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Formulation of the problem. The motivation of students to study a subject at school largely depends on the methodology used by the teacher in the teaching process, and his or her ability to convey new knowledge to students in an interesting and accessible form. This problem becomes especially relevant in the context of the New Ukrainian School project, which involves shifting the emphasis in the learning process from the teacher to the student and puts in the forefront the needs of the latter. For a child to be interested in learning and sufficiently motivated, a teacher should have an answer to the question "Why do we need to learn this?" The method of expedient problems gives one of the possible answers to this question, helps the teacher to motivate the student to study mathematics, and indicates directions for further use of mathematical knowledge. The importance of developing students' ability to apply mathematical knowledge in practice is further confirmed by the results of the International Comparative Studies PISA 2018 and PISA 2022, as well as statistical reports of the Ukrainian Center for Educational Quality Assessment in Mathematics. Materials and methods. To achieve our goal, we use a theoretical analysis of the methodological literature related to the chosen research topic. We also implement empirical methods, including conducting our own survey via Google Forms, observing the educational process in secondary schools, and analyzing students’ performance. Results. To study the feasibility and possibility of using the method of expedient problems in teaching mathematics in the NUS, we surveyed 290 mathematics teachers with different pedagogical experiences and qualifications from all regions of Ukraine. In particular, we assumed the effectiveness of using expedient problems in the process of teaching mathematics. The survey was conducted anonymously and online via the Google Forms platform. The results of the survey show that a significant number of respondents are familiar with the method of expedient problems and regularly or constantly use such tasks in the learning process. In addition, they are convinced of the need to include such tasks in existing math textbooks. The survey also shows at what stages of the lesson and when studying which content areas of the mathematics course, in the opinion of the respondents, it is most appropriate to use the method of expedient problems. Conclusions. To ensure the proper quality of students' acquisition of the necessary competencies envisaged by the New Ukrainian School project, the use of appropriate tasks at different stages of the lesson and in the study of different content areas of the school mathematics course is quite appropriate and possible. Although only half of the surveyed teachers currently use such tasks in their pedagogical activities regularly, most of the respondents consider them useful. In addition, teachers express a wish to provide methodological support for the effective implementation of appropriate tasks in the educational process, in particular, in the form of ready-made didactic materials and methodological recommendations for their creation.

In the modern world, the concepts of a successful state and a successful person are very close to the notion of economic success. Despite the fact that economic success is not yet a guarantee of a successful state or a person, the reverse one is also true: without economic prosperity, a successful state cannot exist. The economic prosperity of states in the modern world is inextricably linked with the development of a free market economy based on entrepreneurship and innovations. Computers, cars, delicious coffee, supermarkets, and even the Internet are all the result of a cultural phenomenon that the author proposes to call "entrepreneurial culture". The article examines the significance of the concept “entrepreneurial culture” as a fundamental basis for developing modern views of the world and the prerequisites for the development of society. For this purpose, the concepts such as culture and entrepreneurship are analyzed, a definition of "entrepreneurial culture" is introduced. The author concludes that the development of entrepreneurial culture is important from the viewpoint of state development, the development of science, and the development of young people acquiring school education. The author examines the history of perceptions of entrepreneurial culture in Ukrainian society and analyzes contemporary views on entrepreneurial activity. The article also raises the questions: “What the teaching of entrepreneurship courses in the new Ukrainian school should be like?” and “Who should be involved in this?” As it is known, in 2017, the reform of Ukrainian school education began, which was named the New Ukrainian School. Among the competencies that learners will acquire, in addition to others, there is entrepreneurship and financial literacy. Therefore, the author asks whether the image of an entrepreneur in Ukrainian culture coincides with the image of a person that the learner dreams of becoming and whether they have an internal motivation to become entrepreneurs. Will they become future entrepreneurs due to acquired competencies if the attitude towards entrepreneurs that exists in our culture does not change?

