ABSTRACT. The research deals with development of mathematical education at Kryvyi Rih State Pedagogical University (KSPU). The goal and objectives of the research include distinguishing and characterizing basic stages of formation and development of KSPU’s mathematical education, informing about the state of teaching, methodological, scientific and research activity, and defining prospects for developing the Department of Mathematics and Methods of its Teaching in future. By stages of developing mathematical education at KSPU, the authors mean periods of its 90-year development noted for certain peculiarities of organization and methods of training Mathematics teachers. Teaching, research and life dedicated to people are criteria that form the basis for determining basic stages in the Department of Mathematics’ development. A special edition Mathematical Education in Kryvyi Rih Pedagogical University: Personality Dimension was issued to honour the 90th anniversary of the Department of Mathematics after analyzing information from the University archive, museum and accessible personal data of Mathematics teachers – University teachers, graduates and researchers. The data also concern their publications in ORCID and Google Scholar databases, the University repository, etc. There are characterized basic stages of developing mathematical education in the educational institution and its research trends.

ABSTRACT. This essay examines the implementation of the educational ideal of Ukrainian Abroad in the Ukrainian Diasporic translation of children literature by such authors as Dhan Gopal Mukerji, Louis Henri Boussenard, Oscar Wilde, Daniel Defoe, Rudyard Kipling, etc. I claim that this ideal was formed in the XXth century in different cultural centers, united by Ukrainian World Congress. The Second Ukrainian World Congress approved main principles of the educational ideal in 1973, summarizing previous achievements. It is based on human values such as love, respect, and tolerance. All of these values got a Ukrainian sense. My focus in this article is on how these principles of the educational ideal are fulfilled in the translation of children literature of Ukrainian Diaspora.

ABSTRACT. Significant transformation processes in Ukraine, inspired by globalization, require a rethinking of educational goals, objectives, and educational imperatives. Within the educational process in vocational (vocational-technical) education institutions, the training system is forced to take into account the global context of actions and consequences in the preparation of a competitive specialist.The purpose of this article is to analyze the current state of development of vocational (vocational-technical) education in Ukraine and the network of institutions of vocational (vocational-technical) education; identifying factors that affect the quality of training of a competitive specialist and controversies that need to be resolved in the training of professionals. To analyze the current state of preparation, a set of theoretical and empirical methods was used, with the help of which a number of problems that inhibit the process of ensuring the quality of training of a competitive specialist were identified. In order to study the current state of preparation, a set of questionnaires was developed and, within the framework of a pedagogical experiment, questionnaires were conducted among entrants, educators, graduates, pedagogical workers, heads of institutions of vocational (vocational-technical) education in the regions of Ukraine and employers, and the results of the questionnaire were analyzed.The concepts of «quality of education», «effectiveness of vocational (vocational-technical) education», «competitiveness» are considered.

ABSTRACT. The article deals with the analysis of the problem of developing the dialogic culture of the future educators in terms of their professionalization. The author has shown that the congruent coverage of the specifics of forming an individual as an entity of professional activity in the continuum of the modern culture can be carried out only within the dialogic mode. It has been found that de-valuing the psychological component and accumulating systems of algorithmic tasks of the test type in the practice of the professional training makes it impossible to develop the communicative (and especially dialogic) culture of a specialist. The dialogic culture is interpreted by the author as an integrative construct of an individual, i.e. a set of communicative and technological indicators of the systemic behaviour (and professional-role one in particular) of the activity entity. The empirical research procedure had as its objective to outline the psychological tendencies in the development of the indicators for the communicative culture of the professionalization entities (bachelor degree and master degree students) in the modern educational space. The dominance of the monologic model of communication in the respondents' behavioural scenarios and the absence of the self-management development dynamics in communication have been statistically corroborated. The findings of the research are interpreted as the theoretical foundation of a modern model for the dialog-phenomenological interaction that is adequate to the new challenges of the time and the educational reform principles.

