ІНФОРМАЦІЙНО-КОМУНІКАЦІЙНІ ТЕХНОЛОГІЇ НАВЧАННЯ АНАЛІТИЧНОЇ ГЕОМЕТРІЇ ТА ЛІНІЙНОЇ АЛГЕБРИ МАЙБУТНІХ УЧИТЕЛІВ ФІЗИКИ Й ІНФОРМАТИКИ

Purpose of research. The purpose of the paper is to describe the possibilities of including tasks for the design, development, use and experimental evaluation of “inverted” educational resources in the professional training of future teachers of mathematics and computer science for the development of their subject-methodical readiness. The formation and development of subject-methodical readiness is the main goal of professional training of future lecturers at a pedagogical university. The process of creating “inverted” educational resources requires from their author quite serious subject and methodological training. Potentially, the inclusion of tasks for the design, development, expertise, practical use and evaluation of “inverted” educational resources in the professional training of future teachers of mathematics and computer science can create conditions conducive to the formation of competencies of future teachers to create a comprehensive educational process in a digital environment. Since, on the one hand, in such didactic means, the educational content should be presented systematized and structured, have logic and hierarchical connections. On the other hand, the problematic issues included in the resources should reflect specific subject educational results in accordance with a given taxonomic model in the curriculum.Materials and methods. Based on the analysis of theoretical and methodological sources, the article substantiates the relevance of the problem of finding new ways and means of implementing additional subject training in mathematics and computer science for both schoolchildren and future teachers in the context of digitalization of education. The analysis of examples of “inverted” educational resources, which are the results of the implementation of project tasks by undergraduate students of the Krasnoyarsk State Pedagogical University named after V.P. Astafiev, is presented. Through theoretical and methodological substantiation, the main possibilities of including tasks for working with such resources at different stages of professional training of future teachers of mathematics and computer science at a pedagogical university are synthesized.Results. In this study, the problems related to the possibility of including “inverted” educational resources as digital didactic tools in the training programs of future teachers of mathematics and computer science were updated. The authors’ position on the issue of the purpose of such teaching tools in the context of the digitalization of education is presented and substantiated. Examples of the results of the implementation of project tasks by senior students during the 2021-2022 academic year were demonstrated. The key didactic and information technology features, possible tools for creating “inverted” educational resources are given. The definition of the subject-methodical readiness of the future teacher of mathematics and computer science as an essential component of professional readiness is concretized. The possibilities of strengthening subject-methodical training by including tasks for work with “inverted” educational resources are described: analytical – in junior courses when mastering disciplines related to the use of digital technologies in education; project – in the middle courses when mastering methodological disciplines; experimental and expert - in the senior courses when passing industrial (pedagogical) practice and mastering the final disciplines of the professional educational program of higher pedagogical education.Conclusion. On a final note, the results and conclusions obtained in the paper are summarized; the key positions of the authors on the inclusion of “inverted” educational resources in the professional training of future teachers of mathematics and computer science are given. The materials of the article may be of interest to lecturers of pedagogical universities who train future teachers, representatives of schools cooperating with organizations of higher pedagogical education, researchers in the field of digitalization and digital transformation of education.

Abstract. This article explores the possibilities and advantages of using the Python programming language together with Arduino robotics kits in the process of training future computer science teachers in pedagogical educational institutions. Considerable emphasis is placed on analyzing the principles of operation of the simplest programs and devices that can be used to visualize the possibilities of using the Arduino platform and Python libraries to create robots that can be implemented in the educational process and everyday life. The authors have developed the program code and presented a working model of a robot assembled and programmed on the basis of Arduino components to measure humidity in computer laboratories and create automatic plant irrigation systems to maintain proper conditions in classrooms. The article presents an example of integrating the learning of the Python programming language with the use of Arduino robotics kits. This method is aimed at improving the quality of training of future computer science teachers, expanding their methodological arsenal and ensuring the ability to teach students using innovative means. The results of the study and the developed teaching and learning materials will help to interest students in STEM education and prepare a new generation of computer science teachers for the challenges of the modern technological world, expand their methodological arsenal and develop the ability to use integrated technical, engineering and mathematical solutions to solve theoretical and practical problems. In addition, this study can serve as a guide to popularize the use of Arduino and Python in educational institutions, and encourage future computer science teachers to implement STEM and hands-on teaching methods, which will contribute to better student learning and improve the quality of professional education in the field of information technology in general. In general, the study opens up a wide range of opportunities for using modern digital technologies in professional education and stimulates interest in STEM education among computer science teachers and students, thereby contributing to the development of a new generation of engineers and technology leaders. Further research could be aimed at developing specific training courses and methods for integrating the Python programming language and Arduino robotics kits into STEM education. It is important to create interdisciplinary STEM courses with the participation of teachers of computer science, physics, mathematics, vocational education in the IT industry, etc.

