Conceptual model of a practice-oriented adaptive technology for reviewing the school mathematics course

Purpose. To present a conceptual model of practical orientation in mathematics education in basic secondary and senior profile schools and reveal some aspects of its implementation. Research methodology. Theoretical methods were used: analysis, synthesis, comparison, generalization of theoretical material presented in educational, scientific sources and regulatory documents; study and analysis of current mathematics curricula, content of alternative mathematics textbooks. Empirical methods: surveys of teachers, mathematics methodologists; experiment, observation. Results. A conceptual model for implementing practical orientation in mathematics education has been developed, which takes into account students' age characteristics and the specifics of the school mathematics course. The model is structured in two directions: vertical (three age periods: younger adolescent, older adolescent, youth) and horizontal (three stages: motivational, practical, practical-applied). Each age period is characterized by specific goals, means, teaching methods and expected results. The motivational stage ensures understanding of the practical significance of mathematical knowledge through solving purposeful tasks, the practical stage forms strong skills and abilities, the practical-applied stage develops the ability to apply knowledge to solve real problems. Detailed examples of model implementation are presented on topics "Greatest Common Divisor" (grades 5–6) and "Systems of Linear Inequalities with Two Variables" (grade 9), which demonstrate the step-by-step formation of practical skills from understanding the origin of mathematical concepts to their application in professionally-oriented situations. Conclusions. The proposed model provides a systematic approach to forming students' mathematical competence in accordance with the requirements of the New Ukrainian School Concept. The model's approbation confirmed its effectiveness in forming both mathematical and key competencies. The model can be adapted by practicing teachers for various topics of the school mathematics course, taking into account the specifics of a particular class and educational institution. Practical implementation examples demonstrate the possibility of integrating mathematical knowledge with real-life situations, which promotes conscious learning of educational material and prepares students for applying mathematical knowledge in future life.

The article defines the peculiarities of managing transformation processes in general secondary education institutions during the period of modernization, transformation, positive changes and their continuous, stable, sustainable development. Our reflections are based on the fact that the management of transformation processes in general secondary education institutions is strategic and should be built in the plane of "Study globally – determine the scientific basis – act locally" and is complex and innovative in content. The strategic problem of transformation processes is the management of the spiritual positive energy of transformation and peace. That is why the management of transformation processes at school in modern conditions is viewed through the prism of strategic management and is carried out taking into account the need to ensure the development of participants in the educational process, subject to overcoming the negative consequences of a pandemic, war, environmental disaster, climate "records", crisis and the presence of educational losses, educational gaps, poor performance, illiteracy, knowledge gaps in students and the need to quickly involve internally displaced children and students in the educational process. Determining the features of the management of transformational processes in the field of education and general secondary education institutions is the highest level of the art of management and is provided by strategic thinking, strategic management and covers the theory and practice of training teaching staff, children, students, and parents to the acquisition by schoolchildren of high-quality scientific knowledge, mastery of a scientific worldview on the basis of harmonious development and education, as well as planning, forecasting and organizing the educational process, researching its regularities, developing and applying methods, options, methods, and forms of learning, studying, and self-education of students. It provides for a rational, competent arrangement of available pedagogical staff, effective use of the material and technical base, information resources, determination of strategic priorities, goals and tasks for class leaders, class teachers, teachers, librarians, heads of circles, sections, creative teams, heads of offices, as well as the use of innovative forms and methods of education, forming the sphere of cooperation with state management bodies, scientific institutions, methodical services, educational institutions, public organizations and professing the ideology of pedagogy of cooperation and mutual understanding between the participants of the educational process. Strategic management of transformational processes in institutions of general secondary education, especially in conditions of war, is closely related to educational policy in the country and stems from the needs of a free creative gifted individual, a social human society, a democratic state, an innovative economy of knowledge and the needs of defense, protection, guardianship, compliance with social guarantees. Legislation, normative legal acts set tasks for educational institutions, and the strategy ensures their fulfillment. The strategy of managing transformational processes in institutions of general secondary education depends on the level, state and pace of economic development and on the actual provision of necessary and sufficient funding, security, including social security, of all participants in the educational process. The strategy of managing transformational processes is, as a rule, the same for all schools and its recommendations, the main provisions should be mandatory for all institutions of general secondary education, regardless of status, type, subordination, location and form of ownership. With regard to tactics, strategic management plays a certain role and at the same time takes into account the powers, status and capabilities of the institution of general secondary education and should serve to realize the basic rights and freedoms of participants in the educational process, and the basic right to a spiritual, happy, safe, protected, joyful life in the plane of observance and fulfillment of the main spiritual laws – Love, Forgiveness and worldview and value categories and principles of Peace, Faith, Hope, unity, solidarity, commonwealth.

