Bulletin of Abai KazNPU. Series of Physical and mathematical sciences https://bulletin-phmath.kaznpu.kz/index.php/ped <p>Scientific journal " Bulletin of the Abai KazNPU, the series of "Physical and Mathematical Sciences" is a scientific and educational publication on topical issues of mathematics, mechanics and physics, computer science, as well as informatization of education and methods of teaching physical and mathematical disciplines in school, college and university.</p> <p>International Standard Serial Number ISSN 2959-5886<strong><em><br /></em></strong>ISSN (Online): 2959-5894</p> <p><strong>Contacts</strong></p> <div class="page"> <p>e-mail: <u><a href="https://bulletin-phmath.kaznpu.kz/index.php/ped/management/settings/context/mailto:Vestnik.KazNPU.FMS@gmail.com">Vestnik.KazNPU.FMS@gmail.com</a><br /></u>Shekerbekova Shirinkyz Tileubergenovna</p> <p>Abdulkarimova Glyusya Alimovna<br />Almaty, Tole bi str., 86 office 312</p> </div> КазНПУ им.Абая en-US Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2959-5886 TRAINING FUTURE TEACHERS OF MATHEMATICS TO DEVELOP FINANCIAL LITERACY OF SCHOOL STUDENTS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2138 <p style="font-weight: 400;">Mathematics is one of the important subjects that allows you to form and develop financial literacy of students through the content and tools of training. The article discusses the issues of improving the professional and methodological training of future mathematics teachers by introducing a special course in the content of the educational program for the formation of financial literacy of students while studying the school course of mathematics. Also, the article presents the content of the course "Fundamentals of financial literacy and their mathematical solutions", necessary for the formation of financial literacy of students, methodology for solving problems of financial and economic content was proposed and specific examples were given. The purpose of the study is to identify the methodological basis for improving the professional training of future mathematics teachers to develop &nbsp;financial literacy of school students. The objectives of the study are to study the condition of training future teachers of mathematics to developfinancial literacy of school students, to compile substantive and methodological recommendations for the course "Fundamentals of financial literacy and their mathematical solutions". The effectiveness of the methodological recommendations of the research work is confirmed experimentally by introducing them into the process of teaching mathematics in general education schools in Almaty. The significance of the study is that the result of the study contributes to the integration of the content of the mathematics course with financial knowledge by introducing a special course into the educational program of pedagogical universities, the formation of financial literacy of school students using financial and economic content tasks.</p> A.K. Ardabayeva Y.A. Tuyakov Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 70 82 10.51889/2959-5894.2024.87.3.006 ABOUT ONE METHOD OF PRESENTING THE TOPIC “COMPLEX NUMBER” https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/1997 <p>In this article, teachers of a higher educational institution are offered a way to present the topic “Complex Number” to students and we share our opinion.</p> <p>In the course of presenting the topic, firstly, it is expected to give examples of problems that lead to the need to expand the search area for solutions not only to the set of vertex points of real numbers, but also to at least the set of points of the &nbsp;plane, i.e., the set &nbsp;of ordered pairs of real numbers.</p> <p>Subsequently, having shown that only the relations of addition, multiplication and equality characteristic of the set of real numbers can be introduced into the set , the set &nbsp;can be considered as a set of numbers other than real numbers, and since it is its element &nbsp;can be considered as complex of real numbers, set of complex numbers. It is justified that it is logical to name it.</p> <p>Then, having shown that it is possible to introduce into it a subset Z of the set of complex numbers with all relations characteristic of the set of real numbers, i.e., take it as the set of real numbers, it is proved that the set of complex numbers is indeed an extension of the set of real numbers, and any &nbsp;complex. It is shown that the number can be written as an algebraic expression , consisting of real numbers &nbsp;and one &nbsp;complex number. The authors present the topic with the idea that it will have a great impact on the complete assimilation of the topic materials.</p> P.B. Beisebay G.H. Mukhamediev Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 83 94 10.51889/2959-5894.2024.87.3.007 DEVELOPING STUDENTS' REFLECTION SKILLS THROUGH THE INTEGRATION OF PROBLEM-BASED LEARNING AND THE METHOD OF BUILDING ALGORITHMS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2100 <p>This article describes how problem-based learning and algorithm design methods were integrated in action research and how effective this integration was in developing students' reflective skills. Literature related to problem-based learning, as well as the method of creating algorithms and reflection skills, was studied and analyzed. During the observation of lessons, it was found that difficulties arose with fully describing the ways to solve tasks. The purpose of the study was to develop students' reflection skills when solving a problem situation by creating algorithms for completing tasks. Research objectives: clarification of the research question; formation of a strategic plan; data collection; reflection; determination of new steps for the completed research. The study consisted of the following stages: study, analysis, selection of topics and