Table of contents

This paper represents a preface to the Proceedings of the XII International Conference on Mathematics, Science and Technology Education (ICon-MaSTEd 2020) held at the Kryvyi Rih State Pedagogical University, Ukraine, 15–17 October 2020. Background information and the organizational structure of the meeting, and acknowledgements of the contributions of the many people who made the conference a success are presented.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

• Type of peer review: Single-blind

• Conference submission management system: EasyChair conference submission management system, https://easychair.org/conferences/?conf=iconmasted2020, and HotCRP for the final papers, https://notso.easyscience.education/icon-masted/2020/

• Number of submissions received: 110

• Number of submissions sent for review: 110

• Number of submissions accepted: 76

• Acceptance Rate (Number of Submissions Accepted / Number of Submissions Received X 100): 69.09

• Average number of reviews per paper: 4.1

• Total number of reviewers involved: 131

• Any additional info on review process:

• Contact person for queries: Serhiy O. Semerikov, Kryvyi Rih State Pedagogical University, semerikov@gmail.com

This article discusses some use of cloud technology in mathematical calculations using Remote Desktop Ulteo OVD. To use such technologies, it is enough to have access to the Internet through a suitable browser to access an open virtual desktop on a powerful remote computer and then use the resources of the remote computer (server) to solve their problems in processing various information resources – solving mathematical problems, working out texts, translating from one language to another, help on the interpretation of different terms, their origin and more. You can organize access to Ulteo OVD from two servers (Application Server (Windows 2008R2) and Session Manager Server (Linux Ubuntu)), using the Proxmox web-based virtual environment. Gran1, Gran2D, Gran3D software can be installed on the application server. The article also examines in detail some examples of the use of the pedagogical software for educational purposes Gran1. In particular, the calculation of the approximate value of the double integral; graphical two-dimensional problem solving, the so-called linear programming problems; two-dimensional problems, including convex programming – finding the smallest value of a convex downward function (or the highest convexity of a function) on a convex set of inequalities (including linear ones). However, the use in the educational process of any technology, including modern information and communication, as well as the content of training, should be pedagogically balanced, which will allow to avoid any negative effects on the formation of personality of a future member of society, his mental and physical development.

The research analyzes experience of implementing the courses Mathematical Analysis 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 Mathematical Analysis performed by students independently in the computer mathematics system CoCalc.

I have been working on an educational project called Comparative Geometry for decades. The project is based on teaching and learning plane geometry and spherical geometry simultaneously, mainly through direct experimentation with hands-on tools, and intensive use of discussion between classmates. This work has gravely been affected by the changes that occurred two months ago because of the pandemic, still causing emergencies in many areas of education. In this article, I describe how I tried to adapt the work of a university course to an emergency; the methods by which I enabled direct experimentation and personal communication that were not possible in the given situation; my efforts to reduce the drawbacks of the situation and take advantage of the potential benefits.

The paper deals with issues of the metric geometry basics. In particular, the concept of rectilinear placement of points is considered, based on the axioms of the distance between two points of metric space. This approach allows forming a modern view of the property of straightness in the pupils. This paper analyzes the content of existing mathematics textbooks for general educational institutions to acquaintance of pupils with the elements of metric geometry. The first part of the paper provides information about the rectilinear placement of points; it can be used in Geometry lessons in the 7^th – 9^th grades. Set of linear functions are considered as examples of points of metric space. The similar work was done in the second part of the work for geometric material of the 10^th – 11^th grades. In addition, some simple examples of metric spaces that may be accessible to pupils of the relevant classes are discussed. The purpose of the work is gradually introduction of pupils to the elements of non-Euclidean geometries, to form a generalized notion of the distance between the points and rectilinear of their placement. The work can be used for Mathematics teaching at school and for retraining of teachers of Mathematics.

Students in many countries have problems with learning of mathematics. Many students do not like mathematics. Teachers and parents are mostly aware that the style of teaching of mathematics and "the atmosphere" around mathematics are the main reasons for this state. For the society it is clear that something must be changed. Maybe methods of teaching, maybe the whole system? Copernicus Science Centre in Warsaw 18 years ago proposed the idea of Young Explorer's Club (YEC) as the environment where students can discover knowledge by making experiments. Learning by experimenting, by own activity of learners makes the whole educational process more interesting and less frustrating for students. This also applies to mathematics education. Experiences from mathematical Young Explorer's Clubs established at the Centre for Creative Mathematics Learning at the Faculty of Mathematics University of Bialystok as the possible way to more effective mathematics education will be presented in the paper. Experimenting and using functional strategy of teaching of mathematics is the basic form of activity in the Clubs.

The article reveals the issue of the appropriateness of training pre-service mathematics teachers to use the techniques of mnemonics in professional activities. This issue is caused by the intensification of the educational process, when the amount of information accumulated by mankind is many times greater than the amount of knowledge that can be learned by a particular person. It is established that in the process of teaching mathematics, mnemonics should be used as a way of perceiving new information due to the formation of associative connections using special methods and techniques. The expediency of training pre-service mathematics teachers to use various methods of mnemonics ("Binding", "Transformation", "Amplification") is substantiated. A positive attitude of mathematics teachers towards the use of mnemonics techniques was revealed, as well as a low level of students' understanding of the advisability of using mnemonics techniques in professional activities. The classification of software used to create visual models is presented. A training was developed and introduced into the practice of university education on the development of mnemonic techniques for the presentation of educational mathematical material. The prospects of scientific research through the development of methodological support for the training of pre-service mathematics teachers to use the techniques of mnemonics in professional activities are determined.

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.

The present article considers the issue of developing motivational and value-orientated readiness of Math students at teacher training universities for implementing educational innovations. The method, chosen for the present research is the analysis of the scientists' viewpoints, on-line resources and reports regarding the issue of designing and using Rich Tasks when teaching Mathematics, methods and means for developing students' motivation for implementing educational innovations. This paper describes the methods, aimed at developing in students motivation and ability to systematize, devise, use Rich Tasks in their professional activity and to combine them with other innovational learning methods and means. The analysis of the teacher training internship results and the surveys in the experimental group give ground to make a conclusion about efficiency of the methods offered.