В даному дослідженні розглядаються питання модернізації змісту навчання у процесі професійної підготовки майбутніх вчителів інформатики. Важливою передумовою для оновлення освітніх програм для підготовки майбутніх вчителів інформатики є швидкий темп розвитку інформаційно-комунікаційних технологій, виникнення нових міждисциплінарних напрямів, поява нових професій, пов'язаних з активним використанням новітніх технологій у виробництві, а також змінами в структурі та змісті навчання шкільного курсу інформатики протягом останніх років. Стрімкий розвиток вищезазначених прикладних галузей спричинює потребу у підготовці відповідних кваліфікованих фахівців, для навчання яких необхідне оновлення змісту шкільної та вищої освіти відповідно до вимог сьогодення. Таким чином розробка змісту і методичних систем навчання нових дисциплін запропонованих вибіркових блоків сприятиме підготовці педагогічних кадрів, здатних працювати в умовах становлення інформаційного суспільства. Метою даного дослідження є окреслення напрямів модернізації змісту професійної підготовки майбутніх вчителів інформатики відповідно до нових вимог суспільства. В статті запропоновано напрями модернізації змісту навчання майбутніх вчителів інформатики з врахуванням сучасних досягнень науки, техніки, інформаційно-комунікаційних технологій та оновленням змісту шкільного курсу інформатики. Модернізація змісту навчання у процесі професійної підготовки майбутніх вчителів інформатики, його узгодження із найновішими досягненнями сучасної науки та інформаційно-комунікаційних технологій дозволить вдосконалити процес підготовки висококваліфікованих педагогічних кадрів, сприятиме формуванню у студентів значущих особистісних професійних якостей майбутнього вчителя і науковця, а також забезпечить їх неперервний розвиток, професійне та особистісне самовдосконалення.

Digital transformation has revolutionized the field of computer science, and as a result, education and student training in the field has also evolved. The article, based on the analysis of scientific literature and statistics, reflects the current trends in the training of future computer science teachers in the conditions of the digital transformation of education. In the process of analysis, general trends in the training of future informatics teachers were revealed, such as computer literacy, use of interactive technologies, development of practical skills, and improvement of teachers' qualifications. Particular attention was paid to the specifics of training future computer science teachers in the conditions of digital transformation of education, such as the use of online courses and webinars, the development of pedagogical skills in the use of the latest technologies, and the creation of a creative and innovative environment. The requirements for the competencies of future informatics teachers were analyzed, in particular, attention was paid to the need to possess not only technical knowledge, but also communication skills and the ability to adapt to new technologies and situations. The article highlights key concepts and practices that shape the preparation of future computer science teachers in the age of digital transformation, including interdisciplinary approaches, experiential learning, industry partnerships, and ethical considerations. The article also discusses the challenges and opportunities associated with these trends and provides recommendations for educators and institutions to effectively prepare students for the digital age. Based on the analysis, it was concluded that the training of future informatics teachers needs constant updating and adaptation to the new requirements of the digital age. To achieve success in this field, it is necessary to use the latest technologies and innovative approaches to learning. Summarizing, the article proposes orientation to ensure access to quality education for all students, use of the latest technologies and development of general competencies of future teachers as important directions in the development of training of future informatics teachers. The specified research results can be useful for teachers of higher educational institutions who are engaged in the training of future informatics teachers, as well as for heads of educational institutions who plan to introduce a digital environment and contribute to the development of digital transformation. For this, it is important not only to provide students with the necessary knowledge and skills, but also to create conditions for their development of creative thinking and innovative activities. In addition, it is important to increase the level of motivation of students to study computer science, for example, by using the latest technologies and interactive teaching methods. These approaches will make it possible to prepare future informatics teachers who will be able to work successfully in the modern digital world and will contribute to the further development of digital transformation in education.