educational goals in a calendar-thematic plan according to the eleventh grade curriculum; development of structured tasks; identifying solution steps; presentation and comparison of ready-made algorithms and evaluation tables; defining a joint solution; reflection and evaluation. The results of our previous study on identifying occupational dynamics were combined with this study. The study took into account the results of external summative assessment after the tenth grade, as well as the physiological, general and personal abilities, and practical abilities of students. The research process included four main cycles, including methods of problem-based learning and algorithm creation. Analyzing students' written reflections after each round of inquiry helped determine next steps. In general, according to the results of the study, we were able to promote the formation of reflective skills in students and the development of design and research skills.</p> G. Syzdykova G. Zhampeissova S. Janabekova Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 95 105 10.51889/2959-5894.2024.87.3.008 HEAT TRANSFER MODELING IN SOLAR COLLECTOR ABSORBER WITH PHASE CHANGE MATERIAL https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2122 <p>A numerical model has been proposed in this work for predicting the energy performances of the solar channel absorber plate under Kazakhstan climates. The numerical model is based on energy and mass balance. A new solar channel absorber plate configuration is proposed to improve the performance. A comparison of results has been made between the conventional solar absorber plate and solar channel absorber plate with PCM. The numerical simulation was performed for wide range of ambient temperatures of continental climate with wide range of solar intensities between 100 W/m<sup>2</sup> and 900 W/m<sup>2</sup>. The influences of solar intensity and ambient temperature are discussed. The proposed technology can be used in the following systems: solar water heater, solar assisted air/ground source heat pump, solar thermal energy storage. The developed calculation algorithm based on the heat balance can be used to simulate the thermal performance of solar thermal collectors of various configurations. Various PCMs will be considered in future research, in the heat storage tank.</p> A. Aliuly Y. Karlina Y. Yerdesh M. Mohanraj E. Belyayev Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 7 16 10.51889/2959-5894.2024.87.3.001 JONSSON EXISTENTIALLY CLOSED UNARS OF EXPANDED SIGNATURE https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2053 <p>Being one of the important parts of fundamental mathematics, Model Theory is a young subject for modern researchers in this area. However, according to the last obtained results, this discipline will play a crucial role in the future of mathematical science. As well-known, the name "Model Theory" was introduced in 1954. It is important to distinguish that classical Model Theory introduces concepts based on considering complete theories. The given article is dedicated to the research of Jonsson theories of unars. Jonsson theories are, generally speaking, not complete. Hence, the results obtained in this article are strengthened. Firstly, we considered the theory of all unars and a class of existentially closed models of this theory. Secondly, we expanded the signature of unars that contains only one unary functional symbol by a new unary predicate and constants. Thirdly, we obtained some results concerning the universals and primitives of considered theory’s existentially closed Jonsson unars. Since we are using the new methodology (so-called semantic method) for the research of Jonsson existentially closed unars. Semantic methods consist of transferring properties of fixed complete theory to considered Jonsson theory.</p> A. Yeshkeyev A. Yarullina M. Kassymetova Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 17 26 10.51889/2959-5894.2024.87.3.002 STUDY OF A MODEL FOR CALCULATING A QUANTITATIVE CRITERION FOR ASSESSING THE STABILITY OF INFORMATION AND TELECOMMUNICATION SYSTEMS OF CRITICAL INFRASTRUCTURE FACILITIES https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/1786 <p>Given the global trends towards an increase in the number and complexity of cyberattacks, there is an urgent need to ensure the resilience of information technology systems (ITS), especially sectoral systems that play a critical role in public functioning, socio-economic development and national security. In this regard, at the level of the state, the solution of the problem of ensuring the security of critical infrastructure becomes a priority in the process of reforming the defense and security sector of the Republic of Kazakhstan. In this context, there is an urgent need to develop methods and models for attributing IS to critical infrastructure objects in order to ensure national security of Kazakhstan. This study presents a model for calculating the quantitative criterion of information systems sustainability based on the method of hierarchy analysis. This approach allows us to obtain quantitative indicators of IS sustainability by processing expert evaluations. The application of this model simplifies the procedure of expert selection, avoids the complexities of expert data processing and provides IS assessment with limited statistical data. The developed model allows us to move from a qualitative assessment, represented by an ordered series of alphanumeric combinations reflecting the levels of realized services, to a quantitative assessment in the form of a ratio of functional profiles of security.