ABSTRACT. The article presents the authors’ bilingual model of future specialists’ training by means of artistic design. It outlines the content, forms, methods, criteria, and indicators of future specialists’ training in the conditions of bilingual educational process. The authors demonstrate that the development of the bilingual model contributed to the variety of students’ artistic and creative activities forms (team, group, individual) and to a wide range of methods used. The formation of the analyzed skills manifests itself in the level scale (primary, sufficient, high). The primary level of creative skills formation is realized on the basis of the developed criteria (motivation-oriented, content-procedural, evaluative-reflexive). The experimental study was carried out in several stages using theoretical, empirical methods of research. The authors also used the Pearson’s consistency criterion x2 to analyze statistical hypotheses based on observational data. The research outlines the levels of future specialists’ abilities development (association, visual (figurative) creativity, transformations, variability of thinking). The authors used the N. Vyshniakova and R. Tkach’s "Creativity" test, the S. Zievert’s "Freedom of associations" modified test.

ABSTRACT. In this article the author views philosophy questions of language and identity on bilingual education. There are two philosophies of bilingual education: maintenance and transitional, which influence on the way of learning foreign language and, as a result, on a person’s development in society – awareness of human identity. The author describes functions and structures of a bilinguism, a sociocultural competence, a language and an identity and says that learning languages and personality formation are connected. So that way what language and how we learning it define us in society.

ABSTRACT. The article is devoted to the actual problem of contemporary art education - to improve the professional training of future music art teachers for children’s inclusive education. Its purpose is to present the results of theoretical understanding of the developmental and healing potential of music, to develop technological support in future music art teachers’ professional training for children’s inclusive education. According to the results of the study, the basic concept of the study was defined as: "professional training of future music art teachers for inclusive education". To improve the professional training of future music art teachers for children’s inclusive learning, the findings of the latest research in the field of art and music-pedagogical theory concerning the harmonizing and music-therapeutic influence of music on the personality of a child in need of educational inclusion were used; criteria of musical works selection for children with psycho-physiological disabilities have been identified; there was developed and substantiated developmental and corrective technique of training singing that can be used in inclusive classes of different age, gender and cognitive abilities of children. Developmental and corrective technique of training singing includes innovative content of children’s teaching, comprising a specially selected vocal repertoire; lesson and extracurricular forms of training; specific teaching methods for students with special educational needs.

ABSTRACT. The article deals with the use of suggestive techniques, which by influencing the conscious and subconscious sphere of future music arts teachers through the use of verbal and non-verbal, external and internal means of influence, will contribute to the disclosure of their inner potential, the development of creative thinking as well as the realization of their abilities into the practical activities. The author defines various spheres of the suggestive techniques use, in particular, in the process of future music teachers training and provides own interpretation of the concept of "suggestive technique in the music-performing training of future music teachers". In addition, the author offers methodological developments aimed at conducting creative music-performing activities − suggestopedic self-training of self-regulation skills along with suggestopedic method of forming the skills in artistic interpretation of a musical work, which is presented as a chain of suggestopedic classes, where each stage corresponds to a certain interpretation phase. Furthermore, it is noted that the developed methodological toolkit with the complex involvement of suggestive techniques with a number of methods, tools and approaches to art education along with the varied application of these methods in the process of students’ professional training, methods of performing reliability formation and innovative methods, provides to carry out pedagogical influence on independence as well as performing activities effectively. Admittedly, the introduction of typical suggestopedic forms of classes (concert sessions, classes involving related arts, class performances, storytelling, play sessions) into the methodological toolbox brings additional aesthetic coloring into the interpretative processes, which, in combination with the globalization of the learning material, have led to the reconsidering of musical works artistic interpretation techniques on the whole.

ABSTRACT. Abstract. The paper deals with ways of developing critical thinking by means of literary works. It represents a number of analytical, searching, and cognitive tools aimed at activating thinking operations in the process of reading and interpreting fiction texts. It also focuses on the active methods of studying literary words (event analysis, fishbone structures, socionist analysis) which develop student critical thinking. The results of the research have proved that modern openness of literary education allows diversifying the ways and tools of studying linguistic and fiction “fabric” of the literary text.

ABSTRACT. The article is devoted to the problem of political-linguistics education at universities of Ukraine. The place of political linguistics is defined as a new interdisciplinary branch of scientific knowledge. The necessary of learning this discipline is argued at higher education institutions, especially at the postgraduate studies (PhD’s level). The paper touches upon the problem of political discourse determination as the main subject of the political linguistics. Although it is comparatively the young discipline and the definitions of its main categories aren’t universal enough, but the learning of political linguistics and its general components comes actively into educational and scientific syllabuses of Ukrainian higher education. The aim of the article is defining of the main specific principle and features of political linguistics learning at higher educational institutions in Ukraine. Such principles and features depend directly on specific peculiarities of political discourse and the interdisciplinary character of political linguistics. The author analyzes the problem of political discourse understanding as the subject of political linguistics study and the features of its categories representations in different syllabuses. She explores the researches about the learning methodology of political linguistics and of some tangent disciplines at universities of Ukraine.

