ИСТИНА

The significance of the research. The President's Strategic Development Plan till 2050 states: "Success will require an independent scientific base, based on the experience of many generations of scientists, a large amount of specialized knowledge and knowledge of historically formed scientific schools." In order to fulfill the requirements set out in this public document and to reach the outcome, we need to study the history of the scientific schools and to incorporate the results into the context of contemporary education. In this regard, it is important for the school not only to educate students in the classroom but also during extracurricular activities. Out-of-class educational work with students is called extracurricular work. Extracurricular activities are organized in sessions with students to enable the students to absorb the knowledge, skills, abilities, extend and deepen the students' out-of-class hours, to develop autonomy and personality, and to ensure that their leisure time is active and meaningful. At the moment, extracurricular activities play a special role in the learning and upbringing processes. In the updated curriculum, "extracurricular activities are part of a single educational process, which is a form of organization of leisure of students. The organization of extracurricular work in the educational process provides the spiritual, moral, civil-patriotic, artistic-aesthetic, labor and physical education of students. The study of extracurricular work is reflected in the works of several prominent teachers such as M.S.Esipov, M.N.Skatkin, S.P.Rubinstein, A.S.Akramova, M.S.Sydykov. Extracurricular work in mathematics and computer science have been studied by P.U.Bayramukova, A.V.Alekseev, F.M.Zakirova, V.A.Lokalov, V.N.Pinaev's, K.I.Kanlybayev, I.R.Kenzhebekova, R.A.Buyova and others. Continuous interest of the student in the discipline, the need to focus on the things that are high in need, and its up-to-date information technology education is a requirement of a modern educational system. That is why extracurricular activities are organized to maximize the students' knowledge and to improve their knowledge. There is a need to embrace science by introducing the prerequisites for understanding of the basics of performing the tasks taught in the classroom. Necessity to educate a person who can pursue a profound, contemporary information, educating the national-spiritual roots, ie, modernizing the heritage of our domestic scientists, is clearly outlined in the article "Orientation to the Future: Spiritual Renaissance" by N.A.Bazarbayev. In the article titled "Orientation to the Future: Spiritual Renaissance" by the President of the country, it has been stated that the country announced a new era of modernization. "The revived society will have a spiritual code that begins with the depth of its history. The most important condition for a new type of renewal is to maintain that national code. Without it, it is easy to become a modern echo ", and should be able to overcome the craving and retarding habits of the past and to make the most important prerequisites for successful modernization of contemporary traditions. If the country is not able to get enough of its nationalspiritual roots, it will start to err. It has highlighted several aspects of Kazakhstani consciousness: competitiveness, pragmatism, preservation of national identity, celebration of education, non-revolutionary evolutionary development of Kazakhstan and transparency of consciousness. Spiritual revival is a clear indication of "preserving national identity", not forgetting an old one and moving to a new one. "The concept of "national renewal" is the perfection of national consciousness. It has two sides. First, expand the horizons of national consciousness. Second, it is necessary to change some of its characteristics, preserving the core of the national identity. One of the core and main of our national identity here is social and cultural development of the educational process. In this case, the use of scientific heritage of our great scholars is one of the topical issues. Such scientific heritage includes mathematical heritage of al-Farabi. Al-Farabi is one of the founders of the leading philosophical thought in the Muslim East, including Central Asia and Kazakhstan. Like Aristotle, al-Farabi has studied many spheres of science and wrote many scientific puzzles. Audanbek Kobesov (1932-2008) has studied Al-Farabi's mathematical heritage. His monograph "Mathematical heritage of Al-Farabi" is a valuable work that shaped Farabi's mathematician-scientist's image based on published and unpublished manuscripts of the scientist. A.Kobesov in his book "There is no way out of science" says: "In the great history, as more the wealth of humanity has been accumulated, so abundant its fund of spiritual values is. All of them have the same common treasure. It is the honorable duty of the next generation to analyze, select, respect and esteem those cultural heritage. Now science is a major cultural phenomenon of our time, an integral part of our common civilization. That is why there is no question that culture is a good thing for every citizen to be aware of the history of science”. Therefore, it is necessary to bring A.Kebesov's spiritual values to the next generation to form knowledge, skills and knowledge about our national scientists. It is important to propagate Al-Farabi's mathematical heritage in order to integrate mathematical science into the education of the younger generation”. This can be solved through extracurricular activities at school. The reason is that al-Farabi's scientific heritage will be used to improve the child's personal social experience, enrich his knowledge based on his spiritual values and create the necessary practical skills and abilities. At the