In the modern conditions of the dynamic development of the information society, the training of specialists in the field of pedagogy, in particular computer science teacher, becomes especially relevant. The priority task of higher pedagogical education is the formation of a new generation of educators, who must possess not only thorough knowledge of the subject, but also developed skills of social interaction, cooperation, teamwork, freely navigate in the information space, use modern electronic didactic tools, specialist services, information resources etc. The article examines the essence of the concepts «group educational and cognitive activities», «collective forms of learning», «electronic cooperation», «mind mapping techniques». The author analyzed the possibilities of mind mapping techniques as a means of visualizing thinking processes and structuring information. The classification of digital tools for creating mind maps (free and licensed programs and webservices) is presented. Their advantages and features, methodological techniques and basic principles of working with them are considered. The practical experience of using mind maps to activate the group educational and cognitive activities of students is presented. The method of using mind maps in the training of future computer science teachers is proposed, which includes: determining the purpose and tasks of using mind maps; choosing an online service for their creation; acquainting applicants with the basic principles of working with mind maps; their performance of practical tasks using mind maps; discussion of the results of tasks and summing up. Practical tasks and samples of the results of students' joint work on creating mind maps within the educational component «School computer science course and its teaching methods» are presented. It was found that the use of mind mapping techniques is a promising method of activating the group educational and cognitive activities of future computer science teachers, which contributes to the formation in them of the necessary competencies for successful professional activities in the conditions of the information society.

The article considers the relevance of quality training of future teachers of natural sciences in modern conditions, which is due to the processes of reforming all links of the education system, global changes in the European labor market, the development of world science and pedagogical practice, as well as the shift of emphasis from the accumulation of knowledge to the mastery of methods of activity. The main strategic tasks and requirements for the quality of the educational process and the professional level of modern teachers are analyzed. The need for future teachers to master new functions, new content of activities, search and introduction of modern methods of teaching and learning was determined. Special attention is paid to the formation of ten key competencies among graduates of general secondary education institutions. The article deals with scientific studies of the problems of the individual's scientific research activity, which focuses on the formation of research skills in various categories of subjects. The importance of the formation of scientific-research competence in the system of training future specialists, researched by many Ukrainian and foreign scientists, is emphasized. The multidimensional process of scientific research activity in the formation of the personality of future technology teachers, which includes the development of research skills, independence and competences, is analyzed. The essence and theoretical justification of the students' research activity is defined, which involves the analysis of the concepts «scientific activity» and «research activity», especially in the context of the organization of such activity in higher education. The distinction between the concepts of «scientific activity», «scientific-organizational activity», «scientific-pedagogical activity» and «scientific-technical activity» is outlined. It is emphasized the need to refer to the reference-source base to clarify the specifics of the interpretation of the term «scientific-research activity».  The article examines the importance of research activity in the context of personality formation of future technology teachers. The role of innovative learning technologies, such as problem presentation, heuristic methods, game methods and case methods, in the development of critical thinking, research skills and independence of students is analyzed. The growing importance of information and communication technologies in education requires from future teachers the ability to critically evaluate and use online resources to ensure the quality of learning and active scientific research. The training of future technology teachers should include the development of skills to work in a hybrid research environment, using both traditional and digital resources. Developed research competence is a key aspect of improving the quality of the educational process and includes a system of motives, states, special attitudes, research knowledge, skills and abilities. 

The paper considers the principles and content of training future computer science teachers to develop and use open educational resources. Computer science plays an important role in education, so training qualified teachers in this area is becoming necessary. At the same time, currently, open educational resources are widely used at all levels of education. Open educational resources are available online materials that everyone can freely use. Future computer science teachers should have access to interactive textbooks, video lectures, online courses, etc., and they should familiarize themselves with the types of open resources and the principles of their development. Training future computer science teachers to develop and use open educational resources is based on several principles and includes several key aspects. During the research, the main criteria and principles of developing and using open educational resources were identified. The paper also considers the methods of using open educational resources in the educational process, the advantages and difficulties of using open educational resources, and provides recommendations for the effective use of such resources in the educational process. The research results may be used in the future in the process of training computer science teachers to develop and use open educational resources.