ABSTRACT. The article analyzes the scientific literature in order to determine different approaches to the interpretation of the concept of "critical thinking", describes its components, discusses the basic concepts, functions of critical thinking in teaching. Critical thinking is presented as one of the main competences of STEM education. The conditions for the development of critical thinking in the process of STEM-learning are determined. Methodical problems are solved, which should help students to develop STEM competences based on the development of their critical thinking.

ABSTRACT. The article looks into the issue of developing an interest in mathematics students’ research activities in the teacher training universities. The study is dedicated to the feasibility of involving the 5E Instructional Model to the organization of students’ scientific research during the workshop on the Approximation Theory and Fourier Series. The research considers the results of the survey among students who helped to evaluate their emotional state during the workshop. To collect the data we used the tool of express evaluation of positive and negative emotionality the Differential Emotion Scale. The article discusses the positive influence of the environment developed through the 5E Instructional Model on students’ emotional state and forming their interest in scientific research while organizing workshop classes. We have grounds to conclude that there is the efficiency of implementing workshops based on the 5E Instructional Model. The index reduction of students’ negative emotions encouraged their activity during the workshop and the improvement of interest in research activities.

ABSTRACT. The research aim is to develop the learning resources for the design of virtual reality (VR) and augmented reality (AR) systems adapted for different types of learners. To achieve the aim of the research there were solved the following tasks: an analysis of the experience of using AR tools for the development of educational materials was done; the software for the design of AR tools for educational purposes has been identified and the technological requirements for the course "Development of VR and AR software tools" have been characterized; the individual components of the training complex for the design of VR and AR systems for future teachers majoring in STEM disciplines have been developed.

ABSTRACT. In the article, taking into account the challenges of the global information revolution, modern socio-educational realities, the authors substantiate the need for a communicative approach in teaching physics as one of the methodological approaches of a new scientific direction – psycho didactics of physics. The purpose of the article is defined as the coverage of some results of experimental teaching of physics to high school students of a secondary school based on a communicative approach with elements of bilingualism, its essence is characterized. Using a specific example, the author’s methodology for implementing this approach was first demonstrated, the need for its integration with other psycho-didactic approaches with the aim of comprehensive development of the student’s personality in the process of teaching physics is emphasized. Some experimental data are presented that make it possible , as a first approximation , to optimistically evaluate the results of testing the methodology of the communicative approach with elements of bilingualism in physics education , the prospect of further studies to obtain data on a more voluminous statistical sample is outlined , as well as to identify the possibility of using the proposed methodology in studying other disciplines in natural sciences in both secondary and high school.

ABSTRACT. The article substantiates the necessity to develop training methods of computer simulation of neural networks in the spreadsheet environment. The systematic review of their application to simulating artificial neural networks is performed. The authors distinguish basic approaches to solving the problem of network computer simulation training in the spreadsheet environment, joint application of spreadsheets and tools of neural network simulation, application of third-party add-ins to spreadsheets, development of macros using the embedded languages of spreadsheets; use of standard spreadsheet add-ins for non-linear optimization, creation of neural networks in the spreadsheet environment without add-ins and macros. The article considers ways of building neural network models in cloud-based spreadsheets, Google Sheets. The model is based on the problem of classifying multi-dimensional data provided in "The Use of Multiple Measurements in Taxonomic Problems" by R. A. Fisher. Edgar Anderson’s role in collecting and preparing the data in the 1920s-1930s is discussed as well as some peculiarities of data selection. There are presented data on the method of multi-dimensional data presentation in the form of an ideograph developed by Anderson and considered one of the first efficient ways of data visualization.

