Table of contents

This paper represents a preface to the Proceedings of the XIV International Conference on Mathematics, Science and Technology Education (ICon-MaSTEd 2022) held at the Kryvyi Rih State Pedagogical University, Ukraine, 18-20 May 2022. Background information and the organizational structure of the meeting, proceedings structure, and acknowledgments of the contributions of the many people who made the conference a success are presented.

All papers published in this volume have been 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: Double Anonymous

• Conference submission management system: Morressier

• Number of submissions received: 94

• Number of submissions sent for review: 69

• Number of submissions accepted: 42

• Acceptance Rate (Submissions Accepted / Submissions Received × 100): 44.7

• Average number of reviews per paper: 3

• Total number of reviewers involved: 81

• Contact person for queries:

Name: Serhiy Semerikov

Email: semerikov@qmail.com

Affiliation: Kryvyi Rin State Pedagogical University

The article discusses the solution of the spatial traveling salesman problem (TSP 3D variation) using Ant Colony Optimization (ACO). The traveling salesman problem considers n bridges and a matrix of pairwise distances between them. It is necessary to find such an order of visiting cities so that the total distance traveled was minimal, each city was visited exactly once and the salesman returned to the city from which he began his route. In the TSP 3D variation problem, each "city" has 3 coordinates x, y, z. The analysis of the main methods of solving, in particular, the metaheuristic algorithms to which ACO belongs, is performed. At each iteration of these methods, a new solution of the problem is built, which is based not on one, but several solutions of the population. The ACO uses an idea that is based on collecting statistical information about the best solutions. The program code is implemented in MATLAB. During computational experiments, various network topologies were randomly generated, and the number of iterations at which the optimal cycle was achieved was recorded. The execution time of the code for the TSP 3D task is almost the same as the execution time of TSP 2D. The results can be used for spatial tasks of the salesman (TSP 3D-variation), which arise in the process of 3D printing, planning UAV trajectories (UAV) in mountain conditions or multi-story urban development, road planning in multi-story buildings.

Computer Vision is a multidisciplinary field, a unit of artificial intelligence and machine learning. It includes the specialized methods and general learning algorithms use. More and more scientists are becoming interested in Computer Vision researching. Therefore, it is important to train future professionals in this area and develop special study programs. We reviewed the development of Computer Vision technologies in the world and in Ukraine, considered the challenges facing professionals and gave an example of Computer Vision project development.

In general, polymer photodegradation is an important aspect of polymer science that is of great interest to chemistry, materials science, biology, and physics students who engage in this field of research. Wood consists of three main polymers, which makes it a good candidate for such photodegradation studies. Aside from structural changes based on chemical analysis, color change assessment can also be employed to check any extent of degradation on wood without the need for sophisticated analytical equipment. This study presents the application of two image processing programs in color analysis of wood photodegradation: ImageJ and Colormath library, which are Java-based and Python-based software, respectively. Images of unexposed and UV-exposed wood samples were taken using a smartphone as an affordable digital camera. RGB channel values from these images were analyzed and quantified by ImageJ software. These values were converted to the corresponding CIEL*a*b* parameters using the Colormath library to calculate the color change, ΔE. For the 3-hour exposed sample, ?E is equal to 4.29. This value indicates appreciable color change, according to the criteria from literature. Regardless of the exposure time, the wood samples become darker as indicated by the negative value in the change in lightness L*

The rapid development of computer biometrics over the past 2-3 decades is largely due to the development and widespread introduction into clinical practice of new methods of studying the human body health, including pulse methods. It is possible to judge changes in hemodynamic characteristics, heart rate and blood flow rate in the studied part of the body based on the parameters of the pulse wave signal. At the same time, the physical processes of formation of the pulse wave shape have not been fully studied, although the number of biophysical models of blood circulation is quite significant. The development of such a model will allow to effectively apply modern developments in digital signal processing to the pulse wave and increase its diagnostic value. Qualitative model of pulse signal can be entrusted to the development of the base unit of the biotechnical system as a type of edge devices. The work is devoted to the improvement of methods of rapid diagnosis of the cardiovascular system based on the analysis of model pulsegrams. An adequate mathematical model of the pulse wave, which corresponds to real pulse signals in different states of the human body and contains mathematical relationships between the main parameters of pulsegrams, has been refined. The algorithm of express diagnostics with the established criteria of the analysis of pulsograms is offered.