The article reveals the theoretical aspect of the problem of the formation of transversal competencies of future teachers. The material contains a presentation of a pilot program for the formation of transversal competencies of future teachers. The purpose of the study was to highlight the category of "transversal competencies" and develop a plan for a pilot (experimental) program for the formation of transversal competencies of future teachers in the educational environment of the pedagogical university. The study was performed using the following methods: synthesis of information contained in the scientific literature; systematization of the author’s positions of scientists who studied the category of "transversal competencies"; represent the plan of the experimental (pilot) program for the formation of transversal competencies of future teachers in the educational environment of the pedagogical university. Analysis of scientific sources allowed to fix that transversal competencies are characterized by the following features: integral interdisciplinary and territorial transferability; be able to form both in a professional and in a personal environment; dependence on social and interpersonal relations; cross-culturality and cross-functionality in the study; the possibility of development in mixed learning; active communication and interactive character; significance for the production of the "Life-long learning" system. The content of the category "transversal competencies" (for Kopus, Babiy) as a system complex of instrumental (practical-realizable), interpersonal (individually generated) and system (integral) competencies that implement the parameter of transfer (transfer) of the system of acquired knowledge, skills and skills of the individual into the plane of solving professional and pedagogical tasks and situations of educational practice on the basis of introduction of individual metacognitive and professional potential of the person.

The article surveys the most acute problems and challenges that the Ukrainian educational system has faced since February 24, 2022 as a result of Russian aggression. For a certain time, the education of children and youth generally took a back seat to the basic task of survival. A significant proportion of Ukrainian children, especially displaced persons and refugees, had to miss school in the spring semester. However, despite the ongoing hostilities, educators are heroically continuing their work, even from bomb shelters. The most important problem facing school education is its transition from the domain of the state to the civil or personal sector. A child's education and its quality now primarily depend on the parents, their efforts and conviction in the need for education. The insufficient level of state funding negatively affects the entire education system, leading to a decrease in the number of teachers, lack of new curricula, lack of printed textbooks and educational materials, etc. Educational standards also suffer from the online format, which mostly presupposes self-teaching and requires self-discipline from students. Students lose motivation, and sometimes (especially at the elementary-school level) do not understand and are not able to absorb learning at all. The war is not over yet, and Ukrainian children and young people continue to live in constant psychological tension, with deep psychological trauma and fears caused by the war. A serious challenge for all educators and students is the impossibility of consistently teaching and attending online classes due to planned and emergency power outages that can last for many hours at a time. However, the search for a new format in which the Ukrainian educational system can be rebuilt and restructured is already underway. There is an active discussion of possible solutions to the problems of the Ukrainian educational system both at the international level (see for instance the International Conference on the Restoration of Ukraine, Switzerland – URC 2022) and within the country.

Based on the online survey conducted among school principals, the paper demonstrates the main problems when making management decisions in an extreme situation caused by the war in Ukraine. The author identified social risks and unforeseen challenges faced by principals of the Ukrainian general secondary education institutions (GSEI) when performing their functional duties during the war. It was revealed that in the current situation, the school principals fulfil not only traditional functions oforganizing the educational process but also new ones, determined by the current situation, i.e., guaranteeing the safety of all process participants; ensuring their all-round support, legally accurate registration of educational activities in wartime conditions, etc. It is shown that the change in the functionality of the general secondary education institutions principal under the influence of certain events and public requests is not an accidental phenomenon caused by the current war situation but is more a historical regularity inherent in the development of Ukrainian education from the very origins of its creation. The paper demonstrates that the list of functions and competencies defined by the professional standard “Principal of a general secondary education institution” did not cover the entire scope of processes provided by the head of the general secondary education institutions, their managerial actions in extreme situations, that is, the implementation of the crisis-resolving function, which requires appropriate training. In this regard, the results of the conducted research allow us to see that in the current situation of a full-scale invasion of the Russian Federation on the territory of sovereign Ukraine, school leaders need enhanced legal training, deepening of financial literacy, psychological and other types of support. Recommendations have been developed for bringing the training in the system of advanced training of the heads of the general secondary education institutions to new demands, caused by the need to deepen knowledge for making effective management decisions in war conditions, in particular, regarding the strengthening of the legal component of training plans; introduction of training courses with working out cases of sharing one’s own experience in solving non-intersecting issues in particular situations; preparation for work in extreme situations as a core component of the block of psychological disciplines; deepening of financial awareness in conditions of funding uncertainty; familiarization with fundraising, the need for which became acute during the war and will remain relevant in the post-war conditions of recovery of the country’s economy; the expediency of developing an innovative course to strengthen the formation of national identity, national stability, loyalty and the value field of the Ukrainian people not through the traditional transfer of knowledge about historical facts and the literary works, but through awareness of the historical mission of Ukrainians in the struggle for their right to life in an independent state.