In the article, authors have considered the implication of ICT into mathematics educational strategies in the inclusive class of secondary school. The research includes also a presentation of a teacher's tool, prepared by an author group, on the use of ICT in teaching planimetry and stochastics of children with special educational needs (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 disorder. 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.

The paper is dedicated to the problem of true and pseudoreplication of a biological experiment, in particular in the educational process. It was found that this issue is relatively new and actual for the methodology of biological experiments in general. Its solution in science ensures the veracity of the results obtained and the relevancy of the formulated conclusions. In biology teaching methods at school, the problem of true and pseudoreplication of the experiment was not reflected. The author covers an issue of true replication teaching when setting up a model experiment to study genetic-evolutionary processes in populations. The paper discloses the experience in evolution of a model experiment and its development aimed at formation of ideas about technical and biological replication by the example of study of the genetic structure of an ideal population in generations. For this purpose, there was developed a web page that allows to automatically implement technical and biological experiment replication. There was described an experience of approbation of the proposed variant of the experiment, and its difficulties and advantages were revealed.

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): 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").

The paper goal was to analyse the typical mistakes in the learning of the university course of inorganic chemistry, determine the origin of misconceptions and estimate the effectiveness of the use of computer simulations to correct false chemical concepts. Ten problems that are the most typical for students were revealed. One of the leading causes of their occurrence is the failure of many students to form mental relationships between different levels of representation of chemical knowledge - microscopic, macroscopic and symbolic. Other reasons include an insufficient understanding of the material, the incompleteness of the knowledge of the microscopic basis of processes, and inability to work with different models, including misunderstanding of their purpose and constraints. NetLogo programming environment was used for students' self-administering tests to study gas laws. Scope for the usage of NetLogo models was estimated in correcting of incorrectly formed conceptions of the chemical knowledge. Independent work with NetLogo models facilitates the formation of stable relationships between multiple levels of representation of chemical information. It improves an understanding of the studied topic fundamentally, and this holds for all students practically independently of their grounding level in chemistry. The introduction of computer simulation into the practice of teaching chemical subjects shows promise. Still, it requires the solution of several scientific, methodological, logistical and organisational issues.

It is beneficial to study chemical disciplines, applying the Augmented Reality for the upcoming chemistry teachers, as far as the visualisation of the demonstration material in the 3D helps students understand various processes and phenomena, the structure of chemical compounds and the mechanisms of their correlation in a better way. The object of the project is the development of program and printed tools, designed to visualize the education process within chemistry disciplines according to the augmented reality technology. The authors have developed applications, designed for visualisation of the study material with AR. When a mobile phone is pointed on a marker, the image "comes to life", its three-dimensional model appears; it can be manipulated in some way (inversion, enlargement, viewing from different sides) to understand its structure, operating principle etc. better. Applying augmented reality objects gives the teacher an opportunity to explain big amount of theory quickly and effectively, and the students – to memorise it effectively, develops creativity and boosts motivation for study. Applying AR while training the upcoming chemistry teachers gives the ability to prepare them for applying this technology during the education process in the general secondary education establishments.

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.

This paper presents a computational method for studying the thermal conductivity of molecular crystals that can be used in the educational course of condensed matter physics. This method is based on the Debye model of thermal conductivity in the approximation of the corresponding relaxation times and allows studying the heat transfer processes features in simple molecular crystals at temperatures close to or above Debye temperature. The thermal conductivity is analysed in the framework of modified Debye model in which heat is transferred by low-frequency phonons and above the phonon mobility edge by "diffusive" modes migrating randomly from site to site. The mobility edge ω₀ is found from the condition that the phonon mean-free path cannot become smaller than half the phonon wavelength. The contributions of phonon-phonon, one-, and two-phonon scattering to the total thermal resistance of molecular crystals are calculated under the assumption that the different scattering mechanisms contribute additively. The presented computational method will be useful in pedagogical activities for teaching students of physical faculties.

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.

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 20^th century) is the beginning of the first educational GIS programs and partnership agreements between schools and universities. The second stage (mid-90s of the 20^th century – the beginning of the 21^st 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.

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.

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.

The conceptual and mathematical models of the agents' knowledge potential redistribution considering their constituent components are constructed in the paper. A nonlinear model describing the dynamics of agents' knowledge potentials is developed taking into account the feedback effects (agent – student) on the source of knowledge (teacher / lecturer). In particular, the procedure of constructing a multicomponent two-dimensional array of discrete values of the knowledge potential constituent components for generating procedures to enhance (improve) the professional competences of knowledge sources, is generalized and specified.

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.

The main aim of this research is the creation of information technology for mobile (of rapid deployment) security systems of the area perimeter. This system appears to be a complex of models and methods, information, software, and hardware mean that have interacted with users during decision-making and control of implementation for management solutions. The proposed information technology aimed at improving the protection level for security departments by automating the process of danger detection for perimeters and decision-making for alarm. The structural model of the system, the model of the system's components interaction, and the model of identifying the subjects of emergency threats have been proposed. A method for identifying unauthorized access to the perimeter of the secure facilities, using the production model of knowledge representation, was created. It is a set of linguistic expressions (such as "IF-THEN") and the knowledge matrix. The method of ranking for objects, which are threats of unauthorized access to the perimeter for secure facilities, has been proposed. The practical value of work consists of the possibility of the use of this information technology by perimeter's security systems of various objects. Proposed models are complete and suitable for hardware and software implementation.

The paper describes the gravity acceleration sensor (GAS) design, the technical characteristics of which provide an increase in the static transfer constant of the GAS, the ability to determine the current static transfer constant of the GAS, reducing the level of noise effects in the output signal of GAS. The acceleration vector components from the side of a moving vehicle add a noise to the gravity vector components. These investigations give an answer how to obtain of GAS's desired metrological features by the developing of new GAS based on pendulous integrating gyroscopic accelerometer. The presented material can be seen as an example of how to explore a gyro system mechanics and how to develop new gyro systems structure. The presented methods and the sequences of expressions can be used in master's and bachelor's disciplines in the field of applied mechanics, instrument development and automatic control.