On the basis of the content analysis of the scientific literature on the outlined problem and the study of practical experience of organising the educational process of higher education applicants studying on an individual training programme and options for using various learning formats, the authors reveal the essence of adaptive learning and describe the features of its application in higher education institutions (HEIs) under martial law. The methodological foundations of the study are the conceptual developments of domestic and foreign scientists in the field of organization of adaptive learning, the study of innovative methods of organization of the educational process in institutions of higher education using adaptive learning formats. The methodological foundations of the study are the conceptual development of domestic and foreign scholars in the field of adaptive learning, the study of innovative methods of organising the educational process in higher education institutions using adaptive learning formats. The research was organised using a set of general scientific methods: theoretical, empirical and data content analysis methods. Theoretical methods contributed to the synthesis and analysis of psychological and pedagogical literature, the regulatory framework for the development and implementation of adaptive learning in the educational space. Empirical methods of selecting scientific and research material (surveys of higher education applicants, development of the regulatory framework), interviews with academic staff on their readiness to implement ideas, forms and models of adaptive learning in the educational process of modern educational institutions. The use of adaptive learning technologies in the educational process of higher education institutions allows to prevent the appearance of educational losses and gaps in knowledge, provided that students are individually trained, and acquire the desired level of knowledge. The authors emphasise that adaptive learning provides a flexible system of organising training sessions taking into account the individual characteristics of higher education applicants. In this process, special attention is paid to the student's personality, the leading kinds of activities chosen by him/her, personal and professional qualities, and the level of competence. It is noted that the optimal solution for the use of adaptive learning technologies is to organise learning interaction with a personal tutor according to an individual schedule at a convenient time for everyone.

The article analyzes the issues of material and technical support of the educational process in institutions of general secondary education, the solution of which lies in the three-level subordination of educational institutions (macro-level – ministries, departments and institutions, meso-level – local executive authorities, local self-government bodies, united territorial communities, micro-level – educational institutions). It is indicated that in order to solve the tasks set at the state level to modernize educational processes, it is necessary to work together at all levels. It is proved that conceptually all issues of the organization of educational space are solved on macro-level, real ways of implementation and financing – on meso-level, and the leading role in the arrangement of specific educational premises is played by managers and teachers of educational institutions. Therefore, our research highlights the importance of training future teachers who are able to implement the concept of a New Ukrainian School in all its areas, in particular from the point of view of updating the educational space.
 The key aspects of forming the educational space of the New Ukrainian School in terms of comfort, safety and aesthetic appeal are identified. Recommendations are given on the color design of the interior of educational premises for primary, middle and high school students, as well as on color solutions for educational premises for various purposes.
 The relevance of zoning the educational environment by centers (discoveries, news, materials, communication, thematic, teachers, silence, creativity, wildlife) of educational activities of participants in the educational process is revealed. The main (permanent) and mobile (variable) zones of the training room are defined, and the approximate equipment of each of them is given. It is proved that the organization of a comfortable educational environment will contribute to the free development of the child’s creative personality. A number of requirements (ergonomics, safety, reliability and aesthetics) for school furniture are defined, as they should first of all be atropometrically appropriate and comfortable.

The article analyzes the proposed effective model of a general secondary education institution in the conditions of the implementation of mixed education (the use of distance, network, home, individual learning technologies), outlines new vectors of development of general secondary education institutions based on the integration processes of the implementation of mixed education, the need for which arose during pandemic and Russian military aggression, pedagogical organizational principles are outlined. The question of solving the problem of assessing the quality of basic secondary education is raised, the points of improvement of the mechanisms of the organization of the educational process in institutions of general secondary education are considered.. The proposed model of the general secondary education institution contributes to the individualization of the educational process, encourages teaching staff to continuous self-education, promotes the formation of an information culture in them, sets them up for mastering innovative means of obtaining and applying information, and creating an individual educational trajectory. The system of organization of the educational institution as a social phenomenon is considered in several aspects: the study of the conditions of management of the institution of general secondary education in the context of the implementation of mixed education; determination of the index of cognitive activity of pedagogical workers of the institution of general secondary education in the conditions of mixed education; determining the effectiveness of the institution of general secondary education in the conditions of the implementation of mixed education.