</p> D. Zhaxsygulova S.Zh. Rakhmetullina S.O. Gnatyuk Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 27 39 10.51889/2959-5894.2024.87.3.013 CONSTRUCTION OF A SOLUTION IN A BROAD SENSE OF A LINEAR COUNTING SYSTEM OF PARTIAL DERIVATIVE EQUATIONS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2085 <p><em>The article discusses the existence and uniqueness of solutions in the broad sense of a first-order partial differential counting system that are periodic in some variables. </em></p> <p><em>The study of periodic solutions of partial differential systems occupies a special place in the modern theory of differential equations. A wide variety of problems in mechanics, physics and technology come down to the study of oscillatory solutions of systems of differential equations, both ordinary and partial derivatives.</em></p> <p><em>The article applies the method of characterization and establishes sufficient conditions for the existence and uniqueness of a periodic solution in a part of variables in the broad sense of a linear infinite system of first-order partial differential equations. Definitions of a solution in the broad sense of an infinite first-order partial differential system are given.</em></p> E.K. Kurmangaliev A.U. Bekbauova Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 40 48 10.51889/2959-5894.2024.87.3.003 DERIVATION OF THE GRADIENT OF THE INVERSE PROBLEM FUNCTIONAL FOR THE HELMHOLTZ EQUATION https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2061 <p>This paper considers the continuation problem for the Helmholtz equation. The solution to the original problem is reduced to solving the inverse problem with respect to the direct ( well-posed) problem. The inverse problem is formulated to clarify the boundary condition with the help of additional information about the solution of the direct problem. The inverse problem is written in operator form. The solution of the operator equation is reduced to the problem of minimizing the objective functional. The paper also examines issues of convergence of gradient methods for solving the inverse problem. An algorithm has been developed for solving the inverse problem using the theory of conjugate optimization and the Landweber method. Detailed calculations for obtaining the associated problem are presented. The results obtained show that the use of the theory of conjugate optimization and the Landweber method makes it possible to effectively solve inverse problems.</p> A. Sarsenbayeva S. Kasenov Zh. Askerbekova A. Tleulesova Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 49 56 10.51889/2959-5894.2024.87.3.004 ON LIMIT ERROR OF THE OPTIMAL DISCRETIZATION OPERATOR FOR SOLUTION OF POISSON EQUATION https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2011 <p style="font-weight: 400;">The purpose of this study is to construct an optimal discretization operator for the solution of the Poisson equation and find its limit error. The research methodology is based on considering the problem of discretizing the solution of the Poisson equation as one of the concretizations of the general problem of optimal recovery of the operator and using well-known statements of approximation theory. In this study, within the framework of this general optimal recovery problem, firstly, in the uniform metric, the exact order of the smallest discretization error of the solution of the Poisson equation with the right-hand side &nbsp;from the multidimensional periodic Sobolev class is established; secondly, based on a finite set of Fourier coefficients of the function , a discretization operator &nbsp;is constructed that implements the established exact order; thirdly, the limit error of the optimal discretization operator &nbsp;was found. Poisson's equation describes many physical phenomena such as the electrostatic field, stationary temperature field, pressure field and velocity potential field in hydrodynamics. Therefore, the relevance of the research conducted here is beyond doubt.</p> G. A. Utessov R. Shanauov N. Amanov Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 57 69 10.51889/2959-5894.2024.87.3.005 ANALYSIS OF TOOLS FOR MEASURING PROFESSIONAL COMPETENCES OF GRADUATES IN THE DIRECTION OF ICT TRAINING https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2083 <p>The article presents an analysis of the tasks used in the qualification exams in Kazakhstan and Russia. The analysis showed that in the CIS countries, qualification exams are held in the form of final certification after graduation. There are no additional certification exams for future IT specialists. The content of the test tasks used in the final certification is aimed at checking the assimilation of the educational materials of the studied disciplines by graduates, that is, compliance with the requirements of general educational standards. Whereas, in addition to general educational standards, when developing educational programs, both the Russian Federation and the Republic of Kazakhstan are guided by professional standards. Based on the results of the work, a problem was identified - the compliance of the skills and abilities of future specialists with the requirements of professional standards is not assessed. Consequently, employers do not have the opportunity to check the readiness of young specialists to perform specific work functions when hiring.</p> K.S. Abdiyev М. Zhassandykyzy D.M. Maintcer V.V. Naumenko G.S. Primbetova Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 190 206 10.51889/2959-5894.2024.87.3.017 DEVELOPMENT OF A CRITERION-ASSESSMENT COMPLEX FOR MONITORING THE EDUCATIONAL ACHIEVEMENTS OF SCHOOLCHILDREN IN COMPUTER SCIENCE https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2145 <p>The research is devoted to developing a criteria-based assessment complex for monitoring students' academic achievements in computer science. The study aims to create a program implementation of an effective monitoring system that will improve the quality of the educational process and the satisfaction of both students and teachers. Within the framework of the study, the following tasks were set: analysis of existing methods for evaluating educational achievements; development of the architecture of a criteria-based assessment complex, including automated assessment mechanisms; and conducting an empirical study to validate the developed complex and its impact on student academic performance. The research methodology includes theoretical analysis, survey, and data analysis methods used to assess the system implementation's effectiveness and to receive feedback from teachers and students. The significance of this research lies in developing an innovative approach to assessing educational achievements, which can be adapted and applied in various educational institutions. The study's results can serve as a basis for further research in educational technologies and assessment of the quality of education.