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The aggravation of economic, social and environmental problems of today necessitates their reflection in the research sphere and in the educational process of higher education institutions. Nowadays it is important to ensure the restoration of the regenerative properties of the natural resource potential and the development of a circular economy. The aim of the article is to highlight the possibilities of introducing the principles of development of regenerative entrepreneurship and the implementation of the circular economy in Ukraine in the training of future managers. Currently, the theoretical provisions of management and economic science are being criticized; there is an urgent need to bridge the gap between theory and management realities. The practice of regenerative entrepreneurship is becoming more and more widespread, which, in relation to business, is combined with the positive impact of entrepreneurial activity on the environment, primarily natural. The dynamism of market conditions requires continuous improvement of methods and techniques of teaching students in accordance with the requests of stakeholders and trends in the development of the higher education system. The article reflects the need for the development of responsible management education and the reflection of the principles of regenerative entrepreneurship in the process of training management specialists. The interest of business entities in solving individual management problems contributes to the establishment of close ties between the research, training and production spheres, which is a prerequisite for attracting effective methods in the training of management specialists. At present, along with traditional teaching methods, the use of interactive teaching methods, in particular the analysis of specific situations, has become widespread in the training of future managers, which provides a combination of mastering theoretical provisions and acquiring practical skills in the field of management. The authors consider possible objects for the use of the method of analysis of specific situations regarding the development of regenerative entrepreneurship in the training of specialists in agrarian management. The method of analysis of specific situations is successfully combined with other innovative technologies for training managers (simulation modeling, immersive learning, experimental method, etc.), capable of reflecting the implementation of the principles of regenerative entrepreneurship in the practice of organizations.

This paper is devoted to changes in the way in which mathematical assessment is conducted in Russia and Ukraine, the two largest states formed after the collapse of the Soviet Union. Previously, in the USSR, there existed two parallel systems of examinations, as follows: "exit exams," which were taken by schoolchildren graduating from high schools, and which were conducted using the same texts across the entire territory of each Soviet republic; and "entrance exams," which each college conducted independently (with the approval of the Ministry). In the new states, a gradual transition occurred to conducting so-called uniform exams, in which exit and entrance exams were combined. This change reflected society's quest for a fair and effective system, which could avoid corruption, unfairness toward different categories of students, and the like. In this paper, examinations are analyzed as an expression of society's influence on the teaching of mathematics. Consequently, the paper analyzes, on the one hand, the stages in the appearance and formation of examination procedures, the problems offered on exams, and the influence of exams on the teaching of mathematics; and on the other hand, the attitude toward exams in society, discussion of them in the press, and other general issues. A necessary space in the paper is allocated to background information, with a discussion of how exams were conducted in the USSR and of the general changes that have taken place in both countries.

Results of research prove that use of «smart» technologies is one of the ways to solve the problems of city. The involvement of projects, which are aimed at the smart city development, contributes to achieving the effective management of economic resources, innovation development, and improvement of the well-being of population. The dynamic nature of «smart» cities that has been evaluated using the indicators of economic development, human capital, technological support, environmental protection, international recognition, social cohesion, transport service, regulatory mechanisms, urban planning and public administration is a prerequisite for developing the global competitive advantages. The functional spheres of the smart city project have been analyzed with emphasis on energy, transport, water supply, housing and the local government system. The example of the Metropolregion Hamburg illustrates the possibilities of strengthening competitive advantages through the «smart» logistics solutions. The need to harness the best global experience in the development of smart cities in order to enhance the global competitiveness of the domestic economy has been identified.

In the article, we analyze the survey results on employers’ (administrators of schools and vocational colleges) interest, readiness and opportunity for cooperation in training math teachers in a dual form of education. The opinion of employers regarding the advantages, disadvantages and obstacles in the implementation of such a study mode was studied. Several specific issues that need to be resolved in order to effectively implement a dual mode of study in math teacher training have been identified. The obtained results could be used by universities that provide training in pedagogical specialties, experts in the field of education, state authorities and local government organizations that take care of education issues, as well as other specialists interested in the spread of the dual form of obtaining education in Ukraine and abroad. [ABSTRACT FROM AUTHOR]

The problem of forming the professional competencies of a math teacher in the process of his (her) training at the pedagogical university and in the system of continuing education is extremely relevant not only in Ukraine but also abroad. This is especially true for the methodological competence of teachers, which largely determines the quality of the educational process in general and student achievements in particular. To solve this problem, we propose to create an educational environment, which, in addition to math teachers, includes specialists in mathematics teaching methods from pedagogical universities, instructors of teacher’s in-service training courses, master’s students in pedagogical specialties, who, in particular, are trained in dual form of education. As the results of the experiment show, such educalional environment allows to realize professional training of mathematics teachers more effectively and qualitatively compared to traditional methods. [ABSTRACT FROM AUTHOR]

The evolution of the content and quality of written state standardized final and entrance testing in mathematics in Ukraine, from the first attempt to implement in 1994 until now, is considered in the article. We describe the features and stages of development of Ukrainian standardized tests in mathematics (external independent assessment and state final attestation), analyze the causes of successes and failures and also prospects for their further improvement. Based on our own statistical experiment, we compare the quality of mathematical preparation of Ukrainian graduates who entered the pedagogical universities of Ukraine in 1994, 2005 and 2020. According to this experiment, we draw conclusions about the existing problems of ensuring the proper quality of mathematics education in Ukraine and give recommendations on possible solutions to these problems. [ABSTRACT FROM AUTHOR]