This article summarizes research on the development and evaluation of a set of software usability measurements. Today they are called "ergonomic criteria". The authors summarize the research work carried out on the development and evaluation of a set of software usability measurements. The paper contains a description of each such criterion. All of them together provide a quality user interface. The authors highlighted the significant advantages of a well-designed and well-thought-out interface. The paper also contains an analysis of each of these criteria. The authors of the article discuss ergonomic problems of software development. As a result, some characteristics of the software are identified. They reduce the ergonomics of the user interface. The paper also discusses ergonomic issues and the things developers need to get rid of to make the app enjoyable. The success of solving this problem in software development largely depends on how functional, clear and user-friendly the interface is. The authors give some examples of bad user interfaces. They are accompanied by an explanation of the problems and solutions to these shortcomings. The systems, designed with practicality in mind, are ergonomic and work exactly as users expect, allowing users to focus on their own tasks rather than the specifics of interacting with the system.

This article presents data mining, which is based on the methods of mathematical statistics and machine learning, describes the features of applying regression analysis methods in the machine learning systems. The developed machine learning model includes the regression analysis modules based on the Bayesian linear, artificial neural network, decision tree, decision forest, and linear regressions. In the process of applying this machine learning model, using the mentioned algorithms, the corresponding regression models were constructed and their comparative analysis was performed, the results were analyzed. The results obtained indicate the feasibility of using data mining in the medical research using machine learning systems. The presented methods can serve as a basis for strategic development of a new directions of the medical data processing and decision-making in this field. We have identified the prospects for further research aimed at applying data mining methods to the healthcare system, namely, clustering, classification, anomaly detection.

The information and communicative competency today is an integral part of professional training in any sphere. Due to the fact that nowadays big amount of work is done or monitored in the remote mode the requirement is stipulated for every specialist to be able to use digital technologies professionally. For a future seafarer it means, first of all, the ability to use modern technologies as the information and data resource and also it presupposes the ability to work with software libraries, to create data bases, to perform necessary calculations by means of cloud services inclusive. This component is of extreme practical importance as it enables the satisfaction of the social mandate to prepare future seafarers for the living in the information environment. The task is quite challenging so it requires the adequate knowledge level. That is why the main objective of the course "Information technologies" together with other subjects within the curriculum for the professional training in maritime academy is to develop the reliable scientific and methodological grounds for the realization of any professionally related tasks of future merchant feet officers. Specially selected tasks acquaint cadets with information technology in terms of implementing the solution of applied professionally oriented tasks, such as navigating the course, determining the location of the vessel, calculating stocks for the trip, etc. Therefore, the obligatory elements of the tasks are: construction of mathematical (computer) models;analysis of possible solutions to the problem; of technological processes, taking into account all factors influencing the process and methods of decision-making;implementation of mathematical models of problems in spreadsheets. This article proposes a strategy for solving an applied problem using an information-modeling approach to the analysis and evaluation of the technological process, namely, the algorithm for calculating the required voyage and storm fuel reserves of a marine vessel. Both office spreadsheets and cloud services were used to implement the mathematical model for solving this problem. The use of "cloud computing" technologies in the training of seafarers is due to the fact that, firstly, while on board, the master or ship mechanic can perform some components of their work, especially joint projects, in modern services, and secondly, these technologies, supporting traditional forms of education, is a new stage in the development of education and a cost-effective, efficient and flexible way to meet the needs of students in acquiring new knowledge.

In accordance with its aim, the paper highlights practical aspects and experience of the functional approach applying to the development of contemporary digital learning aids in the progress of project-driven activity of the pre-service IT specialists at their holistic vocational training. Theoretical framework of the work is made by holistic educational paradigm and functional approach to digital learning aids development. The specific examples of such an experience of the functional approach applying to the design of digital learning aids within project-based activity of the pre-service IT-specialists at their holistic vocational training: project activity on the design of (1) English digital tutorial for schoolchildren and (2) e-guide on the cryptography fundamentals for university students, are depicted in details. The analysis of such an activity is provided from the standpoint of the benefits of holistic and functional approaches. The prospects of following up research are covered.