Over the last decade, earlier named self-organizing mobile computer networks, MANET (Mobile Ad Hoc Network), including those based on unmanned aerial vehicles (UAV) – FANET (Flying Ad Hoc Network), have become widespread. In FANET, the UAV is connected to the network using wireless technology. Due to the constant dynamics of the nodes of such FANET, in this network, there are sometimes lost connections between the nodes. Modern wireless technologies such as WiFi, ZigBee, AirMAX, and others, have different technical characteristics that significantly affect the ability to build FANET. In the article developed a software model that allows you to study the statistical characteristics of mobile networks. The motion of each object (network node) is described using a quaternion model. The software model is developed in the Python programming language. The obtained software model for the given conditions allows us to estimate the basic statistical characteristics of FANET and to make recommendations to their construction and application.

The article deals with the development of a web application on forecasting the dynamics of prices in the residential sector of Ukraine. The classification of economic forecasting methods according to which they are divided into formalized, extrapolated, intuitive methods of forecasting the financial state is presented. It has been established that forecasting methods should meet the following requirements: a combination of subjective value and objective significance of estimates; clear application of estimates, which does not allow different interpretations regarding the choice of methods; create the ability to accumulate statistical information and use it for forecasting. The model of standard square collocation for the real estate market is presented. A web-based application for forecasting the dynamics of prices in the Ukrainian housing sector was developed and tested.

The use of augmented reality-enabled scenarios in cybersecurity teaching is proposed in the article to respond to new requirements for the rapid adoption of new technologies and profound knowledge of cybersecurity issues by professionals. Implementation of project-type activities based on real cybersecurity issues in application fields of cyber-physical systems is suggested to improve the competence forming. A use-case of agricultural cyber-physical system of systems is discussed as a viable example of augmented reality-enabled prototyping of cybersecurity risk-aware architecture. The necessary steps are analysis of general and business-specific tasks on cybersecurity, creation of a list of competencies, formalized in educational standards and curricula, development of gaming scenarios for the formation of hard and soft skills, development of the scenario management system for AR interfaces. The system using AR tools can be easily adapted to different cybersecurity training activities. Industrial cyber-physical systems may be vulnerable due to insecure wireless connectivity, lack of encryption, inadequate access policy. The project-based learning complex is focused on the implementation of a data acquisition, storage and processing platform for new sensor networks and instruments. Representing all the diverse information on different layers will be greatly improved by use of the developed holographic projection AR tools.

Modernization of the education system and the emergence of innovative learning technologies can improve the educational process. The use of augmented reality technology improves the learning of individual students, their motivation, as well as helps in organizing teamwork, group cooperation. As the topic of augmented reality in education is quite new and little studied for STEM education, the study reviews publications on this topic, describes the concept of augmented reality, the analysis of augmented reality technologies is carried out, which are adapted to the teaching of natural and mathematical disciplines. The role of STEM approach with augmented reality in the educational process is determined. An example of the use of augmented reality as part of a robotics project is given.

Career guidance quests that involve solving intellectual and search problems in a game are associated with one's future career, being one of modern means of recruiting school leavers to vocational and higher educational institutions. Such specific computer tools of virtual and augmented reality as pupils' mobile Internet gadgets can enhance visual character and interactivity of quest problems. The article deals with applying augmented reality in the web environment to solving these tasks. The authors propose a prototype of a career guidance quest system using WebAR technology.

This study analyzes various publications of scientists on the training of future IT specialists and the features of training programming using online simulators. The authors of the article made a comparative description of different online platforms for teaching programming according to certain criteria, selected interesting tasks from the online platform hackerrank.com, which have already been used to teach students. Online programming simulators have significant potential in organizing an effective distance learning system in Ukrainian universities. It is important to use online simulators in the learning process as an additional tool for the formation of professional competencies, which provides more intensive involvement of students in the process of writing code and practical (situational) application of existing knowledge. Gamification of the process of training future IT specialists helps to increase cognitive activity, and hence – the quality of the educational process and distance learning in particular. The authors recommend the use of online programming simulators as an additional tool for teaching computer science disciplines, taking into account their functionality, as well as the level of preparation of students and the expected learning outcomes.

In today's IT industry, it is important to develop the ability of IT students to collaboratively develop software, professional and personal skills. An effective method for developing such skills in future IT specialists is to organize different types of educational projects related to different programming technologies during the execution of mini projects, group and individual project assignments, term papers, academic training within the academic disciplines. The paper summarizes the results of a pedagogical study involving 29 expert students who study Computer Science and Software Engineering and used cloud service for GitHub collaborative IT development projects. The research findings testify, the most effective characteristics of this service, according to experts, identified the possibility of collaborative development of software (i1), the convenience of bug tracking (i3) and the convenience of the code editor (i7). It offers examples and results of using GitHub cloud service in the process of executing educational projects by future IT specialists.

The subject of the study is the formation of communication and teamwork skills of future IT-specialists, using project technology in teaching the administration of computer systems and networks. Content analysis of research has shown that communication and teamwork skills are the most requested and necessary soft skills for future IT professionals. It is offered to use project technology of training for their formation. This technology consists of the approaches and tools application used in real-world software development. To implement this technology, we propose to use mind maps for design. The organization of the working process on the project is implemented in Jira Software, Asana or Trello. Communication among project participants should be implemented with the help of several means: video chats (Zoom, Skype, Google Meet) and written communication in corporate messengers (Slack, Zulip). Experimental verification has shown the efficiency of the proposed design technology implementation.