The authors reveal the issues of partnership between the preschool institution and the school in preparing children for study at New Ukrainian School. The main condition for ensuring continuity in education and training is determined by the orientation of the educational process of the preschool institution and the New Ukrainian School on the comprehensive development of the child’s personality. It is emphasized that the knowledge, skills and experience gained in preschool and family will be used to actively use them in the educational process, as the interest of preschool educational institution and New Ukrainian School will make the transition from preschool to school painless for the child. Emphasis is placed on the fact that partnership in relations between the participants of the educational process is a guarantee of their productive interaction, one of the ways to solve educational problems. The object of the study is the partnership between the preschool and school in preparing children for study at New Ukrainian School; subject of research - preparation of children for study at New Ukrainian School; The purpose of the article is a theoretical substantiation (based on a holistic analysis of scientific sources) and an empirical study of the problem of implementing partnership between preschool and school in preparing children for study in the New Ukrainian School. The authors came to the conclusion that according to the Law of Ukraine «About Education» the aspect of pedagogy of partnership between all participants of the educational process acquires great importance in the Concept of New Ukrainian School. The pedagogy of partnership is based on the principles of humanism and a creative approach to personal development. Its goal is to develop a humane society free from totalitarianism. The New Ukrainian School stipulates that teachers, together with parents, form a partnership centered on the child. The current state of preschool and primary education is characterized by diverse coverage of many issues in the interaction of the pedagogical process of preschool educational institution and New Ukrainian School, and the partnership of related levels of education, i.e. preschool educational institution and New Ukrainian School, will help unite the efforts of preschool educational institution educators, primary school teachers and parents in continuing education.

The formation of a powerful, active, and dynamic axiological foundation of personality is one of the essential tasks of the competency approach because even a high level of knowledge and skills acquired in the process of learning and education cannot ensure the integrity and progressively oriented unity of personal and professional competencies for future successful life, socio-cultural and professional self-realization. Given this, within the competence paradigm of education, qualitatively new content is the unity of learning and education. If before a significant amount of theoretical knowledge, detached from real life, had a shallow educational potential, now any pedagogical action, even focused on the cognitive assimilation of basic scientific knowledge, will have a worldview. An essential characteristic of the competency approach in education is that it can ensure each student’s unique structure the unity of knowledge, competencies, and values.

A theoretical outline of the concept of "emotional intelligence" is provided in the article (EQ). Analyzed are the viewpoints of several local and international psychologists on the definition, history, and structure of EQ. The New Ukrainian School (NUS) places a high premium on studying emotional intelligence and potential avenues for its growth. The interplay of the "emotional - intellectual" notions is chosen as the foundation of EQ research. Advanced emotional intelligence has both beneficial and detrimental traits that are highlighted. For EQ studies, a methodological toolset is created and presented. Some potential paths for its ontogenetic development under suitable circumstances are supported. For the intricate consistent work on EQ development, an algorithm has been developed.

This article is devoted to the analysis of current trends in civic education development and presentation and analysis of the results of the all-Ukrainian study "Democracy in Education" in order to highlight the challenges that arise in the implementation of mechanisms and instruments of civic competence development within the concept of the new Ukrainian school. The analysis revealed the following challenges: the delineation of active citizenship and political participation, the reduction of the concept of citizenship to the legal relations of the state and the citizen, a lack of awareness of the possibilities of using integrated learning and an active approach to promote justice among students. So, there is a need in developing strategies for overcoming them.