Some aspects of teaching classical optimization methods to students of computer science specialties of pedagogical universities are described in the article. In Ukraine pedagogical universities the theory of optimization problems is most systematically considered in the course "Mathematical programming". The paper presents the approximate topics of this course, analyzes the relevant interdisciplinary links, presents the main stages of solving applied optimization problems. The peculiarities of organizing the individual work of students who study according to the dual education system by using the elements of "flipped" learning are considered in the article. New approaches in the educational process with the using of the modern information technologies, in particular Maple computer math system, is demonstrated.

The article discusses the main provisions of a practice-oriented approach to teaching programming in a school computer science course. The practice-oriented approach is implemented using a system of practice-oriented problems of mathematical content. The article reveals the classification of practice-oriented problems. Particular attention is paid to Interdisciplinary problems of mathematical content. The article describes the methodology, the main stages and the results of the experiment, during which the effectiveness of the system of practice-oriented problems of mathematical content in the process of formation of pupils' ability to solve programming problems was tested. Using the methods of mathematical statistics, it was proved that the system of practice-oriented problems of mathematical content is more effective than the system of problems given in school textbooks on computer science. During the experiment, the influence of the system of practice-oriented tasks on the formation of pupils' ability to solve programming problems was also investigated. It was proved that the use of the system of practice-oriented programming problems more effectively affects the formation of the ability to solve programming problems. For pupils of the experimental group, the differences between the initial level of formation of the ability to solve programming problems and the final level were significant, while for pupils of the control group, they were insignificant. The results of the experiment confirm the positive influence of the system of practice-oriented problems of mathematical content on the formation of pupils' ability to solve programming problems.

The importance of studying robotics in the conditions of the Fourth Industrial Revolution for solving the problem of training qualified STEM specialists is substantiated. The technique of using a project-oriented approach in the process of studying technologies for creating robotic systems is disclosed. The stages of implementation of the method based on the project of a maneuverable robotic platform are given. The methodology proposes a step-by-step development of a completed functional product, divided into several stages. At each stage, students get acquainted with the corresponding functions of the software and the theoretical aspects of electrical, physical, mechanical phenomena necessary to solve the problem at this stage. An important aspect of this technique is also the acquisition of practical work skills: drawing up diagrams, soldering individual electrical components to the board, laying electrical connections and manufacturing parts using 3D printing. Work on solving problem-oriented complex tasks allows to consider the problem as a collective, which will create the necessary prerequisites for professional activity. These capabilities of the project-oriented approach allow to implement the key concepts of STEM education: the research process, mastering the technology of manufacture and implementation of technical creativity on the basis of basic mathematical knowledge.

The article is devoted to one of the competence components of a mobile-oriented environment for professional and practical training of future software engineers. It is shown that the introduction of higher education standard 121 "Software Engineering" for the first (bachelor) level of higher education in Ukraine has generated a number of training quality assurance problems associated primarily with the low level of detailed competencies and program learning outcomes. By solving these problems, the detailed design of the system of professional competencies for future software engineers is developed. The article deals with the approaches to developing one of the most important special professional competences of future software engineers – the ability to participate in software design, including modeling (formal description) of its structure, behavior, and processes of functioning. Based on a historical and genetic review of the software engineering training practice of future software engineers in the USA, UK, Canada, Australia, New Zealand and Singapore, recommendations for choosing forms of training organization, selection of training content, ways of students' and teachers' activities in software engineering, modeling and designing tools; assessment of the appropriate competence formation level are formulated. The example of organizing design training in conditions close to industrial-studio training is considered. The problems of transition from architectural to detailed design and project implementation are shown. Prospects for further development of this study are to substantiate the third (after requirements engineering and design engineering) engineering component of software engineering – the software construction.