The article presents an analysis of the problem of succession and one’s own managerial and pedagogical experience in its implementation in the training of future primary school teachers in the college-university system. The purpose of the article is to analyze the possibilities and management mechanisms for implementing continuity in the training of future primary school teachers in the college – university system using the example of the experience of the Faculty of Psychology and Pedagogy of the Kuzbass Humanitarian Pedagogical Institute of Kemerovo State University. The methodological basis of the research is the pedagogical principles of continuity in education and lifelong education. Based on the strategic planning method of SWOT–analysis, an assessment of the readiness of an educational organization of higher education to implement continuity in the pedagogical college – university system was carried out. The strengths of the university and objective opportunities available for this process are highlighted, weaknesses and external threats are analyzed. The management mechanisms for the implementation of the principle of continuity at two levels of professional education are considered. In conclusion, it is concluded that the implementation of continuity in the training of future teachers in the college – university system involves the use of management mechanisms representing a sequence of organizational and methodological actions. At the same time, the development of the learning process at the stage of mastering the higher education program is carried out in dialectical connection with the previous level of education and at the same time in accordance with the current goals, objectives, requirements for the training of a modern primary school teacher and conditions.

The problems of professional training of future teachers in a pedagogical university are considered in the article. The relevance of this study in the regulatory documents adopted in the Republic of Kazakhstan, as well as the structure of professional training of teachers as a pedagogical system in scientific and pedagogical research are analyzed. The essence and place of the school course of Informatics among general education disciplines and the importance of professional training of future teachers of computer science in the context of digitalization of education have been substantiated. The components of the professional activity of a teacher of informatics are determined. The terms information and communication technologies and digital technologies are considered and the differences between these terms are described with examples. The stages of studying informatics in general education secondary school according to the updated curriculum and requirements for the professional training of informatics teachers are described. Recommendations for improving the professional training of future teachers of informatics are given.

Abstract.Modern education faces challenges related to the growing importance of information technologies. Effective training of future computer science teachers becomes a key task in this context. The collaborative open learning (COL) system is a potentially promising approach that combines the principles of didactics and modern educational technologies, the research of which is highly relevant. Students have different learning rates and learning styles. It is possible to adapt the educational process to the individual needs of students, which can increase their motivation and learning outcomes. The relevance is also due to the fact that COL revises traditional teaching methods, providing new opportunities for active and experiential learning. The study of didactic aspects of COL can help computer science teachers to reconsider their teaching approaches and adapt them to modern requirements. Thus, the aim of this study is to analyse and justify the didactic foundations of using COL in the training of future teachers of informatics. To achieve this goal, the following tasks are set: to analyse the theoretical aspects of informatics education and didactic principles underlying the educational process. The subject of the study is the process of using the system of collaborative open learning in the educational programme of training future teachers of informatics. The object of the study is students and teaching staff, as well as the educational programme itself and methods of teaching computer science. The study used a comprehensive methodology, including literature analysis, as well as an analytical review of existing practices and pedagogical methods. The analysis of theoretical and practical aspects of COL has revealed the potential of this system in the training of future computer science teachers. The results of the study provide a basis for the development of recommendations on the integration of COL into the educational process and allow us to draw conclusions about its effectiveness.

As a result of literature analysis the expediency of free access of bachelors majoring in Computer Sciences and Information Technologies to modern information educational resources, in particular, e-learning courses in the process of studying mathematical disciplines is substantiated. It was established that the e-learning course is a complex of teaching materials and educational services created for the organization of individual and group training using information and communication technologies. Based on the outlined possibilities of applying the e-learning course, as well as its didactic functions, the structure of the certified e-learning course “Analytic Geometry” based on the Moodle platform was developed and described. Features of application of cloud-oriented resources are considered: Desmos, Geogebra, Wolfram|Alpha, Sage in the study of the discipline “Analytic Geometry”. The results of the pedagogical experiment on the basis of Borys Grinchenko Kyiv University and A. S. Makarenko Sumy State Pedagogical University are presented. The experiment was conducted to verify the effectiveness of the implementation of the e-learning course “Analytic Geometry”. Using the Pearson criterion it is proved that there are significant differences in the level of mathematical preparation of experimental and control group of students. The prospect of further scientific research is outlined through the effectiveness of the use of e-learning courses for the improvement of additional professional competences of students majoring in Computer Sciences and Information Technologies (specialization “Programming”, “Internet of Things”).