The paper reports authors' experience of implementing educational projects in a computer modelling course offered to the students majoring in "Secondary Education (Computer Science)" at Ternopil Volodymyr Hnatiuk National Pedagogical University. We analyze approaches to teaching mathematical and computer modelling such as: integration of modelling tasks, naturalistic case study, using of role-playing games, possibilities of STEM-education, motivation and positive attitude to modelling training, etc. Then we illustrate the implementation of the project to study the population dynamics of the grape snail Helix pomatia. The implementation of the project splits into several stages: formulation of the problem, presentation of project tasks, brainstorming, development, testing, presentation of results. The study was conducted at Ternopil Volodymyr Hnatiuk National Pedagogical University within the Norwegian-Ukrainian Project "Development of students' mathematical competencies through Digital Mathematical Modelling" (DeDiMaMo) in partnership with the University of Agder (Norway) and Borys Grinchenko Kyiv University.

Building models of various processes and their further investigation has been always in focus of different specialists' training. There are some quite well known mechanisms and tools of modelling. However, Petri nets theory has found its wide application to the real-life parallel processes modelling. Petri nets give powerful facilities for dynamic models building and enable comprehensive learning of the process peculiarities. Hence, it is important to have relevant tools which allow to apply Petri nets potential to educational practice on purpose of earning by students skills of models building and investigation. The aim of the paper is to depict the functionality of the authors' mobile Android application "Petri Nets Tool-Kit", and to specify facilities and examples of its using for mastering modelling by students. Developed and represented in the paper mobile application provides students with the set of tools which enables to create, edit, save their own Petri nets as well as to change their parameters, visualize changing and play various scenarios of the modelled process. The "Petri Nets Tool-Kit" also contains relevant theoretical materials and the set of ready-made Petri nets examples, which makes the application attractive for mobile learning both in classroom activity and in students' independent work in the context of their vocational training in terms of different specialties. The proper stages of learning activity for step-by-step mastering by students the basics of modelling and simulation are disclosed. It is shown that "Petri Nets Tool-Kit" is available exactly in its portable form for Android OS, which encourages students to mobile learning and arms them with a convenient simulation tool provoking them to improve their modelling and investigative skills anywhere during the day. The prospects of the work are outlined in terms of the empirical research as for validating the impact of modelling activity in the elaborated application on the trainees' level of modelling skills.

The article substantiates the necessity and expediency of using the dual form of education in training specialists in the field of information technology in technical universities of Ukraine, interprets the concept of "dual education" from various sources, including UNESCO documents and the Law of Ukraine "On Education", analyzes some international experience of using dual study in higher education, in particular in Germany, considers the tasks to be solved for successful implementation of the dual form of higher education in Ukraine, and the main stages of this implementation for the period up to 2023. The paper considers some existing models of dual education that can be used in domestic universities. Also considered one of the approaches to the formation of methodological and information support for training of future specialists in information technology in the dual form of education based on distance learning support system developed on the basis of Moodle system, presented experience in implementing elements of dual education at the Faculty of Information Technology and Systems of Cherkasy State Technological University.

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. Nowadays, 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.

This article is an attempt to rethink the concepts of "methodic" and "methodologic / methodical system" as basic to educational technology. What should be the structure of a methodical system? What is primary – the methodical system or the methodology? How are methodical systems created and developed? How do educational technology and a methodical system relate? How does changing the components of a system make it emergent? These and other issues are explored through the development of a new class of teaching methods – computer-based training systems.

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 No 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.

The article considers the problem of the development of soft skills of teachers of Physics and Mathematics in higher educational institutions in the process of certification training in the system of postgraduate pedagogical education of Ukraine. The experience of foreign countries on the relevant teachers' course training has been analyzed, the essence and significance of such soft skills as sociability, creativity, empathy for the professional development of teachers of Physics and Mathematics in higher educational institutions in the process of certification training has been characterized. The state of these skills development in teachers of Physics and Mathematics was studied, the average level of the development these skills has been stated. The possibilities of the soft skills development were determined, the four-stage process of their transition from unconscious incompetence to unconscious competence in the system of postgraduate education was substantiated. The principles, forms, methods, technologies of the development of soft skills in the system of certification training of teachers of Physics and Mathematics were discussed with the emphasis placed on the role of heuristic methods and forms, creative technologies of the soft skills development.

The publication considers factors that are influencing formation of scientists image especially: availability to inform scientist or scientific organization about the registration, scientometric indices, use of global identifiers to improve accuracy in calculating indicators, publication of papers in journals with high impact factor, publications in resources that provide visibility in global information space, involvement in global communications system, level of competence. Specialists in various fields of science developed a number of practical recommendations for various techniques and tools that can be used and are helpful to create and to make, both personal image and image of the organization, institution, firm, etc. Also, main directions of using digital technologies to create the image of scientists are identified and substantiated. Scientists formulated recommendations to make their own image using digital systems based on analysis of scientific literature and personal experience: author's digital identifier ORCID, profiles in international scientometric systems, saved publications in electronic libraries, profiles in social and scientific electronic networks, etc.

Current trends in scientific research and the development of information technologies cover more and more areas of business. In these conditions, the findings of scientific-technical revolution and the innovations most important factors for the country's economic development and crucial to become a competitive state. The gradual establishment and the scope of use of artificial intelligence on the world innovative technology market increases daily. The purpose of this work is to investigate its impact on business based on the experience of the world and particularly, in Georgia. Accordingly, the study discusses the stages and main trends of artificial intelligence development. Depending on the scale of implementation, Georgia's current trends in job cuts / disappearances along with automation are analysed and future prospects are assessed. The paper discusses the use and increased importance of artificial intelligence 4.0 industry in the context of pandemic restrictions in various sectors of the economy and assessed the role in the post-pandemic period. The paper uses both qualitative and quantitative research methods. Content analysis of the scientific literature, statistical indicators and practical examples of different countries and international organizations is provided. Studies of leading analytical institutions are also included to analyse the current situation and prospects for development.

The article discloses the peculiarities of developing professional competence in professional training teachers. This process mostly involves using traditional pedagogical technologies. The article presents results of the ascertaining experiment and indicates the need for continuing professional development of teachers based on innovative principles. It also suggests using up-to-date pedagogical technologies of distance and project-based learning and production technologies to develop professional competence in actors in the educational process (teachers and students). This refers to the implementation of a competence-based approach in the professional education system. It is reflected in the development of professional competence based on some steps. They include expanding informational and educational space for actors in the educational process and individualizing learning using modern information resources (distance technologies); ensuring the interaction between actors in the educational process, as well as the joint realization of searching, cognitive and research activities (project-based technologies); organizing the educational process under the social partnership, taking into account the timely response of the professional education system to the emergence of innovations in production and the service sector (production technologies).