</p> G. Abdulkarimova D. Issabayeva А. Akanova Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 207 218 10.51889/2959-5894.2024.87.3.018 FEATURES OF THE METHODOLOGY FOR TRAINING FUTURE MEDICINES IN COMPUTER MODELING https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2002 <p>The relevance of the problem of using computer modelling in medical education is due to the rapid changes in modern medicine and the requirements for the training of medical specialists. The aim of this study is to investigate effective methods of introducing computer modelling in the educational process of medical schools. The methods of analysis, synthesis, generalisation and systematisation were used to achieve the goal. The results of the study revealed the key stages of computer simulation training in medical education, covering theoretical lectures, practical classes, laboratory work, specialised internships, projects and research, and multidisciplinary training. Theoretical lectures provide fundamental knowledge of computer modelling principles including anatomy, physiology and mathematical principles. Practical classes and laboratory work enable students to master the skills of working with software tools and creating virtual organ models. Specialised internships provide opportunities to apply the skills learnt in real clinical settings. Participation in projects and research focuses on the application of computational modelling to clinical problems, and multidisciplinary training develops a comprehensive understanding of methods in medical science. These results highlight the need for a systematic and fundamental approach to computer simulation training in medical education. The integration of computer simulation training into the curricula of medical schools requires a systematic approach, including both theoretical foundations and practical training, as well as internships in specialised medical centres. The practical significance of the study lies in the substantiation of effective methods of computer simulation training in medical education, contributing to the improvement of medical staff training through the introduction of innovative educational tools and emphasis on practical skills.</p> A.B. Baimakhanova L.B. Rakhimzhanova А.А. Belkhodzhayev Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 219 235 10.51889/2959-5894.2024.87.3.019 MODERN SCHOOLCHILDREN'S VIEWS ABOUT THE LEVEL OF THEIR OWN DIGITAL LITERACY https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/1862 <p>The article understands the problem of developing digital literacy of a modern schoolchild as a necessary competence in the era of the digital economy. Аim of the article is to empirically explore school students’ ideas about the level of their own digital literacy, to formulate principles, the implementation of which in teaching computer science to schoolchildren will ensure the development of a set of digital literacy components. The study, based on an analysis of scientific literature, summarizes approaches to defining the concept of “digital literacy”. Schoolchildren's ideas about the level of development of their digital literacy were obtained based on a survey of two age groups of schoolchildren: grades 5-8 and grades 9-11. It is concluded that there are differences in the levels of proficiency in the components of digital literacy among different respondents and the uneven representation of each of these components in an individual student. The role of school informatics in increasing the level of digital literacy of schoolchildren is substantiated. The research materials can be useful in determining ways to develop digital literacy of modern schoolchildren</p> S.A. Kalinichenko I.B. Shmigirilova Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 236 248 10.51889/2959-5894.2024.87.3.020 THE POSSIBILITIES OF USING VIRTUAL LABORATORIES IN ROBOTICS TRAININGS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/1843 <p>In teaching robotics, many tools are used in the implementation of laboratory work, but their provision in full composition is problematic due to the high cost. Assembling robots requires students to devote a lot of time, diligence and responsibility. The virtual laboratory solves these problems, inspires students and Awakens motivation, interest in classes, allows you to carry out full-fledged laboratory work with the fact that it is publicly available, easy to use and some platforms are free. Therefore, the problem of determining the possibilities of using a virtual laboratory in teaching robotics is relevant.</p> <p>The purpose of our study is to identify the possibilities and needs of using virtual laboratories in teaching robotics. The objectives of the study are to analyze the effectiveness of virtual laboratories for teaching from different online platforms, to show ways of using robotics in modeling, and to identify the need to use robotics in teaching among university teachers.