ABSTRACT. The paper studies peculiarities of introducing the course of “Fundamentals of Academic Writing,” into the Ukrainian education and scientific process. The integration of the Ukrainian science into the European space caused the necessity of including “Academic Writing” into the Ukrainian curricula. Fundamentals of a new academic course are represented through the prism of world and national achievements, which determine such concepts as “academic communication”, “academic etiquette”, “academic integrity”, “the quality of academic text”. This research focuses on the following major issues: What is the essence of “Academic Writing”? Is it a brand new course? How does it affect the ranking of higher education institutions? How should intertextual tools be used to keep the academic integrity? How does the level of English proficiency affect the quality of the Ukrainian scientific products? Is the course of “Academic Writing” a tribute to fashion or a vital necessity? It also investigates the peculiarities of academic fundamentals required for development of certain knowledge, skills and abilities of the Ukrainian language academic writing. The latter aims not only to promote academic integrity by following ethical principles and statutory rules that should guide the participants of the education process while studying, training and conducting research activities, but also to represent the concepts, strategies and tactics of organizing the processes of academic text creation, analysis and editing.

ABSTRACT. The paper concerns the paradigmatic approach in the philosophy of education. In the introductory part, the author considers the possibility to apply Kuhn’s concept of “paradigm” to education. The paper also defines the concept of an educational paradigm. According to J. Dewey, P. Freire, and other prominent educators, two main paradigms can be distinguished in the philosophy of education: the teacher-centred and the learner-centred. The second section is dedicated to the characteristic of teacher-centred paradigm. The third section outlines the main features of the learner-centred paradigm. Then, the author considers several philosophical ideas and concepts that shape a person’s worldview principles. They are the following: four-dimensional ontology, constructivist epistemology, agency, personal identity, and the narrative approach to identity and cognition.

ABSTRACT. Abstract. In the 21st century, more attention is drawn to the development of ecological thinking. Instead of explicating treatment of nature, a human being should take care of it. Such a caring attitude should become an educational universal, so it is to be transmitted as value. However, the ecological-discursive paradigm is still problematic in education. Therefore, the objective of the paper is to analyze it as a complex approach in philosophy of education. The paper considers environmental anthropology as the methodological basis of the ecological-discursive paradigm. Ecological culture is analyzed as ethnics of conservation. The paper emphasizes that ecological thinking cannot be developed without changing an epistemological model. Thus, instead of facts and competences, the person’s cognition should be based on values. The paper highlights the idea of diagnostic cognition, which is based on values. Its development in the process of education is the first step to the ecological-discursive paradigm.

ABSTRACT. The article examines a concept of narrative tolerance as the basic structure of cultural tolerance and modern civil society. It is proposed to consider narrative tolerance as an effective methodological tool to create a tolerant inclusive sociocultural world paradigm. The tolerant sociocultural approach in history studying and teaching is a crucially important condition that makes it possible to resolve protracted historical conflicts both within and beyond countries and, as a result, leads to reconciliation and mutual forgiveness.

ABSTRACT. This article explores the model supervision inclusive education retrainig of school key stakeholders, empirically revealed using the model for conducting supervisory interagency groups includes four steps: report of case, sharing, conceptualization, summary. This empirical study is introduced model of retraining through a socio-political and educational description of the current situation in Kriviy Rih. That’s why for planning the implementation model of supervision was testing 124 key stakeholders from 20 schools with inclusive education (teachers, tutors, service staff, psychologists and parents were invited to participate from the 7 regions of Kryvyi Rih City). For the successful work we offer in article the adaptation of the unstructured interview of the specialist, who describes the situation for the educational supervision. Analysis of the system of organizational and methodological and informational retraining, implementation of the pilot project of supervision groups for the team of psychological and educational support in inclusive education made it possible to offer a program of supervision: І. Training members of the team to work with the objectives of the individual development plan of a child: working with tools for preparing a case; ІІ. Key features of performing observations in the class; ІІІ. Environment factor analysis; ІV. Support team interaction supervision.

ABSTRACT. The article is devoted to the research of the hearing-speech memory as the basic modality of the mnemonic processes necessary for successful reading skills mastering. In particular, we trace the correlation between the non-formation of a number of mental processes and obstacles in the perception and active processing (decoding) of information for elementary schoolchildren. We see that impaired memory greatly impacts the mastering of the reading skill for children with a specific disorder of psychological development. The normative indexes of hearing-speech memory were obtained, its qualitative and quantitative characteristics were determined for the younger students with Dyslexia.