Endocrine disrupting chemicals (EDCs) are a group of compounds that affect the endocrine system, frequently found in everyday products and epidemiologically associated with several diseases. The human population is now ubiquitously exposed to EDCs in daily life. The main way of getting xenoestrogens to the body is the contaminated food. The effects of xenoestrogens on the proteolytic processes of different age rats were determination. The experiments were conducted on Wistar rats exposed to exogenous estrogen for 45 days. At the beginning of the experiment 3-month-old pubertal animals and 6-month-old sexually mature rats were involved. The research materials were organ tissue and blood serum of the rats. The objects were indexes of activity of trypsin and its obligatory inhibitors α1 - antitrypsin (α1-AT) and α2-macroglobulin (α2-MG), cysteine cathepsins B and L, the molecules of middle mass (MMM) level. In summary, the eating food contaminated by exoestrogens led to changes in the proteolytic system and the development of endogenous intoxication, which are also organ-specific and dependent on the age of the animals: a higher level of activity of the inhibitory link and the content of MMM was observed in rats in the puberty period, which leads to a decrease in the potential of the protective mechanisms of the organism and can become a trigger dysfunctional systems of natural detoxification and biotransformation. Inhibition of apoptosis is the main consequence found in the body of experimental rats. This phenomenon can lead to processes that inhibit one of the main mechanisms that reject damaged cells from the population. Females who were in puberty were more susceptible to dietary synthetic estrogens. In contrast to adult animals of the same sex, whose indicators indicate the importance of age characteristics of the body for the ability to perceive the effects of xenoestrogens. Rats became less sensitive to the effects of these substances with age. The diference in experimental animals was due to changes in the rate of detoxification pathway reactions, and not in the metabolism of estrogens entering the body, in particular, with food.

The article deals with the adoption of computer modeling as one of the leading areas of introduction of modern information technology in the modernization of content, forms and methods of teaching. In order to implement interdisciplinary integrated learning, the possibilities of interdisciplinary integration of learning content have been identified, the practice of using software environments in the process of modeling biological problems based on mathematical models has been analyzed, the possibilities of implementing algorithms of mathematical models in computer modeling have been investigated. A set of research tasks in biology as a basis for the implementation of interdisciplinary integration: nature - mathematics -computer science has been introduced into the educational process. The mathematical models of Verhulst, Arim, Leslie and the exponential law of direct proportional dependence or proportional rate of reproduction depending on the number of individuals of a population were used to design computer models of reproduction of ecological processes. They were implemented using the computer mathematics system MathCad and using programming environments Python, C#, C++. The expediency of the proposed method of interdisciplinary integration of learning content has been justified through a developmental and productive integrated approach, the use of certain collective forms of activity, the practical orientation of professional training disciplines to form algorithmic competence of students as a basis for professional competence in computer modeling of mathematical models of biological processes.

This study investigated the effectiveness of flipped classroom model (FC) and traditional classroom model (TC) in Biology on the quality of the high school students' performance. The research sample consisted of a total of 280 first grade high school students in Novi Sad, Serbia. The students in the experimental group learned Biology topic through the FC model, whereas the students in the control group were taught the same topic by the TC model. The instruments used in the research (the pretest and the posttest) contained the questions belonging to three different levels of cognitive learning according to the revised Bloom's Taxonomy. The results indicated that students that were instructed by the flipped classroom in Biology performed better on the posttest as a whole, and in solving the tasks of all three levels of knowledge (remembering, understanding, and applying) than those instructed by the traditional teaching method. On the basis of the obtained results, a grater implementation of FC model in high school biology teaching is recommended as a way of improving the quality of biology teaching in our and other countries over the world and the level of our students' digital competencies.

The article is devoted to studying and preventing an excessive increase in the cognitive load of university students studying chemistry using various electronic resources. The experiment involved 49 third-year students of the Faculty of Chemistry who studied organic chemistry. A homemade software was developed to measure the level of cognitive load using the secondary problem method. Cognitive load levels were studied depending on the types of used electronic resources. The studied resource types are texts of different levels of complexity, audio and visual materials in different combinations. The load values were measured for each respondent, expressed in relative quantitative units and averaged over the whole student group. In parallel, the preferred learning styles among the respondents were identified according to the Index of Learning Style of Felder-Soloman. A correlation was established between the preferred learning styles of students and the cognitive load they feel when working with electronic resources. The factors that affect an optimal set of educational resources were identified for student groups with various learning profiles. The results of factor analysis allowed the authors to assess the contribution of different learning styles in the formation of cognitive load in the use of different electronic resources. The techniques described in this article allow one to control cognitive load, predict and prevent its excessive increase.