</p> <p> The article examined virtual laboratories in robot building, identified the effectiveness of the Tinker Cad virtual laboratory for analyzing the most effective for teaching robotics among online platforms. An example of using the Tinker CAD virtual laboratory in modeling a robot assembly is explained. This example report deals with the task of burning traffic light LEDs using Arduino in a Tincer Cad virtual laboratory environment. In addition, the results of a survey among teachers to determine the need, the possibility of using virtual laboratories in teaching robotics are presented. According to the results, the effectiveness of the work performed in the Tincer Cad virtual laboratory was demonstrated by example, and it was proved by the results of the survey that the dynamic and interactive nature of virtual laboratories contributes to the development of students ' creative abilities and task-solving skills.</p> <p>In the course of the study were used such common research methods as survey, analysis, synthesis and interpretation of data.</p> G.D. Koshanova M.D. Koshanova A.Zh. Abdulatipov Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 249 262 10.51889/2959-5894.2024.87.3.021 THE USE OF AUGMENTED REALITY TECHNOLOGY IN ROBOTICS TRAINING https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/1683 <p>This article discusses the latest trends and innovative approaches in the field of robotics education, particularly among students from kindergarten to high school. The article notes the growing practical understanding of the impact of robotics on the learning process, including technologies such as proximity sensors, motion detectors, and light-sensitive sensors. In order to involve students in the field of STEM and develop skills for applying their theoretical knowledge in practice, robotics-oriented teaching methods are provided. In addition, it describes the development and development of a mobile application using augmented reality aimed at enriching the educational process and developing the creative potential of students. This application is created through the Unity and Vuforia platforms, which offer significant opportunities to create immersive and interactive virtual experiences.</p> Zh.K. Kulmagambetova A.A. Rysdauletova Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 263 273 10.51889/2959-5894.2024.87.3.022 CREATING DESCRIPTORS FOR EVALUATING ACADEMIC ACHIEVEMENTS IN COMPUTER SCIENCE https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/1776 <p>The scientific article analyzes the methods of assessing students' knowledge in computer science, examines the possibilities of their application in the educational process. Special attention was paid to the specifics of assessing academic performance using tests, projects, essays and other assessment tools and how to choose and use them. The expert examination of scientific works of scientists on the use of assessment tools was carried out, foreign and domestic experience was analyzed.</p> <p>The main factors were the purpose of the lesson, the level of training of students, the time spent, the availability of resources, the advantages and disadvantages of various assessment tools were studied. Based on the results of the analysis, the study analyzed examples of using an assessment tool for a specific task. The main feature of teaching computer science is that students are given many tasks to create a project and write an essay. For teachers, the lack of assigned descriptors for project and essay assessment creates a number of problems.</p> <p>Based on the results of the study, a project was created to create websites and descriptors for evaluating the essay "the role and influence of artificial intelligence in the modern world". In order to increase the effectiveness of computer science lessons, descriptors of an objective assessment of students' knowledge were substantiated. In the study, descending descriptors were created (a decrease in the point value when evaluating readability). This approach not only contributes to the objective assessment of students' knowledge, but also reduces subjectivity in the assessment process. The use of decreasing descriptors complements the methodological complex and affects the adaptation of the level of training of students.</p> A.E. Orazaliyeva G.A. Madyarova B. Moldabekov S.N. Yerniyazova Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 274 286 10.51889/2959-5894.2024.87.3.023 INTEGRATION OF EDUCATION, SCIENTIFIC ENVIRONMENT AND PRODUCTION: METHODOLOGICAL FEATURES OF PRODUCT DEVELOPMENT IN THE STEM LABORATORY https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2076 <p>The STEM-based laboratory is a module that combines elements of science, technology, engineering and mathematics from both a theoretical and practical point of view. In the educational process, this module examines the elements of problem-based learning to improve active learning and the learning process. In particular, teaching physics allows students to learn about digital engineering, work in educational and practical laboratories on their projects related to curricula, and improve their professional skills. This scientific study examines the methods of using the possibilities of the scientific environment and the integration of production in the development of the quality of education in physics educational programs. The purpose of this study is also to determine the impact of interdisciplinary STEM education on the labor market, factors determining the continuity of production and educational organizations. In the course of the study, multimethodic quantitative and qualitative research methods were used. A meta-analysis and systematic analysis of articles in highly regarded journals from Wos and Scopus sources was carried out. About 200 respondents participated in the quantitative data collection in the study. The STEM laboratories used the method of constructive research in order to combine physical knowledge with practice, to improve the work on the development of STEM products in scientific environments. The results of the study showed that the effective implementation of the links between the scientific environment and production in the educational process makes students competitive in the labor market. The research also revealed the technology of product development in the STEM laboratory and the methodological features of the use of products in the educational process. The results obtained correspond to global trends and have a positive impact on the development of scientific and technological trends in the country, the further development of the educational process, and the systematic formation of necessary 21st century skills among students.