The experience of application of methods of problem-based and project-based learning was described in the training of future engineers for the light industry. Methodological issues are considered, as well as practical recommendations are formulated, for the application of these methods in teaching professionally-oriented disciplines. Examples of project design and their content are given for two specialised disciplines. They are aimed at the development of students' ability to creative thinking and problem-solving when working both independently and in a team. The method effectiveness is illustrated by the formation of students' new competencies, and an increase in their motivation and experience in teamwork. The preferred styles of students' learning were studied for student groups of four different enrolment years. The learning preferences are relatively stable over the four study years. On average, engineering students minoring in textile engineering and design demonstrate a tendency to active, visual, sensing and sequential learning styles. Project-based teaching methods are not universally suitable for students with different learning preferences. Moreover, the success in projecting under the studied conditions correlates with the existing learning preferences of student teams. Student teams succeed in the implementation of projects if they have a balance in the ref-act dimension with a limited preference of the active style. In other words, excessive activity and lack of reflective reflection hindered the successful completion of projects. In the sen-int dimension, the presence of a pronounced sensitive style is also favourable for design and implementation of class projects. Successes in projecting are mostly insensitive to changes in the vis-vrb and seq-glo dimensions. The introduction of the problem and project-based learning methods is useful for engineering students. They acquire new competencies, gain real experience of teamwork, and increase motivation to learn and develop creativity.

The article describes the analysis of computer-aided manufacturing systems introduction for the control program machines preparation with the numerical control into the technical students' educational process. The main stages of teaching students the basics of control machines programming by means of addressing to manual programming and CAM-systems are considered. Recommendations for the control programs testing implementation without a numerical control machine, by means of numerical control machine simulators introduction into the educational process are given.

The article is devoted to the urgent topic of using new modern information technologies in lessons in general and in the Ukrainian language lessons in particular. The authors of the article prove that multimedia presentations have become one of the most popular ways of visual accompaniment in the presentation of theoretical material. In the article the authors analyze the results of the external independent evaluation (EIE) of the Ukrainian language and literature from 2015 to 2018 as well as online testing results of students from the Australian, Canadian and Polish diasporas on the level of Ukrainian language proficiency. According to this analysis it is determined that the level of knowledge on this subject deteriorates every year. Relying on these statistics, scientists have proved the need to improve the quality of knowledge using multimedia presentations, which provide more effective perception of educational information by helping students to visualize it. The researchers have proved the effectiveness of using the PowToon service in teaching philological disciplines in the educational process. This article is a practical step-by-step assistant for teachers and academic staff in creating a scribe-presentation. The authors have analyzed in detail the peculiarities of the methodological approaches that are worth using for effective implementation of PowToon and PowerPoint in the educational process (competence (the ability to actualize available knowledge, skills, experience to solve the difficult tasks in professional activities), systemic (forms the relationship in the study of philology disciplines, systematizes and structures complex information, using them in teaching), informative (use of information and communication technologies in the study of philology disciplines). The effectiveness of using online (PowToon) and offline (PowerPoint) services to create multimedia presentations has been compared. The key stages of the scribe and the advantages of the scribe-presentation have been considered. Taking into account that information is absorbed and reproduced better when it is visualized, that is, through visual perception, therefore, it is proved that use of PowToon service is accompanied by positive emotions and high indicators in the students' learning outcomes. It is confirmed by a reflection questionnaire at the end of the lesson. The questionnaire consists of five questions and is evaluated on a 10-point scale. After analyzing the responses to the questionnaire the authors have come to the conclusion that the use of the script-presentations has a better influence on the perception of new visual information; increases the motivation for learning, interest in a subject that prompts subjects of the educational process to develop their creative projects and use their knowledge in everyday life; saves teachers' time while preparing for a lesson; inspires teachers and academic staff to give unusual lessons and provide new interesting teaching ideas, as well as create integrated lessons.

The article deals with the concept of student-centred Personal Learning Environment (PLE) in the context of higher education, which is used as a means of transforming foreign language learning and teaching practices. It aims to reveal the opportunities for creating PLEs through incorporating Information and Communication Technology (ICT) in the process of foreign language education. The study focuses on the roles of teachers and students of non-language University majors in designing efficient learning environments highly adapted to changing objectives and student personal needs. The authors reveal the unlimited potential of ICT in constructing PLEs for both in-class activities and informal learning, providing a scope of practical student activities, which imply their active engagement both in and outside the classroom, as well as constructing a flexible, personalized, time and space independent learning environment. Students, teachers, ICT, which is a set of resources based on the use of educational technology tools thoroughly selected and organised in order to manage the content, applying relevant methods of teaching and learning strategies, as well as a learning process, are all regarded as constituents of PLEs aimed at mastering four foreign language skills when taking the course "Foreign Language for Specific Purposes": reading, listening, writing and speaking within personal, academic, and field-related contexts.

The authors search the solution to the practical tasks of the contemporary education characterized by the increasing role of individual work in implementation of ICT at the lessons and in the independent work, the development of new principles, strategies and methods of teaching within the framework of integrated learning. These novelties can be applied when teaching professional subjects and foreign language and will provide the effective learning process aimed at acquiring the necessary competencies. The research discusses the process of integrated teaching using ICT and defines the organizational and educational conditions of integrated building of professional and foreign language competences using ICT. The authors generalize the experience of implementation of contemporary innovative technologies in integrated teaching of the professional subjects and foreign languages and analyze the ways of the effective ICT use in the integrated teaching of the management core courses in a foreign language. The content analysis performed in the research provides the basis for classification of both positive and negative aspects accompanying ICT use in education.