Nowadays, studying natural sciences, as well as chemistry, is impossible without good-quality visualization of the theoretic data. Supplying mobile apps with augmented reality give the opportunity to visualize the study information for the students and make its perception and learning easier. The paper is dedicated to developing a lap book and mobile app LiCo.STEAM Sugar with augmented reality and studying the "Carbohydrates" topic according to the 10^th grade chemistry program, and also to investigate it's effciency within the chemistry lessons. The developed lap book includes the theories with carbohydrate molecules' images, an experimental part designed for performing chemical experiments and studying properties of organic compounds, and also tasks of different levels. Molecules of carbohydrates, their structure can be visualized with AR, and also video-experiments on this subjets can be played. Using the lap book "Carbohydrates" with augmented reality together with LiCo.STEAM Sugar mobile app allows to upgrade the content and the volumes of the theories, apply modern ICT within the study in order to build students' skills of a new level. Applying educational data with augmented reality give students the ability to memorize the theories in a better way, which is shown with the increased results of educational achievements of students in chemistry.

A training kit has been created to study the topic of "Oxygen-containing organic compounds" using augmented reality. We chose the Blippar platform to work, it is quite simple and relatively free. The kit contains markers we have developed, on which, with the camera from the Blippar application, students will be able to observe thematic experiments and molecules of individual substances with the help of augmented reality. There was also a study on the effectiveness of our developments to implement augmented reality in the course of chemistry. The study results showed an increase in pupils' motivation to study chemistry and their level of interest, facilitating the perception of the theoretical foundations of organic chemistry related to the spatial structure of molecules. Also, the use of augmented reality technologies creates the conditions for improving the level of digital and technological competencies of students, provides support for high quality teaching of chemistry in distance learning.

This paper presents a vision of a team of researchers on solving a problem of engaging future Mathematics teachers into a research activity through implementing person-centred approach to learning and teaching. The authors of the given article present a designed Learner-Centered Syllabus of a training research workshop in Mathematical Analysis for Master students, majoring in Mathematics at teacher training universities. This study presents the structure, the components and the content of a Learner-Centered Syllabus. When giving content to the sections of the syllabus, the developers take into consideration the conditions for person-centredness; creating the atmosphere of acceptance and congruence; shaping in students the personal qualities, which contribute to their research activity; arranging collaboration; engaging students into the assessment process. The researchers in the present study identify orientation at self-development as a key concept of the course policy and make each section of the syllabus personal. The following sets of attributes were used to evaluate the designed Learner-Centered Syllabus: Community, Power and Control, Assessment and Evaluation. The experimental study was done over four years, two groups of Master students majoring in Mathematics became its participants. One group was given a conventional Content-Focused Syllabus of a training research workshop in Mathematical Analysis, while the second group received a Learner-Centered Syllabus, designed in accordance with the Person-Centered Approach to Teaching and Learning. The analysis of the findings of this experiment justified the effciency of creating a learning environment, which is determined by the emotional components, such as Congruence, Acceptance and Empathic understanding. The present paper also shows a positive impact of the syllabus on the degree of students' motivation to choose the training research workshop in Mathematical Analysis.

The article considers the development of the online educational model "Creative Thinking through Learning Elementary Maths" and the results of the effciency to implement this course for students of the specialization "Mathematics" while learning Elementary Mathematics. The research represents the development of learning materials for the online course posted in free access on the educational platform "Higher School Mathematics Teacher". The course components (theoretical, practical, and feedback) are focused on the organization of motivated and consistent students' activity; open and integrative Rich tasks of three levels of complexity. The course participants' activity, focused on the recognition, classification, solution, creation of Rich tasks, encourages the formation of the main components of creative thinking that include a problem statement, fluency, flexibility, originality, and elaboration. The first version of the course materials was improved following course users' wishes, and then the effciency of online course education was checked using an experiment. The analysis of results of the experiment allows concluding about the effciency of the developed model of learning an online course.