</p> Sh.Zh Ramankulov N.P. Mussakhan J.M. Bitibaeva B.A. Kurbanbekov D. Berdi Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 287 295 10.51889/2959-5894.2024.87.3.024 USING SCRATCH SOFTWARE TO DEVELOP THE COMPUTATIONAL THINKING OF PRIMARY SCHOOL STUDENTS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2010 <p>The article examines the impact of using the Scratch program on the development of computational thinking in younger schoolchildren.</p> <p>The purpose of this study was to teach primary school students the subject of "Digital literacy" tasks "Creating an online game with codes" on the topic "Logical operators" were proposed, and studies on the development of students' computational thinking were developed. Task execution planning provides for the desire to create independently created games, successfully complete the stage of their execution in the Scratch program, and share your tasks in the Scratch program with classmates, introducing them to the network. Some elementary school students got acquainted with the tasks shared by their classmates and showed a high level of computational thinking and motivation to create additional games from them for the online platform. As a result, the influence of students on the skills of computational thinking, communication and independent development is shown. Due to the development of information technology, learning programming at an early age is important because they should not have problems understanding the logic of programming when they reach the age of a bachelor's degree. Using visual, two-dimensional Scratch for this purpose allows children to express their ideas and thoughts interactively. They can create their own projects using blocks with various functions such as motion, sound and animation. This teaching of children to present their ideas and concepts in a certain form shows the impact on the development of their representational abilities, that is, on their computational thinking.</p> L.Sh. Sabyrkhanova L.K. Zhaidakbayeva A.B. Seitkhanova Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 296 306 10.51889/2959-5894.2024.87.3.025 THE NECESSITY OF IMPLEMENTING SMART CLASSROOMS IN THE TRAINING OF FUTURE INFORMATICS TEACHERS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2136 <p>The article discusses the need to introduce smart classrooms into the educational process and their impact on the training of informatics teachers. Modern trends in educational technologies are analyzed, the importance of smart classrooms as a means of improving the effectiveness of teaching and organizing the learning space is emphasized. Special attention is paid to the training of teachers to work in such conditions, including the necessary qualifications, skills and methodological approaches. The article presents examples of successful practices, as well as discusses the challenges and difficulties that educational institutions may face when integrating smart classrooms. The article also describes an experimental study that substantiates the need to introduce smart classrooms into the educational process of training future informatics teachers.</p> I.T. Salgozha Sh.P. Turashova K. Seiduali A.A. Amangeldin Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 307 319 10.51889/2959-5894.2024.87.3.026 THE ROLE OF GENERATIVE ARTIFICIAL INTELLIGENCE TECHNOLOGY IN CONTROLLING THE KNOWLEDGE OF UNIVERSITY STUDENTS IN PROGRAMMING https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2125 <p>The article examines the role of generative artificial intelligence (GenAI) technology in assessing students' knowledge of programming in higher education institutions. In the modern education system, GenAI allows you to develop automated assessment systems, effectively carry out the process of checking the code and providing feedback to students. The article discusses the advantages of GenAI such as automation, objectivity and personification, as well as demonstrates its capabilities and ways of applying it in assessing students' knowledge. In addition, the ethical and technical problems arising in the process of integrating GenAI technologies into the educational process are considered. As a result, it turns out that GenAI offers a new approach in the field of programming knowledge assessment and contributes to improving the quality of knowledge.</p> A.E. Sagimbayeva A.E. Zhaxylykov Sh.T. Shekerbekova A.B. Zhamkeeva Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 320 330 10.51889/2959-5894.2024.87.3.027 SUCCESSION IN TEACHING 3D MODELING AND AR/VR TECHNOLOGIES https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2107 <p>This article is devoted to the continuity in teaching 3D modeling, augmented (AR), and virtual reality (VR) technologies. The authors pay special attention to the integration of these technologies into the educational process, their interrelation, and their importance for the formation of professional skills of future computer science teachers. Topics were considered in two disciplines: “Computer graphics and 3D modeling” and “Augmented and virtual reality”, which have a systematic character and continuity. The project works of students within the framework of studying these disciplines are presented, which were evaluated according to a specially developed assessment scale according to 6 main criteria. The article presents the results of a pedagogical experiment conducted in teaching 3D modeling and AR/VR. 72 students of the educational program “6B01506-Computer Science”, “6B01514-Computer Science-Robotics” and the educational program “6B01505-Physics-Computer Science” took part in the experiment. The phased nature of the study helped to reveal these research questions comprehensively. The phased nature of the study helped to reveal these research questions comprehensively.