Relevance of the research is related to the methodological and technological imperfections of the educational process in educational institutions, its fragmentation, and the insufficient level of psychological and pedagogical readiness of teachers for innovative changes in educational work in the context of the modern information society and the large-scale war in Ukraine. The aim of the article is to reveal the theoretical and methodological foundations for organizing an innovative educational environment in general secondary education institutions. The author analyzed scientific sources concerning the problems of educating youth and various aspects of developing innovative processes in education. The main problems in the educational and upbringing space in Ukraine are analyzed. It is noted that innovations, under current conditions, are becoming one of the most important directions of educational activities in educational institutions; however, new educational practices are being implemented slowly and are often carried out without consideration of changes in social and regional conditions. A new format of educational work is characterized, defining the personal development of students as the primary goal of education in all educational institutions. Factors affecting the quality of the educational process have been identified. The interpretations by Ukrainian scholars of the concepts of «innovation in education,» «innovativeness,» «innovative process,» and «innovative educational environment of general secondary education institutions» are highlighted. The innovative educational environment of the New Ukrainian School (NUS) is characterized, and pathways for its creation as an innovative educational interaction between teachers and students on a subject-subject basis are outlined. The professional mission of NUS teachers in educational work is defined as the pedagogical support of the process of individual formation and development of students’ personalities during their school education, including forecasting, organization, control, and analysis of the daily lives and activities of schoolchildren. It is emphasized that modern technologies are at the core of developing a new educational system, the main principles for selecting which are prospectivity, democratic nature, humanistic orientation, integrativeness, realism, wholeness, manageability, economy, and relevance. A values-based approach to education is defined as the most important condition for the personal development of students, realized through the construction of the structure of the value-oriented educational space of a modern educational institution. Education is recognized as the leading priority in the educational space, the expected results of which can only be achieved through updating its content, corrected to new goals and benchmarks of competency-based education. Keywords: general secondary education institution,

One of the higher-priority directions concerning improvement of the institution of general secondary education is the adaptation of teachers’ educational, scientific methodological and organizational activities to the modern challenges. The orientation of the new Ukrainian school to the world educational standards calls for new approaches to the organization of the educational process in institutions of general secondary education, the formation of up-to-date effective innovative competence of teacher-practitioners. In order to diagnose the level of formation of teachers’ innovative competence a summative experiment was conducted as a method to obtain and fix theoretical and empirical data. In the course of the research the criteria for innovative competence evaluation were developed, diagnostic tools were selected, diagnostic procedures and the analysis of the obtained results were conducted. A methodological workshop was held for teachers aimed at defining such basic concepts as «innovative pedagogical activity», «competence», «innovative competence» The level of the formation of teachers’ innovative competence was diagnosed taking into account its components, namely: operational (the formation of intellectual abilities, the quickness of mental operations, ability to solve problem situations), professionalvalue (motivation to obtain innovative competences, professional orientation, ability to self-control and urge for constant professional self- improvement, formation of individual style of pedagogical activity, professionally important personal qualities). Having generalized the results of applying various diagnostic methods (the technique «Six Thinking Hats» by Edward de Bono, the technique of studying the value scales by M. Rokeach, the diagnostic test «Readiness for self-development», «Strategies to form a higher level of basic need for cognition» by Palchevsky, «The methodology of limit meanings» by D. Leontiev) the level of formation of innovative competence of the teacher of the institution of general secondary education was determined.

The article is devoted to the research of the essence of intellectual games and analysis of the experience of their use in the educational process of institutions of general secondary education. The author’s position on understanding the essential traits of intellectual games has been expressed. The article presents the classification of board intellectual games into games on a special board, card games and dice games. It is stated that various activities aimed at popularizing desktop intellectual games among schoolchildren are supported by of certain international non-governmental organizations. Particular attention deserves the activity of the World Chess Federation, which in its structure created a special unit on school chess and initiated the adoption by the European Parliament of the Declaration on the implementation of the program "Chess in School", which became a significant event for the development of school chess. In the article on the example of chess, draughts and Go, the positive influence of desktop intellectual games on the development of many qualities of pupils is substantiated. These games contribute to improving mental skills, develop memory, attention, thinking skills, increase interest in schooling, and provide ample opportunities for self-knowledge and self-realization. The level of mastery of such games is an indicator of the intellectual development of students. Using the methods of analysis and comparison, the experience of using desktop intellectual games in the educational process of Ukrainian and foreign institutions of general secondary education was investigated. The problems of the domestic educational process are described. It is emphasized that chess is the most preferred among the whole set of desktop intellectual games in the institutions of general secondary education of Ukraine. Desktop intellectual games have significant pedagogical potential. The conclusion is made on the expediency of using such games in the educational process of institutions of general secondary education as a means of versatile development of a student.