same time, extracurricular educational work has a strong impact on pupils' interest in different attitudes towards activities and their desire to participate actively. In extracurricular studies, the mathematical heritage of the scientist will be considered as a historical, cultural, educational and scientific aspect. Competence is the ability to effectively resolve problems and tasks that arise in every-day-life situations. Informational competence is the ability to apply the capabilities of information and communication technologies in solving the problems of learning, living and professional. In our country, the idea of competence in education begins with the preparation of a 12-year SES curriculum, and today is considered as the main for purpose and value in education. Thus, the problem of formation of the information competence of the younger system. In this regard, it is necessary to create conditions for the formation of informational competence of pupils in line with modern requirements, preserving the continuity of the national heritage and cultural heritage of our people. Therefore, in the informational society, students should pay particular attention to national culture and conscious understanding of the history of the country, economic, ecological, social status, and formation of information competence. Consideration of competence formation as a qualitative indicator of personality is reflected in a number of philosophical, psychological, pedagogical and methodological researches. Philosophers U. Waller, D. P. Sorokin, D. Dyui, A.N Nysanbayev, G. Nourisheva and others explain the competence in terms of interest, aspiration, desire, desire, knowledge and high moral norms as a qualitative sign of the person. In recent years, many scientists of pedagogical and psychological sciences have conducted researches on the formation of competence and competence of students in pedagogical science. Those included V.V. Brezhnev, K.S. Sheryazdanova and others, who explain that competence is a unique qualification which allows to effectively address the real situations and problems arising in daily practice, while I.M Zimnya, J. Raven, Zaitseva, A.V Hutorsky, S.V Trishina, N.I.Pak, A.M.Mukhanbetzhanova, Sh.T. Mukanbetova and others considered competence as the result of education. A.N. Zavyalov, L.G Osipova and others have studied the role and place of computer technologies in the formation of students' information competencies. Also, while K.S. Kudaibergenova studied the theoretical foundations of formation of informational competence of students, S.N. Isabayeva worked on the pedagogical conditions of formation of students' bases of informational competence. Place and importance of information technologies in formation of competence of pupils was explained by Е.I. Baydekbekov, G.B. Kamalova, B.D. Sydykov, Zh. Karayev, S.M. Kenesbayev, and S.T. Mukhametzhanova's studies. By combining the views of different researchers, we believe that competence is the achievement of a well-acquired knowledge, skills, abilities, and academic activity that is targeted at achieving a goal in a specific educational system. And we have determined that the concept of information competence is the ability to use information technology, knowledge, skills and information technology in the learning process. The algorithmic sequencing of the actions to be taken in solving problems in help of information communication technologies, can be achieved through the use of the knowledge gained by students in computer science and mathematics combined with Farabi's mathematical heritage. And this, in its turn, will lead to the need for the formation of students' informational competence on the basis of mathematical heritage of al-Farabi in extracurricular activities to prepare pupils to acquire modern knowledge and skills. The above arguments imply the significance of the dissertation theme. Nowadays, the names of E. Bidayov, E.E. Medeuov, G.B. Kamalova, B.G. Bostanov, M.T. Oshanova, K.U. Umbetbayeva can be mentioned as those the works of which are devoted to informatization of Al-Farabi mathematical heritage . By analyzing the above-mentioned findings, we can see that now the formation of informational competence of out-of-class work in the general secondary education is not sufficient, and that important aspects such as the formation of informational competence of students in extracurricular activities are not fully understood in their sense. It is worth noting that studying the mathematical heritage of al-Farabi and introducing them into the content of modern education is not enough. Thus, there is a contradiction between the necessity of introducing the results of the study of al-Farabi's heritage into modern education for the formation of informational competence and the lack of its implementation. Decision to solve this contradiction was taken as a basis for the research and for the topic to be as “Formation of informational competence of students by mathematical heritage of al-Farabi in extracurricular work”. The purpose of the research - develop and establish the methodology for forming informational competence of students by the mathematical heritage of al-Farabi in extracurricular activities. The object of the research - the process of teaching computer science and mathematics in general secondary school. The subject of the research - the methodology for formation of informational competence of students in organization of extracurricular work at school. The scientific hypothesis of the research - if the informational competence of pupils in the extracurricular work of the general secondary education is carried out by the mathematical heritage of al-Farabi, the effectiveness of the formation of informational competence of pupils in extracurricular activities will increase. The objectives