</p> P. Tazabekova Zh. Nurbekova T. Sembayev Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 331 339 10.51889/2959-5894.2024.87.3.028 A SYSTEMATIC REVIEW OF EXISTING TOOLS TO AUTOMATED PROCESSING SYSTEMS FOR KAZAKH LANGUAGE https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2082 <p>The development of automated processing systems for the Kazakh language has gained significant momentum in recent years, driven by the growing need for natural language processing (NLP) tools tailored to underrepresented languages. This systematic review aims to critically evaluate the existing observational tools and methodologies employed in the creation and enhancement of automated systems for the Kazakh language. Through a comprehensive analysis of academic literature, technical reports, and practical implementations, this review identifies key trends, challenges, and advancements in the field. The review highlights the various linguistic complexities unique to the Kazakh language, such as its agglutinative nature, vowel harmony, and rich morphological structure, which present unique challenges for developers. Additionally, the study examines the effectiveness of current tools, including tokenization, part-of-speech tagging, syntactic parsing, and machine translation, in processing Kazakh text. The findings reveal that while substantial progress has been made, there are still significant gaps in the availability and accuracy of these tools, particularly in comparison to those available for more widely spoken languages. The review concludes with recommendations for future research and development, emphasizing the need for more robust datasets, improved algorithms, and collaborative efforts to further advance the field of Kazakh language processing.</p> A. Aitim R. Satybaldiyeva Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 106 122 10.51889/2959-5894.2024.87.3.009 BIDIRECTIONAL LONG SHORT-TERM MEMORY IN HATE SPEECH DETECTION PROBLEM ON NETWORKS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2089 <p>The pervasive problem of hate speech on social media has received much attention in the fields of computational linguistics and artificial intelligence. The abstract summarizes the results of a groundbreaking study investigating the use of Bi-LSTM models to detect and analyze hate speech. This study highlights the need for modern machine learning algorithms to analyze the large and ever-changing volume of material on social media. The goal is to accurately detect and reduce instances of hate speech. The paper reviews several procedures used to detect hate speech and traces their evolution over time. It highlights the shortcomings of traditional models and emphasizes the need for more sophisticated, context-aware approaches. The use of Bi-LSTM structures, known for their effectiveness in capturing long-term relationships in sequential data, marks a methodological advance in the field. The results of this study demonstrate that Bi-LSTM models have a greater ability to understand the complexities of language on social media. As a result, they offer a more efficient and effective method for detecting hate speech. This study makes a valuable contribution to the ongoing debate on digital politeness through rigorous experimentation and analysis. It proposes a robust framework that can be adapted and extended across various social media platforms to create safer online communities.</p> Zh.Zh. Azhibekova A.O. Aliyeva N.F. Sarsenbiyeva B.S. Kaldarova A.B. Toktarova Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 123 131 10.51889/2959-5894.2024.87.3.010 OPEN DATA AND ARTIFICIAL INTELLIGENCE: A COMPARATIVE ANALYSIS OF THE USA AND CHINA https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2055 <p>The purpose of this study is to examine the openness of big data practices among major IT companies in the United States and China, with an emphasis on their implications for the development of artificial intelligence and international cooperation. The study employed a qualitative analysis framework incorporating case studies to evaluate data availability, transparency, and collaborative initiatives. The findings indicate that American companies such as Microsoft and Google exhibit higher levels of data openness, supported by a regulatory environment that balances innovation with privacy protection. In contrast, Chinese companies like Tencent and Alibaba prioritize internal data use under stringent regulatory control, emphasizing data security and sovereignty. These differences pose challenges for international cooperation in the field of artificial intelligence, exacerbated by geopolitical tensions and divergent regulatory landscapes. Despite these barriers, there are opportunities for harmonization through common frameworks and collaborative initiatives aimed at leveraging collective expertise to advance AI technologies globally.