The terms "Olympic education" and "Olympism" cover a variety of educational initiatives aimed at children and youth in general secondary education. The article presents a critical analysis of these initiatives, as well as a review of the relevant secondary literature, including a small but significant number of studies that develop a genuine critique of Olympic education and Olympism. The history of the Olympic movement is partially revealed and identified with the development of the educational space surrounding idealistic Olympic education, with an emphasis on the generally undeniable value of Olympism as a key tool in character formation. The program for introducing Olympic values into the educational process of Ukrainian schoolchildren is considered, and the hidden and explicit corporate messages embedded in these materials are identified. The authors looked at the educational program of educational institutions that try to challenge the hegemony of the Olympic industry in educational institutions to study how the pedagogical process works in general secondary education institutions. This is a scientific novelty of our time. Olympic education, combining the ideas of universal values, offers various methods of their realization. Purpose: to analyze the implementation of an educational program based on the principles of Olympism in the educational space of general secondary education institutions. Conclusions. If Olympic values are reflected in the behavior of primary school children, it can be assumed that the educational process has achieved results, and that the pedagogical process of Olympic education ensures the development of the Olympic movement.

Formulation of the problem. The article raises the problem of inconsistency between the existing state regulations on the final repetition and systematization of the school mathematics course in the context of a competency-based approach on the one hand and its practical implementation according to the current programs and textbooks for senior grades on the other. Taking into account cognitive theories of memory development and challenges during the final testing of senior students in mathematics, the relevance of researching effective approaches to the repetition of educational material, which would contribute to the reduction of educational losses and the proper formation of mathematical competence and other competencies in accordance with the concept of the New Ukrainian School (NUS), is substantiated. Materials and methods. Theoretical analysis of methodological literature, comparative analysis, systematization, and generalization of existing theoretical research on the topic of the article, as well as pedagogical observation and generalization of one's own pedagogical experience in repeating and systematizing the school mathematics course, were used. Results. As a result of the analysis of current textbooks and collections for preparation for external independent assessment (EIA) in the form of a national multi-subject test (NMT) in mathematics, a variety of approaches to the implementation of current and final repetition were revealed. It was found that textbooks differ in the presence, structure, and content of review rubrics, and theoretical materials for systematizing knowledge are practically absent. Textbooks, in particular, comprehensive publications for preparation for EIA (NMT), partially compensate for these gaps, but do not provide sufficient differentiation and require the active participation of the teacher in the process of selecting material to ensure the proper quality of final repetition. Conclusions. It has been established that the existing textbooks and manuals on mathematics only partially provide the conditions for high-quality summative repetition, not covering the need for differentiation and feedback. The effectiveness of this stage of learning largely depends on the professional skills of the teacher and the ability to combine different sources and approaches. The development of adaptive repetition technologies using digital tools has been identified as a promising direction.

The urgency of the problem is based on the ideas, goals, organization of the process of education and upbringing, on the features of profiling of modern upper secondary school and on the phenomenon of society as an indicator of the quality of vital activity of the individual. The author is theoretically substantiating the content of elective courses, noting that it is necessary to take into account the trends in the development of the theory of the content of school education. He believes that the axiological aspect of the content of elective courses influences the professional formation, the subjective experience of the personality of upper secondary school pupil in the system of social and pedagogical relations.In the content of profile education, it is important to actualize the perspective needs of society, to motivate the educational needs of children, and to teach correlation of these inquiries with the requirements of production spheres or individual production, as well as the needs stemming from social relations. Social, pedagogical and content components directly affect the management activities of institutions of general secondary education. Management, respectively, must be understood as a complex spiritual and social phenomenon of human life, as a distinct cognitive system.Clarification requires the theoretical and methodological approaches to the development of all aspects of subject preparation of pupils within the limits of the invariant and variable educational components. The profilization of a modern Ukrainian school (including social partnership) requires a didactic rethinking of the phenomena of the social sphere, which reacts to the results of scientific and technological progress. The organization of the educational process in institutions of general secondary education depends on a large extent on the transformational processes taking place in the information society. A characteristic feature of the educational sector is the consistent development and improvement of the content of the courses of choice, in accordance with the traditional and new specialties that are offered now to entrants. It should effectively affect the functioning of the mechanism for managing cognitive and educational activities of pupils, influencing the processes of formation and socialization of upper secondary pupils at the preprofile and profile preparation stage.