ABSTRACT. The article is devoted to current problems of the strategy of inclusion in the education system. The authors attempt to analyze documents regulating legal relations in the field of inclusive education, the accessibility of both educational and medical institutions, the readiness of the teaching community to work with children with special educational needs. The empirical basis formed by an array of empirical data collected by conducting a traditional analysis of documents, interviewing parents and teachers. The conducted research the results an analysis allows us to conclude that informants are fully aware difficulties of inclusive education today the existence. They are associated with the lack of architectural accessibility of the majority of school buildings, proper professional training of teachers, experience in communicating with children with various types and severity of diseases, and lack of readiness of society to adequately perceive the idea of integration.

ABSTRACT. The article deals with multimodal learning strategies aimed at transferring philological knowledge using ICT. Using ICT makes it possible to apply visual association, to create spatial images that express important object properties, and dynamic visualization (animation) allows to define it clearly. An important condition for the integration of these technologies in philological sphere of education is the formation of information and communication competence for higher education institution teachers as well as for philology students. The authors note that using of ICT in the sphere is associated with a number of methodological difficulties, since it requires a philologist-educator to possess a wide range of competences that go beyond the humanitarian knowledge. The optimum software that allows creating audio-visual construct (interactive poster, computer animation, tag cloud, cognitive map, etc.) is offered for studying process. The results of sociological researches of philological specialties of pedagogical universities students’ and different educational units teachers’ readiness for implementation of multimodal strategies of teaching using ICT are presented. The authors proved the need to introduce an integrative course "Use of ICT in the study of philological disciplines". The analysis determined that outlined multimodal strategies are important educational tools for creation of the modern information educational environment.

ABSTRACT. In the article the actual modern problem that is pervasive minutes informatization of modern life, including the education system, which is not only positive but also negative effects on young people. The thesaurus "reasonable information needs" is introduced into scientific circulation and the author's understanding of its content, essence, structure, principles, and factors is substantiated. Attention is focused on the need, in terms of the unauthorized and unlimited influence of information content, including fake and manipulative nature, on the minds of young people, including students, the introduction and improvement of media education in all institutions of higher education. Its purpose, functions, role in the formation of reasonable information needs of students of higher educational institutions of both humanitarian and technical profile of Ukraine and Poland are considered.

ABSTRACT. The article presents an overview of the main possibilities of using information and communication technologies in applied sociology, as well as the urgent need and importance of computer training of the students. Filed the results of comparative analysis of universal, semi-universal statistical packages of computer processing of sociological information and professionally focused software products on the market today. Outlining the advantages and disadvantages of their use in empirical sociology to describe the quantitative and qualitative characteristics of objects of study, explanations of causality, forecasting of social processes. Characterized by modern information technology used for collecting and storing social data. It is proved that the leading component of the computer literacy specialist-sociologist is the formation, the development of algorithmic thinking, the ability to make the right choice in favor of a software package that satisfies all the requirements, and that would efficiently and professionally perform all the tasks of an applied nature.

ABSTRACT. The article considers the use of cloud technologies during distance learning. The implementation of the mechanism of distance learning in general secondary education in two areas is described: distance form as a separate form of education and the use of distance learning technologies in the organization of education in various forms (day, evening, correspondence, etc.). The software for the organization of distance learning of pupils and students is listed. Examples of development of own electronic educational materials for teaching mathematics and computer science are given.

ABSTRACT. The article highlights the urgency of the problem of introducing blended learning into the educational process of institutions of higher education and ensuring the quality of education using the tools of e-learning management system. Subject of research: the improvement of the process of training specialists through the introduction of blended learning. Aim: To study the possibilities of optimal use of the virtual MOODLE learning environment in order to provide methodical and didactic support of classroom training, implementation of control measures. Research methods: theoretical, practical, statistical for processing of results of final control measures. The experience of using electronic testing during the final control of students' educational achievements is covered. A thorough analysis of the results was carried out, in particular the relationship between current and final grades, test scores and its duration was established. The reliability of the test tasks separately and the test as a whole, among other in-dicators, were tested using mathematical statistics methods.

ABSTRACT. In article the definition of the information and consulting environment of educational institution has been formulated. It was found the such environment is a relevant part of the information education society, within which it becomes possible exchange of information and consultative support of subjects of the educational process via the computer focused technologies.