The article deals with the results of experimental work concerning the educational environment formation that is focused on the foreign language training of future energy engineering students. Project learning technology is chosen as the means of formation. A model of the educational environment for the metalanguage studying of the speciality of energy engineering students has been developed. In the educational process, educational projects with elements of professional orientation were implemented in accordance with the subject of the discipline "Business Foreign Language", and the language abilities and internal potential of students were taken into account. The preparedness of energy engineering students to integrate knowledge of professionally oriented disciplines into a foreign language environment for solving project tasks of communicative nature has been determined. According to the results of the pedagogical experiment, it was established that in the process of project activity the mastering level of lexical and speech competences as the components of foreign language competence of students has significantly increased. The developed educational environment is characterized by differentiation, individuality, independence, autonomy, informativeness, creativity, which allows to create the necessary conditions for successful learning of foreign language, development of creative thinking, communicative skills of energy engineering students, formation of foreign, communicative, professional, informational, project, research competencies.

The article deals with the urgent issue of American English learning for IT-professionals under challenging conditions of the changeable economic situation in the world. Some statistical data on global education trends and its analysis are given to confirm the topicality of the problem. State-of-the-art trends in foreign language teaching in the context of global challenges are presented. It is stated that informal education environments, distant learning platforms, virtual reality environments, artificial intelligence applications and collaboration platforms are to be mastered by Ukrainian undergraduates. Certain peculiarities of choosing and studying British and American English course by students of IT-specialities at three Ukrainian universities are given: the course choice procedure, the reasons for course preference, and the syllabus content. The best technologies, applications and tools for classroom activities and independent learning are substantiated, specific examples of their application for British and American English course learning are presented. The transferability of the skills inculcated in the course participants through implementation of the certain tools is founded.

In the present context of COVID-19 lockdown, when pedagogies had to turn from in-person to virtual instructions, computer-mediated communication (CMC), including distance learning and e-learning, has come to the foreground to maintain the barrier-free educational environment. The three-dimensional model of the e-learning, which includes the principles of knowledge acquisition at 'any place', at 'any time', at 'any speed' is incomplete without the organisational culture component. To analyse what e-learning modes are used in a particular institution, to measure the efficiency of distance courses and, further, to suggest the most effective model and the ways of e-learning integration into a particular HEI according to its needs' analysis was set up as the aim of this article. To achieve this aim, a complex of qualitative and quantitative research methods was applied. Therefore, in the first phase of our inquiry, a literature review was conducted in which we analysed the definitions of 'distance learning' and 'e-learning', traced the history of the question, and collected the main characteristics, quality parameters, and models of the distance and e-learning. On the later phases, we introduced the form 'Analysis of the Distance Learning Tools Preferences', disseminated among the teachers; a questionnaire 'Distance Learning Mode of Work Satisfaction/Dissatisfaction', disseminated among students, and 'The Instructional Materials Motivation (IMMS)' online survey by J.M. Keller to measure the efficiency of the distance learning courses design, also disseminated among students. The empirical data was collected at Prydniprovska State Academy of Civil Engineering and Architecture (PSACEA), the Department of Foreign Languages during March-May, 2020. Thirty instructors from the Department of Foreign Languages and twenty-three students from the first-third years of Foreign Languages studies who regularly participated in online lessons took part in the experiment. Based on the theoretical and empirical data, we got a picture of the e-learning state (in its first approximation) in our HEI, proved that the forms and questionnaires used in the experiment may serve as informative tools of quantitative measurement, drafted the format for further improvement of the e-learning in our organisation.

The winter and spring of 2020 was a challenging time worldwide. The COVID-19 pandemic seriously affected all spheres of life: from an industrial decline to educational transformations. In order to continue the 2019/2020 academic year, higher educational institutions had to adjust in-class learning to online. This paper aims at assessing the satisfaction and acceptance rate of Ukrainian lecturers with online education, as well as indicating problems and benefits they had singled out. The technical side of online education was also of interest. Therefore, the study employed an online survey to investigate technical support and tools used during the quarantine, advantages and disadvantages of online teaching, the level of satisfaction and acceptance. The findings from the study suggest that lecturers got different levels of technical support and used an assortment of tools to organise online education. The study revealed that the main advantage was time efficiency, while internet connection and technical problems were the most commonplace problems. Other findings of the survey are that lecturers were partially satisfied with online education but showed low acceptance of online education.

The article substantiates the need to develop and implement a distance course "Cloud technologies in the educational process in quarantine". It is noted that the purpose of the course was to acquaint teachers of general secondary education institutions, college teachers, vocational and higher education institutions with the basic possibilities of using cloud technologies to ensure the educational process in distance learning. The list of topics with which the students get acquainted is given: basic concepts, models of cloud services, architecture and proposals from leading cloud services companies; cloud services in the work of the teacher, the peculiarities of working with mail; cloud storage as an alternative to replacing conventional drives; opportunities to create documents with the provision of sharing rights to multiple users; opportunities to create Internet surveys using cloud technologies; opportunities to create presentations using cloud technologies; cloud-based means of creating smart maps; means of creating sites; cloud-based learning management systems (for example, Google Classroom). The peculiarities of the proposed distance course and the difficulties that the students had in performing certain tasks are identified and described. The statistical results of the course are given.

The relevance of the research is explained by the necessity of developing digital competence of teachers of Humanitarian disciplines at the higher education institutions (HEIs) in the conditions of the quarantine measures to prevent the spread of COVID-19. It is particularly challenging for teachers of Humanitarian disciplines, who are not specialists in the digital sphere as their profession is focused on humans. The purpose of the paper is to define the influence of the quarantine on the work of teachers at HEIs, revealing the level of the development, challenges and peculiarities of enhancing the digital competence of teachers of Humanitarian disciplines, theirs needs in education and giving recommendations how to arrange education and make administrative decisions. The methods of the research are survey, theoretical analysis, others. The results are to define the peculiarities of the influence of the quarantine on the arrangement of distance learning, the peculiarities of developing digital competence of teachers during the quarantine, their needs in education, the challenges in conducting mass distance learning, the determined complex of scientific approaches to developing digital competence. The practical significance of the research refers to developing three internship programs, based on the results of diagnosing teachers' digital competence.