of the research: - analysis of psychological and pedagogical bases for formation of informational competence of pupils in extracurricular work; - determining the peculiarities of Al-Farabi’s mathematical heritage and the optimal conditions for the formation of informational competences of students in extracurricular activities by the mathematical heritage of al-Farabi; - defining the structure and content for formation of informational competence of students in extracurricular work by the mathematical heritage of al- Farabi; - defining the tools and developing the methodology for formation of informational competence of students in extracurricular work by the mathematical heritage of al-Farabi; - experimental verification of the efficacy of the methodology for formation of informational competence of students in extracurricular work by the mathematical heritage of al-Farabi. Research methods: - theoretical analysis of philosophical, social, psychological and pedagogical literature; analysis and summary of the pedagogical experiments; psychological and pedagogical methods (control, interviews, questioning, analysis of learning outcomes); determination and formation experiments. The methodological bases of the research were completed on the work of scientists in the following areas: – studying extracurricular works (E.S. Esipov, M.N. Skatkin, G.E. Kughagulova, R.A. Nabuova, T. Alimbai, A.S. Akramova, M.S. Sydykov, P.U. Bayramukova, A.V. Alekseev, Zakirova F.M., V.A. Lokalov, V.P. Pinaev, E.V. Pavlova - extracurricular work in mathematics and informatics, domestic K.I. Kanlybayev, I.R. Kenzhebekova, R. Nabuova and others); - competence and informational competence (I.M. Zimnya, J. Raven, Zaitseva, A.V. Hutorsky, S.V. Trishina, N.I. Pak, A.M.Mukhanbetzhanova, Sh.T.Mukanbetova, К.S. Kudaibergenova, S.N. Isabaeva, E.I. Bidayabov, G.B. Kamalova, B.D. Sydykov, Zh.K. Karaev, S.M. Kenesbayev, S. Mukhambetzhanova, A.A. Temerbekova, Sh.Kh. Kurmanalina, B.E. Erbolat and others); - mathematical heritage of al-Farabi (A.Kobesov, E.B.Bidaybekov, E.E. Medeuov, G.B.Kamalova, B.G. Bostanov, N.Oshanova, K. Umbetbayev). The scientific novelty of the research: - formation of informational competence of students in extracurricular work has scientifically been founded and its necessity has been proved; - optimal conditions have been defined for the formation of informational competence of students by mathematical heritage of al-Farabi ; - the structure and content has been defined for the formation of informational competence of students in extracurricular work by the mathematical heritage of al-Farabi; - the tools have been defined and the methodology has been developed for the formation of informational competence of students in extracurricular work by the mathematical heritage of al-Farabi; The theoretical significance of the research is determined so that the theory and methodology for the formation of informational competence of students in extracurricular work by the mathematical heritage of al-Farabi has been founded, in other words, contribution has been made to the development of theory and methodology for the formation of students' information competence. The practical significance of the research can be determined so that the results can be used in the process of teaching informatics and mathematics in general secondary school. The methodology developed in the research can be used at different levels of learning, teacher qualification, computer science and mathematics teaching practices. The main principles proposed for defense: - scientific base and necessity of the formation of informational competence of students in extracurricular work; - optimal conditions for the formation of informational competence of students in extracurricular activities by the mathematical heritage of al-Farabi; - the structure and content for the formation of informational competence of students in extracurricular work by the mathematical heritage of al-Farabi; tools and methodology for the formation of informational competence of students in extracurricular work by the mathematical heritage of al-Farabi; Testing the research results. The basic principles and results of the research were presented at the following events: 8 scientific seminars of the Department of Informatics and Informatization of the Kazakh National Pedagogical University named after Abai, 8 International scientific-practical conferences - "Informatization of teaching and learning methods - 2016" (Krasnoyarsk), "Infostrategy 2017" (Samara ), at international conferences: "Mathematical Modeling and Information Technologies in Education and Science" (Almaty, 2015), "Public Awareness" (Astana, 2016), "Mathematical Modeling of Mechanical Systems and Physical Processes (Almaty, 2016), «Problems of applied mathematics and informatics» (Aktobe, 2017), «Current trends and problems of modern science and education» (Turkestan, 2017), «Mathematical modeling and information technologies» (Almaty, 2018), also at the scientific and methodological seminar and the meetings of the Department of Informatics and Informatization of Education of the Institute of Mathematics, Physics and Informatics of Abai Kazakh National Pedagogical University. Publications as the results of the research. The main content of the dissertation has been published as follows: 1 paper in a scientific journal with impact factor in Scopus database, 6 publications in journals recommended by the Committee for Control of Education and Science of the Ministry of Education and Science of the Republic of Kazakhstan, 1 publication in a Russian scientific journal, 1 teaching aid book, (16 scientific papers and 1 aid book in general). The structure of the dissertation. The dissertation consists of introduction, two chapters, conclusion, list of used literature and appendices.