The semantic and functional content of an information and consulting environment of educational institution have been specified. Its social, spatial-object, psychological and pedagogical components have been analysed. The criteria for assessing the quality of the information and consulting environment have been described. The main factors and leading pedagogical technologies of organizing and forming of the information and consulting environment have been determined. The pattern of the information and consulting environment of educational institution covering organizational, technical methodical resource areas have been established. Based on the results of empirical research with use of content analysis and factor analysis the benefits and risks of the information and consulting environment of educational institution have been reviewed and summarized.

It is concluded that the organization of the information and consulting environment of educational institution will promote increase the efficiency of the educational process and the quality of educational services.

ABSTRACT. This article looks into the issue of online-training of master students, majoring in Mathematics for internship in technical universities. This study is focused on arranging students' learning activities with the help of an on-line course “Methods for teaching Mathematics to students in technical universities”. The study considers the issues that students face during the internship in technical universities and debates a possibility to factor in the students’ needs while designing the course content. The present study gives a description of the activities that students do while working with the course materials, requirements, and recommendations on facilitating the learning process through this course. Active participation of students and their contribution to discussing the course, its content and the facilitation of the learning process presume that introduction of the on-line course and its integration into the program of training master students enhances their readiness for internship.

ABSTRACT. The research analyzes experience of implementing the courses Calculus and History of Mathematics for future Mathematics teachers in the system of managing electronic academic courses (SMEAC) at Kryvyi Rih State Pedagogical University (KSPU). To create the courses, there is a block-modular approach enabling not only structuring the process of studying fundamental mathematical subjects in the distance form of training, but also controlling the rate and depth of students’ mastering the material. There are examples of laboratory works on Calculus performed by students independently in the computer mathematics system CoCalc.

ABSTRACT. The subject of research: the improvement of the training specialists process for the student’s education with special educational needs (with SEN). Aim: To study the possibilities of optimal use of interactive exercises LearningApps and GeoGebra Dynamic Mathematics system in order to provide methodical and didactic support of training sessions, independent study, implementation of monitoring activities. The purpose of the article is to reveal the peculiarities of teaching mathematics to students with SEN using information and communications technology. In the article, authors have considered the implication of CT programs into mathematics educational strategies in the inclusive class of middle school. The research includes also a presentation of a teacher’s aid, prepared by a autor group, on the use of ICT in teaching planimetry and stochastics of children with SEN in secondary schools. The research has introduced the model of implication ICT and the influence of effective strategies and methods of inclusive education on the math studying process by children with hearing disoder. The possibilities of using the method of educational projects as one of socialization directions are described. The efficiency of the distance learning was discovered that facilitates the self-representation of students with SEN.

ABSTRACT. The article deals with the theoretical analysis of the traditional approaches to electrodynamics teaching. The authors pay attention to the contradictions arising in the process of combined application of Biot-Savart and Coulomb`s laws. The thesis of some limitation of the traditional presentation of the course of electrodynamics is substantiated. In this connection the necessity of updating methodology of electrodynamics teaching is determined. As an innovative approach to solving this problem, it is proposed to analyze and address the existing contradictions of electrodynamics teaching using a specially developed (copyright) methodology - the methodology of the development of students` critical thinking (MDCT). Using specific examples, the content of each of the stages of the proposed methodology, which can be used in the study of electrodynamics in secondary and higher school, is characterized

ABSTRACT. The method of astronomy homework organization in order to increase students’ cognitive activity is described in the article, as well as the possibility of individualisation and differentiation of homework is shown. Modern methods offer a lot of techniques and innovative forms of teaching methods in order to improve students' knowledge. These innovations are aimed at applying activity-based and person-centered approaches to learning that will help to intensify students’ training activities therefore it will be engaging and productive. Examples of independent practical tasks of different types and use of information and communication technologies are given. The article gives examples of such kinds of work on astronomy classes as: preparation of a textbook, preparation of supporting notes, practical tasks, solution of astronomical problems and creative tasks.