Abstract. Ukraine’s integration into global and European educational space, efficient implementation of educational reforms in this direction, the improvement of the quality of children and young people education is impossible without proper development of fundamental principles of marketing and management of educational innovations, first of all, among the Heads of New Ukrainian School. However, the absence of efficient mechanisms in Ukraine for training the above-mentioned Heads on marketing and management of educational innovations in New Ukrainian School negatively affects the quality of education therein and undermines the State education system in general. Therefore, the pressing issue at the current stage of education development in Ukraine is to determine the modalities and resources for the development of entrepreneurial and managerial competencies among the Heads of general secondary education institutions in the context of the power decentralization and establishment of consolidated territorial communities. With due regard for priority and pendency of the above-mentioned issue, its incomplete study, the principal objective of this study is to determine the key stages and describe the process of developing fundamental principles of marketing and management of educational innovations among the Heads of New Ukrainian School and measures for their efficient implementation. After performing analysis we have found that marketing and management of educational innovations of the Head of New Ukrainian School is his/her integrated, consistent and purposeful activity along with analysis and satisfaction of fundamentally new types of demand for educational services in the context of taking unconventional managerial decisions at his/her institution during such process. Moreover, with due regard to the aforementioned approach, we outlined the key stages of the fundamental principles development of marketing and management of educational innovations among the Heads of New Ukrainian School. So they include: the formation and control of specialists team towards development and implementation of educational innovations; determination of educational services market segment, demand for which needs to be satisfied; definition of criteria and conditions towards formation and satisfaction of demand for providing certain types of educational services etc. It is established that there are problems in the process of implementation of all above-mentioned stages, namely: absence of financial independence of educational institutions; the desire of the Heads of educational institutions to have legal and financial independence; positive managerial experience of the Heads of educational institutions regarding development and implementation of educational innovations etc. In order to avoid all above-mentioned problems, we have determined measures for the efficient implementation of marketing and management of educational innovations by the Heads of New Ukrainian School. They include: providing financial autonomy to educational institutions; performing professional training of the Heads of educational institutions, their deputies and teaching staff in general; forming new and improving the existing material and technical resources of educational institutions; implementing professionally oriented staff policy by the Heads of educational institutions in order to attract the most promising and young professionals to work as teachers etc. The scientific novelty of the obtained results is to determine, substantiate and analyze the key stages of fundamental principles development of marketing and management of educational innovations by the Heads of New Ukrainian School in the context of transformation of regulatory system and scientific and pedagogical approaches to children and young people education (shift in priorities and components of the development in this area of social activity). The obtained results of the research is the ground for studying and providing a practical solution of the problem regarding the formation of high-quality staffing and provision of fundamentally new educational services at educational institutions. Keywords: head of educational institution, educational innovations marketing of the Head of educational institution, educational innovations management of the Head of educational institution, New Ukrainian School, educational innovation. JEL Classіfіcatіon I20, I21, I22, I28, I29 Formulas: 0; fig.: 2; tabl.: 2; bibl.: 11.

Biology is a fairly complicated initial subject because it involves knowledge of biodiversity. Google Lens is a unique, mobile software that allows you to recognition species and genus of the plant student looking for. The article devoted to the analysis of the efficiency of the functioning of the Google Lens related to botanical objects. In order to perform the analysis, botanical objects were classified by type of the plant (grass, tree, bush) and by part of the plant (stem, flower, fruit) which is represented on the analyzed photo. It was shown that Google Lens correctly identified plant species in 92.6% cases. This is a quite high result, which allows recommending this program using during the teaching. The greatest accuracy of Google Lens was observed under analyzing trees and plants stems. The worst accuracy was characterized to Google Lens results of fruits and stems of the bushes recognizing. However, the accuracy was still high and Google Lens can help to provide the researches even in those cases. Google Lens wasn’t able to analyze the local endemic Ukrainian flora. It has been shown that the recognition efficiency depends more on the resolution of the photo than on the physical characteristics of the camera through which they are made. In the article shown the possibility of using the Google Lens in the educational process is a simple way to include principles of STEM-education and “New Ukrainian school” in classes.