedagogy and psychology of vocational education, 4, 51-59).

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