ABSTRACT. The importance of our research is due to the need to introduce into modern biological education methods of predictive modeling which are based on relevant factual material. Such an actual material may be the entry of natural and anthropic heavy metals into the soil at industrial areas. The object of this work: (i) to work out a predictive model of the total heavy metals inputs to soil at the Kryvyi Rih ore-mining & metallurgical District and (ii) to identify ways to use this model in biological education. Our study areas are located in the Kryvyi Rih District (Dnipropetrovsk region, Central Ukraine). In this work, classical scientific methods (such as analysis and synthesis, induction and deduction, analogy and formalization, abstraction and concretization, classification and modelling) were used. By summary the own research results and available scientific publications, the heavy metals total inputs to soils at Kryvyi Rih District was predicted. It is suggested that the current heavy metals content in soils of this region due to 1) natural and 2) anthropogenic flows, which are segmented into global and local levels. Predictive calculations show that heavy metals inputs to the soil of this region have the following values (mg*m2*year-1): Fe - 800-80 000, Mn - 125-520, Zn - 75-360, Ni - 20-30, Cu - 15-50, Pb - 7.5-120, Cd - 0.30-0.70. It is established that anthropogenic flows predominate in Fe and Pb inputs (60-99 %), natural flows predominate in Ni and Cd inputs (55-95 %). While, for Mn, Zn, and Cu inputs the alternate dominance of natural and anthropogenic flows are characterized. It is shown that the predictive model development for heavy metals inputs to soils of the industrial region can be used for efficient biological education (for example in bachelors of biologists training, discipline "Computer modelling in biology").

ABSTRACT. The most important condition that provides the opportunity for the professionalism of professionals is their competitiveness. The current task of vocational (technical) education institutions IP(VT)E is to prepare a qualified and competitive specialist who not only has a certain level of knowledge, skills and abilities, but can practically apply them in their professional activities. The quality of training of future specialists is based on the ability to adapt to rapidly changing production conditions. This is due both to the prospect of Ukraine’s accession to the European Union and to the internal situation in the country, where a large number of applicants in IP(VT)E and institutions of professional higher education (IPHE) do not always meet the requirements of the labor market. This requires a reset of educational goals and objectives of vocational education, taking into account global changes in society, production, technology. The work was performed as part of research on "Training of competitive professionals in the context of educational change" (RK 0117U006772).

ABSTRACT. The article is devoted to the problem of incorporation geographic information systems (GIS) in world school practice. The authors single out the stages of GIS application in school geographical education based on the retrospective analysis of the scientific literature. The first stage (late 70 s – early 90s of the XX century) is the beginning of the first educational GIS programs and partnership agreements between schools and universities. The second stage (mid-90s of the XX century – the beginning of the XXI century) comprises the distribution of GIS-educational programs in European and Australian schools with the involvement of leading developers of GIS-packages (ESRI, Intergraph, MapInfo Corp., etc.). The third stage (2005-2012) marks the spread of the GIS school education in Eastern Europe, Asia, Africa and Latin America; on the fourth stage (from 2012 to the present) geographic information systems emerge in school curricula in most countries. The characteristics of the GIS-technologies development stages are given considering the GIS didactic possibilities for the study of school geography, as well as highlighting their advantages and disadvantages.

ABSTRACT. Information is provided on the number of earthquakes in Kryvyi Rih and their parameters for the period 2007–2018. The types of seismic phenomena, the criteria for their identification are considered. The most probable natural and technogenic factors of the epicenters of local earthquakes are established by analyzing their location and sequence in time from the point of view of the tectonic features of the territory and the nature of the technogenic interference in its structure. The necessity of creating a local seismological network in Kryvyi Rih is substantiated. With a view to predict hazardous seismic phenomena, there is a need to continue hydrogeodynamic monitoring of ground water, to introduce seismic gravity monitoring and to conduct microseismic monitoring at mining enterprises. The results of systematic monitoring shall serve as the basis for seismic microzoning of the city. It is emphasized that popularization and dissemination of knowledge about the seismicity of mining regions among the population shall play an important role in the implementation of this task. The research materials can be used in the master’s degree programme within the framework of higher education system and in advanced training of specialists in the mining industry.

ABSTRACT. The integrated course "Science" is being introduced into school curricula in Ukraine for the first time. The article analyzes the experience of implementing an integrated course "Science" in schools of Ukraine. The advantages and disadvantages of various curriculum projects of the integrated course "Science" are discussed. The analysis of the content of the project №2 of the curriculum of the integrated course "Science" is made. Based on the results of two years of work on the implementation of the experimental integrated course "Science" in the profile school, the analysis of the main problems that arose during the implementation of this course and discusses possible ways to solve them.