The accelerated process of innovation is one of the decisive factors, without which it is impossible to maintain leadership in today's world. The development of technology is actively influencing education, changing the pace of learning. At present, acquiring a knowledge system in an educational institution is no longer a key priority. It is much more valuable to develop students' analytical and modern digital skills, the ability to effectively apply the acquired knowledge in practice. The article is devoted to the problem of using mental maps in the educational process as one of the effective innovative pedagogical technologies for visualizing the process of thinking and an alternative technique for recording information. The features of the use of mental maps as a means of visualizing the level of understanding and application of theoretical material in the process of solving problems in the course “Mathematical Analysis” by future teachers of mathematics, physics and computer science in institutions of higher pedagogical education are described. It is concluded that it is advisable to make mental maps when performing practical tasks on the topics “Graphing a function”, “Finding boundaries”, “Investigation of a function and plotting its graph”, “Finding the largest and smallest values of a function of one and several variables”, “Geometric Applications of the Integral”, etc. It has been established that this technique should not be used in algorithms designed for several steps. It is proved that in combination with digital services designed to create maps, this technology allows you to optimize the process of solving problems, visualize the process of thinking, positively influence the formation of digital competence in future teachers in the context of digitalization of education and is an effective means of increasing the efficiency of the educational process since it helps to restore skills focusing attention and contributes to the structuring of theoretical material. Keywords: education; teacher training; thinking process; mental map; visualization; mathematical analysis; limit; graph; innovation.

The article examines the state of training of future teachers of computer science in higher educational institutions of the republic and the introduction of STEM education and the basics of machine learning into the educational process. The materials on the development of special courses and their implementation in universities in these two areas, on the content of special courses to improve students' knowledge, the formation of new knowledge and skills are presented. The implementation of the training of future computer science teachers in STEM directions within the framework of the Erasmus+ program is also being considered.

The article deals with the formation of information and communication competence of junior high school students in computer science lessons in elementary school by means of project activities. The author emphasizes that the vocation of educational institutions in our time (including elementary school) consists in the formation of competences in the students of education, which today act as a guarantee of a successful professional and personal life of a person. Also, in the conditions of the rapid development of computer equipment and information technologies, the priority of education development is determined by the introduction of modern information and communication technologies in education, which ensure the improvement of the educational process, the accessibility and effectiveness of education, and the preparation of the young generation for life in the information society. And the most effective means of solving the tasks in our time are projects as an activity for solving various problems. Projects have certain features and significantly increase motivation to study, as they form a reasonable balance between academic knowledge and pragmatic skills. The use of project activities in the educational process makes it possible to comprehensively solve the tasks of education, upbringing and development of the school. The implementation of projects by younger schoolchildren makes it possible to form a personality that better adapts to changing conditions and circumstances, orients itself in various situations, successfully integrates into society, defines and implements its life strategy, is capable of self-organization, self-realization, and creative potential. An important role in solving project problems is played by information technologies, familiarization and assimilation of which takes place in computer science classes in elementary school. The use of information and communication technologies in project activities makes it possible to master new ways of working with alternative sources of knowledge, establish new contacts to expand the sphere of communication. The positive emotions that students receive in project activities using information and communication technologies strengthen their self-confidence, contribute to the development of their cognitive activity, and increase motivation to study school subjects. In this case, the implementation of projects using information and communication technologies should be an integral structural element of the educational process of primary school.

The aim of the study is to discuss organizational and methodical bases of formation of ICT competence graduate in the third stage of higher education. Methods. Theoretical methods involve analysis and synthesis, induction and deduction, comparison and classification methods, and empirical method of observation. Results. Trends in the selection of the content of the educational program of graduate students at the third level of higher education in the formation of IT competence are presented: education of the valuable relation to the use of IT in professional activities; the formation of readiness to use IT in education and scientific research; the development of IT skills for processing and visualization of experimental data; modeling of processes and phenomena of professional activities; preparation of the teaching staff to the creation of a new information and educational environment among educational organizations; the development of new social and educational role, forming a system of knowledge and skills of students in the field of information; the development of ready-to-use information technology in the management of education. The discipline content «Information and communication technologies in education and research activities» is selected in accordance with a preferred direction of formation of IT competence. Target indicators and indicators of graduates’ IT competences are developed. Scientific novelty. The concept of IT competence of the teaching staff is introduced. The model of discipline «Information and communication technologies in education and research activities» is designed on the basis of evolutionary development of ICT competence of graduate students in the two-level system of higher education content. Practical significance. The proposed content of the course «Information and communication technologies in education and research activities» which is the basis for the formation of IT competence of the teaching staff at the third level of higher education, allows to generate future teachers’ and researchers’ skills integration of different types of activity (training, educational research, educational, methodical, scientific research, organizational) within a unified methodology based on the use of IT