The purpose of this work is the study of international experience and the substantiation of compliance with basic hygienic indicators when implementing atypical planning and construction solutions in new and existing institutions of general secondary education for the physical protection of participants in the educational process during the war in Ukraine. Materials and methods. Sanitary and hygienic, bibliometric and analytical methods were used in the work. Review. In Ukraine, in connection with the ongoing full-scale war and in order to protect students, there was an urgent need to solve the issue of protecting students, teachers and employees of the general institution of secondary education during the educational process, especially in those located in territories close to territories with active hostilities. The first special underground institution of general secondary education was opened in the city of Kharkiv – a bunker-type school, which corresponds to the current comprehensive policy of the Ministry of Education and Culture "School Offline". This institution of general secondary education is located in an underground space at a depth of 6 m. It is designed for a simultaneous capacity of 600 students of grades 1-11 (or 900 students in two shifts). The high cost of designing and building an underground institution of general secondary education limited its capacity, provision of a full set of functional groups of premises, including recreational, physical culture and sports, educational and production zones, provision of premises with natural lighting and insolation. For the implementation of this project, the architectural and planning and sanitary and hygienic standards have not been partially met, which may negatively affect the health of children and affect their quality of life in the future. In conditionally safe territories, it was proposed to arrange protected spaces in institutions of general secondary education, which also has a number of disadvantages and requires in-depth study. Conclusions. According to the results of the study of the international experience of extensive construction of underground institutions of general secondary education, none were found. However, the experience of building underground institutions of general secondary education with students staying during the school day is isolated, was carried out as an experiment and did not spread. The introduction of the latest constructive solutions (protected spaces) and the possibility of further expansion of the design and construction of underground institutions of general secondary education in Ukraine require careful study. Keywords. State regulation, world experience, institutions of general secondary education, bunker school, construction in underground space, educational protected spaces, children's safety.

The article analyses the main pedagogical and educational technologies. The purpose of the article is a comprehensive analysis of the features of storytelling technology, as one of the leading pedagogical technologies that contributes to the professional development of biology teachers. According to the goal, the following task was set: to determine the expediency and ways of using storytelling technology in the professional development of biology teachers. It is noted that in the modern conditions of the development of society, the change of the educational course to a human-centred personal direction in education, the transition to competency-based training, active, interactive and innovative educational technologies in the learning process are becoming more and more relevant. The levels of functioning of educational technologies are determined as follows: general pedagogical, subject-methodical and local (modular) levels of functioning of pedagogical technology. The importance of understanding the differences between such concepts as “educational technology”, “pedagogical technology”, “learning technology (education, management)” is emphasized. The basic pedagogical technologies, their general characteristics, purpose and functions in the educational process are indicated. In the article, considerable attention is paid to the technology of storytelling, its content and essence are determined, both for the general range of subjects and for biology in particular. Attention is also drawn to the peculiarities, types, forms and other methodical characteristics of storytelling. The key role of storytelling technology as an effective method of presenting information in biology lessons is emphasized. Storytelling has significant practical advantages: it is easily perceived by students, develops creative imagination, overcomes the fear of public speaking and establishes relationships between students. It can be said that the proposed methods of using storytelling in lessons make it possible to implement the educational process in institutions of general secondary education based on a fundamentally different methodological approach, accordingly, the widespread use of multimedia formats for presenting educational materials is gaining momentum; ICT, the use of Internet resources in combination with storytelling remain relevant. The publication highlights the main, in our opinion, recommendations for the effective use of the mentioned technology, outlines the forms of its application in biology lessons. Examples of the use of storytelling technology during the study of a certain topic from a school biology course were given. The recommendations presented in the article are based on theoretical analysis, synthesis of scientific views and personal pedagogical experience. The basic aspects of the use of storytelling technology in the professional development of teachers are indicated. It is emphasized that the technology of storytelling is an effective tool in the professional development of teachers, as it contributes to the enrichment of pedagogical experience, stimulates creativity and contributes to the effective transfer of knowledge and values.

The article reveals the peculiarities of tourist-excursion activity as a complex and integrative educational process. Its role in increasing the effectiveness of the educational process in institutions of general secondary education is shown. The author also provides directions for realizing the potential of tourist and excursion work for the implementation of a competence approach in school geography.

The article describes the problem of educational losses and gains of students of general secondary education institutions with STEM, caused by power outages. Since the distance format was new for teachers and applicants for education, gaps in the knowledge and skills of applicants for education began to arise due to various factors (lack of gadgets, the internet, a separate place to study at home, etc.). The accumulation of gaps in knowledge and skills was cumulative and uneven in the context of different Educational Institutions. To prevent the accumulation of educational gaps among applicants for education and minimize educational losses, it is advisable to organize the educational process so that subject and key competencies are fully formed. The flagship for digitalization of the educational process in Institutions of General Secondary Education is STEM education, which has also gained achievements in these difficult conditions. In particular, it was the knowledge of Natural Sciences, Mathematics, and Engineering that allowed educational applicants and their families to adapt to living conditions in the absence of stable energy supply.