ABSTRACT. Rapidly evolving coronavirus pandemic brings a devastating effect on the entire world and its economy as a whole. Further instability related to COVID-19 will negatively affect not only on companies and financial markets, but also on traders and investors that have been interested in saving their investment, minimizing risks, and making decisions such as how to manage their resources, how much to consume and save, when to buy or sell stocks, etc., and these decisions depend on the expectation of when to expect next critical change. Trying to help people in their subsequent decisions, we demonstrate the possibility of constructing indicators of critical and crash phenomena on the example of Bitcoin market crashes for further demonstration of their efficiency on the crash that is related to coronavirus pandemic. For this purpose, the methods of the theory of complex systems have been used. Since the theory of complex systems has quite an extensive toolkit for exploring the nonlinear complex system, we take a look at the application of the concept of entropy in finance and use this concept to construct 6 effective entropy measures: Shannon entropy, Approximate entropy, Permutation entropy, and 3 Recurrence based entropies. We provide computational results that prove that these indicators could have been used to identify the beginning of the crash and predict the future course of events associated with the current pandemic.

ABSTRACT. The article gives an overview of issues arising in connection with the organization and conduct of the course «Computer game development» in the master’s program 014.09 Secondary education (Informatics). The study of the experience of similar courses in other educational institutions does not give an idea of what conditions are the best for conducting it, because «Computer game development» is mainly present in the curriculum of the Software Engineering speciality and is not limited to one course. The game development course is described in terms of content, software and teaching methods. This course, which was attended by 40 students in three years, was evaluated in the light of the approach proposed by A. Ritzhaupt and based on the students' opinion. As a result of this research, it was concluded that a course in video game development could be based on the Unity Engine, as it has a small entry threshold, free for academic purposes, a crossplatform, real game engine, common in the gaming industry. A team strategy for this course is also effective.

ABSTRACT. The novel turmite-based cryptography algorithm has been designed and implemented. The turmites ability to generate pseudo-random number series makes them promising for cryptographic applications. At the same time, most turmites-related researches concentrate on their mathematical properties and generally don't consider possible applications. Lack of effective implementations of turmites-based cryptographic algorithms makes this research topical. The properties of the proposed algorithm have been examined. The frequency analysis resistance and avalanche criterion have been estimated. The results demonstrate that turmites-based algorithms may be used in cryptography and this application deserves attention and further examination.

ABSTRACT. The announcement of the 2020/2021 academic year as the Year of Mathematical Education in Ukraine and the adoption of the Concept for the Development of Natural and Mathematical Education (STEM-education) until 2027 were a response to the systemic crisis of mathematical training in general secondary education and training of mathematics teachers in Ukraine. The World focus on the integration of natural and mathematics, informatical and engineering education requires rethinking of the role and place of Informatics as a science, as a study discipline and as a basis of computer engineering in training future mathematics teachers. Nowaday, the teacher of mathematics should be capable for effective professional activity in a rapidly changing technology, educational paradigms and catastrophic educational disruptions, such as the current COVID-19 pandemic.

ABSTRACT. The article deals with the use of the Arduino hardware and software system on purpose: to involve students in the study of subjects such as Physics and Computer Science; to provide an opportunity to refine and develop your own engineering ideas. The results of students' research activities can be used in teaching Physics at a specialized school, especially during the school experiment.

ABSTRACT. Machine learning is now widely used almost everywhere, primarily for forecasting. In the broadest sense, the machine learning objective may be summarized as an approximation problem, and the issues solved by various training methods can be reduced to finding the optimal value of an unknown function or restoring a function. At the moment, we have only experimental samples of quantum computers based on classical-quantum logic, when quantum gates are used instead of ordinary logic gates, and probabilistic quantum bits are used instead of deterministic bits. Namely, the probabilistic nature problems that provide for the determination of a certain optimal state from a large set of possible ones on which quantum computers can achieve “quantum supremacy” – an extraordinary (by many orders of magnitude) reduction in the time required to solve the task. The main idea of the work is to identify the possibility of achieving, if not quantum supremacy, then at least a quantum advantage when solving machine learning problems on a quantum computer.