</p> N.Zh. Aitenov B.O. Kulambayev D.K. Zhekenov D.I. Gubina Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 132 145 10.51889/2959-5894.2024.87.3.011 A COMPARATIVE STUDY OF LOAD-BALANCING ALGORITHMS FOR RELIABILITY OF ENTERPRISE INFORMATION SYSTEMS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/1956 <p>Enterprise information systems are always prone to high loads during active sessions. This issue is becoming more and more actual with the increase of digital enterprise systems. The key to the solution is the use of load-balancing algorithms, which ensure system stability at high workloads. This work analyzes common load balancing algorithms and provides a comparison analysis. The paper also performs a complexity analysis of load balancing algorithms, differentiating between the static and dynamic algorithms. The results show that static algorithms are easy to implement, yet they are unable to adapt to different changes. Dynamic load balancing algorithms require deeper knowledge of the system, but at the same time providing higher efficiency in changing environments. This research paper also provides a recommendation for selecting a load-balancer for enterprise information system.</p> M. Zhanuzakov G. Balakayeva Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 146 153 10.51889/2959-5894.2024.87.3.012 STUDY OF THE STATISTICAL SECURITY OF THE AL04 ENCRYPTION ALGORITHM https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2058 <p>Considering that cryptographic algorithms are among the most reliable methods for protecting information in information systems, assessing their cryptographic strength plays a significant role. For this purpose, comprehensive studies are conducted, and one of the primary characteristics of such an assessment is the statistical security of the obtained ciphertexts.</p> <p>This article investigates the statistical security of the block cipher algorithm AL04, developed in the Information Security Laboratory. The algorithm was implemented in software, and the resulting ciphertexts were analyzed using the test sets of D. Knuth and NIST, as well as checked against the avalanche effect criterion (average number of output bits, degree of completeness, degree of avalanche effect, degree of strict avalanche criterion). The statistical tests used are the main tests in the works of many researchers and determine the properties of sequence randomness with high accuracy. The study found that AL04 does not have deviations in the sequences obtained using the algorithm. Thus, it was established that the algorithm possesses high statistical security.</p> A. Khompysh N.A. Kapalova D.S. Dyusenbayev V.A. Varennikov Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 154 163 10.51889/2959-5894.2024.87.3.014 FEATURES OF SPEAKER RECOGNITION THROUGH DEEP LEARNING OF NEURAL NETWORKS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/1872 <p>This article discusses the transition from traditional methods to a new deep learning architecture for speaker recognition. It is aimed at comparing traditional statistical methods and new approaches using deep learning models. In addition, the latest optimization methods are described. There are also several assessment methodologies based on different approaches. The article provides an overview of deep learning methods and discusses recent literature using these approaches for speaker recognition. Speaker verification involves checking the speech signal to confirm whether the speaker's statement is true or false. Deep neural networks are one of the most successful implementations of complex nonlinear models for studying special properties of data. They demonstrated their abilities in speaker recognition and speaker recognition tasks. In this article, we will look at deep neural network (DNN) methods used in speaker verification systems. It will include the database used, the results, the contribution to speaker recognition and related limitations.</p> K. Turganbay S. Issabayeva E. Tenizbaev T. Zhukova L. gnashova Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 164 173 10.51889/2959-5894.2024.87.3.015 REVIEW OF LITERATURE AND PATENT RESEARCH ON STUDENT STRESS CONTROL https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2090 <p>The Internet of Things (IoT) has become the main platform for the interaction of interconnected devices, representing a new paradigm and the next step in the evolution of the internet. Its importance is especially noticeable in health care, where the IoT monitors medical services. By analyzing the data collected from different devices, it is possible to predict the development of certain diseases. One of the promising areas is stress control through wearable sensors and IoT, which significantly increases well-being and improves preventive health management. Medical professionals are already using reliable systems that include wearable devices on batteries and wireless communication channels to economically monitor the state of health in various diseases. Sensors connected to the network, deployed both at home and in the human body, collect important data necessary to assess the health of patients. The integration of machine learning and advanced technologies has aroused great interest in the study and solution of problems related to stress levels. Psychological stress significantly affects the physiological parameters of a person and can lead to negative consequences, sometimes requiring expensive treatment. Acute levels of stress can be life-threatening, especially for people diagnosed with borderline personality disorder or schizophrenia. This article provides a systematic review of the literature on Wearable IoT devices in healthcare. The review begins with a search for publications by given keywords and ordering them by relevance and publication date. The article discusses the use of wearable devices to address health problems such as disease detection, control, and treatment, and describes their architecture. In addition, promising areas of future research are outlined.</p> <p>&nbsp;</p> G.A. Tyulepberdinova M.M. Kunelbayev G.A. Amirkhanova Zh.O. Oralbekova M.G. Zhartybayeva Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2024-09-27 2024-09-27 87 3 174 189 10.51889/2959-5894.2024.87.3.016