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. 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 were established. The reliability of the test tasks separately and the test as a whole, among other indicators, were tested using mathematical statistics methods.

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.

The educational system has undergone significant transformations in recent decades, the main catalyst of which is the development of the information sphere of society. Both individual elements and the structural, substantive content are modified and updated. Among the vectors that determine the dynamics and direction of this process is the growing socio-cultural role of modern media, which are based on digital technologies as a globalization platform and the main type of communication. The change of the information code - digitalization of the media sphere, creation of new media platforms of social interaction initiates the need to build an educational system that meets the demands of today. Among the many factors that are currently relevant in educational approaches are media technologies. Their role in the training of specialists in various fields is growing symptomatically, as it is associated with the functions of "new media", which for the subject of activity become transgressive guidelines for constructing reality. Educational and further professional activity of a social worker needs to be reconsidered in the context of innovative strategies, first of all formation of media technologies in social work. Their formation is based on modern principles of new media: interactivity of communication and gamification of virtual practices. In social work at different levels of activity of the representatives of this sphere, media competencies are in demand, which include mastery of instrumental methods of implementing game, virtual, art practices as a motivational resource, technology of initiating social activity, cultural-adaptive and creative orientation of social assistance clients. This issue includes the specifics of the profession of social worker through the prism of the possibilities of filling his case with a creative resource - the tools of media technology in social work. The article outlines both the potential of gamification and virtualization of media practices in the educational and further professional activities of a social worker, and points out the possible dangers of implementing these technologies for certain categories of people in need. The article is a research exploration in the formation of a professional strategy of a social worker based on the involvement of the latest media practices as an expansion of media tools, the implementation of a creative approach to helping the client of social services.

The article deals with the problem of PhD student training. The Salzburg Principles about the improvement and quality assurance of doctoral programs at universities in every country from European University Association are analysed and materials of LERU on quality culture in Doctoral Education in Europe are used. The three focuses of the research component of doctoral program are proposed. The first focus relates to reproducible research principle. The second focus is related to the use of multivariate models of phenomena's study and SEM methodology. The SEM methodology is mostly based on deductive logic, involves the preliminary construction of a structural model of the relationships between the variables in order to further check for consistency with the experimental data. The third focus combines qualitative and quantitative methods and the use of triangulation (data triangulation, investigation triangulation, theory triangulation etc.). The content of selected courses for doctorate students is proposed: Reproducible Research and Multivariate Methods in Scientific Research courses. The importance of courses related to the future career is demonstrated, in particular the career of academic researcher. Further development of our work is the creation of teaching and methodological support for selected course "Twitter for professional development of PhD students".

Digital transformation of education and science puts forward new requirements for training of graduate and doctoral students, in particular for development of informational and analytical competence. It is described in international documents governing scientific field. Analysis of digital systems and consideration of their services allows us to say that their existing list and functionality can be used to develop informational and research competence of postgraduate and doctoral students. It is confirmed that important role in development of informational and research competencies of postgraduate and doctoral students is given to digital technologies, in particular, to digital open systems. Their use contributes to improving and expanding opportunities in research, presentation of research results and image of the researcher and institution. Digital society requirements to informational and research competence of postgraduate and doctoral students are defined and described. They include: readiness and ability to carry out research activities; ability to search and select necessary information and data, their transformation, storage and transmission using digital technologies; ability to critically evaluate found information (check their accuracy, timeliness, expediency); ability to perform scientific research (organization, planning, conducting) with use of digital technologies. Course of experimental work is presented; the obtained results are given and their interpretation is carried out. Fisher's angular transformation was applied in order to confirm reliability of obtained results of experimental study. Experimental verification of the proposed methodological system of using digital systems in postgraduate and doctoral students training, aimed at the development of information and research competence confirmed its effectiveness and pedagogical feasibility.

The article is devoted to the use of information technologies for pedagogical research aimed at studying the formation of key competencies and learning outcomes in higher education institutions, in particular, the professional responsibility of students of technical specialties. The diagnostic capabilities of the ATutor system, which operates at the Ternopil National Technical University named after Ivan Pului (Ukraine), are presented. The process of data collection involving distance learning technologies and the results of the analysis of the study are described. The state of formation of professional responsibility in students of technical specialties is determined, the main problems and difficulties in the formation of professional responsibility of future specialists in the technical field are clarified, and the possibilities and role of social disciplines are revealed. The structural and logical scheme of integrating disciplines of a humanitarian cycle in a distance learning course "Professional Responsibility of a Technical Specialist in Modern Conditions" is presented.

One of the main challenges of today is to increase the resilience of individuals to stressful environmental factors and preserve the quality of life and efficiency. Hardiness is a psychological phenomenon, the essence of which is a productive way out of the crisis towards personal growth. Taking into account the effectiveness of information and technological progress, the issue of internalization of AR technologies in the process of training a competitive, viable specialist who is able to mobilize and self-realize internal potential resources is vital. The scientific article analyzes the possibilities of using innovative AR technologies in the process of developing the hardiness of the future specialist on the basis of the implementation of competence and subject-personal approach to the introduction of AR technologies in the educational process in the system of higher education. The article describes the experience of integrated implementation of elements of augmented reality in the program of development of hardiness - Hardiness Enhancing Lifestyle Program based on the concept of BYOD. According to the results of the obtained empirical data the efficiency of using innovative AR technologies in the structure of mobile applications in the process of development of the components of hardiness of the personality of the future specialist is proved. Prospect for further research is the development of a methodology for integrated implementation of AR technologies in the practice of higher education in order to optimize the training of future professionals.

In article the definition of the educational institution information and consulting environment 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 educational institution information and consulting environment have been specified. Its social, spatial-object, psychological and pedagogical components have been analyzed. 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 educational institution information and consulting environment 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 educational institution information and consulting environment have been reviewed and summarized. It is concluded that the organization of the educational institution information and consulting environment will promote increase the efficiency of the educational process and the quality of educational services.

The article considers the expediency of developing and using the electronic environment of a higher education institution. It was found that the existence of such an electronic environment of a higher education institution would allow us to effectively use the available resources of higher education. A model of the electronic environment of a higher education institution is proposed, which consists of 4 components: educational, scientific, organizational, and managerial. The structural elements of each of the components are described. An example of the implementation of such an electronic environment on the example of the Zhytomyr Polytechnic State University is considered. The personal offices of the student and the teacher, which are realized according to the given model at the Zhytomyr Polytechnic State University, are considered in detail. It is established that the indisputable advantage is the complete identification of the person who went to different parts of such an environment, another advantage is the integrated use of logins and passwords to all these components.

E-learning courses have become popular means of delivering knowledge to students in higher education institutions. Most participants of learning process note that they benefit from the possibility to gain knowledge regardless of time, location and device they use. Among other advantages possibility to return to learnt material several times, divide material into parts, consume information through different types of educational materials (video, infographics, presentations, text, quizzes etc.) are mentioned. At the same time most of the surveyed students chose that they lack personalization both of materials and studying process, limited in terms of fulfillment and would like to have a choice of the level of study. The educational trend that is able to put into practice the above mentioned requirements is blended learning as it has a range of advantages such as usability, consideration of individual abilities, additional materials introduction, activities monitoring. Although it combines offline and online learning, effectiveness of e-learning courses designed for its implementation play a crucial role. To make a learning process correspondent to the students' needs adaptive learning can be introduced in higher education institutions. Adaptive learning is a methodology that allows to identify level of students' knowledge and their learning styles and transform materials, tasks and ways of their delivery according to the needs of learning process participants. LMS Moodle offers different solutions for adaptive learning. They provide administrators and teachers with tools to vary all stages of a learning process starting with delivery of information and ending with assessment.

The article looks into the effective use of open electronic educational resources. The concept of open electronic educational resources is exposed, their structure and key elements are presented, issues of implementation in educational practice are considered. Requirements for open electronic educational resources are defined, tools for designing and platforms for their support and dissemination are identified. The analysis of the existing open electronic educational resources and the experience of their use is conducted. The principles of open electronic resources design based on crowdsourcing are revealed. The stages of creating e-learning resources that meet open Creative Commons licenses on the examples of pre-service teachers' training are explored. The essence of Creative Commons licenses is reflected. The theoretical and methodological principles of the use of open electronic educational resources in the educational activity of pre-service teachers are considered. There is a direct link between open educational resources and university education.

The article touches upon the problem of introducing professionally oriented software products based on information and communication technologies into the educational process of training managers of the hotel, restaurant and tourism business. The purpose of the study is to prove the effectiveness of the implementation of professionally oriented software products based on ICT in the training of managers. The research is based on the analysis of recommendations of employers and managers of the specialties "Tourism" and "Hotel business", the content of educational programs for training bachelors in management, the content of general professional and special competencies, the structural and logical scheme of disciplines. The most effective information and communication technologies using computer software products that contribute to the formation of a set of professional competencies in future managers have been identified: MS Project, Teamwork, TeamLab, Open Workbench, GanttProject, dotProject, Outlook, OneNote, EverNote, Nirvana, Wunderlist, Toggl, MS Office, Office 365, Document.Online, AllFusion Process Modeler 7, MS Visio, MS PowerPoint, MS Sway, Libre Office.Impress, FreeMind, Mind42, ViSta, MacANOVA, Matrixer. The effectiveness of these technologies has been experimentally tested in the course of practical training in the format of full-time distance learning and practical training of student managers. The research describes the technology of using professional software products in the educational process. The effectiveness of these technologies has been experimentally tested in the course of practical training in the format of full-time distance learning and practical training of student managers. The research describes the technology of using professional software products in the educational process. The results of the pedagogical experiment confirmed that the introduction of information and communication technologies contributes to the formation of professional competencies in the field of ICT among students of this specialty. The conducted research proves the need for changes in the working curricula of disciplines "Information systems and technologies", "Practices of information and communication technologies", "Statistics", "Management and administration", "Finance, money and credit", "Accounting and audit". "Business foreign language", "Professional rhetoric", "Foreign professional language", "PR and advertising technologies", "Business accounting", "International business management", "Electronic business information technologies".

Peculiarities of the usage of the hierarchy analysis method for the making decision on the choice of the most efficient computer mathematics system (CMS) used for the preparation of the IT-sphere specialists are in the focus of the research. Eight alternatives were selected for the hierarchy analysis method and seven criteria were considered. The alternative is chosen by means of figuring of the priority vector corresponding to each alternative. The alternative with the highest value is considered the right decision. The scale of impact was used that is the scale of evaluations for the paired comparisons of the advantage of the first object over other with meaning from 1 to 9. The basic criteria for which the alternatives are calculated were described in the course research; their characteristics were chosen, in particular functionalities, studying materials, on-line mode, mobile application, license, language support and an open code. The matrix of the paired comparisons for each criterion was constructed and numerical characteristics of these matrices were calculated – the highest own value, the index of compatibility and the index of the consistency of formulas. Every matrix is composed of the expert evaluations for the alternatives, which are the systems of computer mathematics used in the courses of mathematics. Based on the results of the calculations carried out the impact of the alternative was shown and the system having the highest impact was chosen.

The article describes the problem of awakening the cognitive activity of students, arising due to revolutionary transformations in teaching technologies. It shows the need to study the factors that affect cognitive activity and assesses the information content of those factors. Based on the method of pair comparisons, a technology for ranking the factors affecting cognitive activity has been developed. A mathematical model of the formation and processing of expert assessment results and an example of calculations are given, and the feasibility of including the subsystem for evaluating factors affecting cognitive activity in the computer control system of the university is shown. The structure of an adaptive e-learning system based on the technology of taking into account the factors that form the cognitive independence of students is described Experiments carried out in 3 universities of Ukraine have shown that the use of the developed mathematical model and information technology allows to increase significantly academic performance and to decrease the frequency of refusals from independent work of students using the e-learning environment.