This article considers the search for new methodological approaches to teaching high school students mathematics that will promote the development of their logical thinking. Based on the analysis conducted by the authors of the study identified an urgent need to develop the logical thinking of students in mathematics lessons through various methods of solving problems. The authors of the article set out to investigate the factors that will ensure the implementation of a problem-based approach to teaching mathematics. These factors include the choice of a certain type of mathematical problem; selection of a method for solving mathematical problems; compiling a system of problems of one type that require the selection of methods for solving them. The authors reveal the introduction of the problem approach as a method of developing students' logical thinking in the article on the example of solving irrational equations with parameters. The authors of the study explain the value of problems with parameters by the fact that the process of solving them contributes to the formation of students' research skills. In the study, the authors focused on the analytical method of solving problems with parameters. Structural analysis of problems allowed the authors to formulate the following didactic requirements for the system of mathematical problems such as compliance with the problems of the course content and the principle of gradual increase in complexity; the rational relationship between the logical and heuristic components of educational activities; the presence of ideological and technical complexity, etc. To confirm the effectiveness of the introduction of the problem-based approach to the educational process, as a method of developing students' logical thinking, an experiment was conducted. The main objectives of the experiment were to identify the level of logical thinking of students; development and implementation in the educational process of a system of problems with parameters in the study of the topic "Irrational equations", which contribute to the development of logical thinking of students; analysis of the results of the experiment. The obtained results and their statistical processing confirmed significant differences in the levels of development of logical thinking in the control and experimental groups, respectively. This proved the effectiveness of a problem-based approach to teaching mathematics and the development of logical thinking of students.

The article considers the problem of the quality of mathematical school education in the context of pupils' ability to apply the acquired knowledge of mathematics to solve practical problems. It is established that this ability is a clear understanding and awareness of the role of mathematical knowledge in the modern world. It is manifested in the ability to explain natural and scientific phenomena, to draw sound conclusions, to understand the impact of science on human life. The results of a study in which 1849 pupils of Kyiv schools took part are presented. Their ability to apply mathematical knowledge to solve life problems has been established. Examples of mathematical problems developed for testing by specialists of the Ukrainian Center for Educational Quality Assessment are given. The typical pupils' mistakes, as well as the most successful solutions are analyzed. Pedagogical recommendations for improving the quality of mathematics education of pupils in the context of the reform of the "New Ukrainian School" are given.

In the presented work, the concept of mathematical abilities is rational as both an essential internal characteristic of mathematical competence and an immanent attribute that prevails in its personal and psychological dimension. In view of the spatial Cartesian implementation the role and place of mathematical abilities in the three-dimensional structure of the internal manifestation of mathematical competence are substantiated. The semantic and system analysis of structural components of the studied phenomenon is made. It is established that complex correlations of four structural components of mathematical abilities (system-forming, coding-formalized, cognitive-generalizing, mnemonic-generalizing) can exist with three dimensions of the external manifestation of mathematical competence (semantic-theoretical, procedural-active, personal-psychological). It is introduced that the development of mathematical abilities is provided by updating the external dimensions of mathematical competence in educational and mathematical activities. The method of developing the mathematical abilities of students is presented according to the results of the implementation of this idea and the principle of developmental continuity. The basis of this technique is the developmental-problem method of teaching mathematics as a four-level problem structure which embodies the methods of mathematical and educational (educational-theoretical) modeling, the method of ascent from the abstract to the concrete, provides a reflection of the process and results of educational and mathematical activities. Due to the problem raised in the work the authors highlight the content and results of a pilot study on the development of mathematical abilities of future mathematics teachers (freshmen and graduates). The effectiveness of the created developmental methods of mathematical education was experimentally tested.

The paper considers the issues of studying method of geometric properties of metric spaces. These questions arise when students learn the basic concepts of the metric spaces theory. Difficulty in the concepts understanding arises due to the lack of the geometric interpretation or appropriate visualization. To build a geometric interpretation of rectilinear and flat placement of points of metric space, it is proposed to build the appropriate analogues in two-dimensional and three-dimensional arithmetic Euclidean spaces. To visualize these concepts, it is proposed to use a dynamic geometric environment GeoGebra 3D. This approach allows to demonstrate both the similarity of individual geometric concepts of metric space with the corresponding concepts of Euclidean geometry, and cases of the "non-Euclidean". The study is useful for teachers and students of higher education institutions majoring in physics and mathematics. Some examples can be used in the study of basic geometric concepts by students of secondary education, in-depth study of mathematics and in various types of informal education.

This article is devoted to the implementation of scientific achievements into the educational process of physics specialties students in the framework of study course "Solid State Physics". In this work, based on our previous scientific results, we present a quantum-mechanical approach that can adequately describe the temperature dependences of the dielectric crystals thermal conductivity. The basic provisions of quantum-mechanical approach are studied by students in the framework of university study course "Solid State Physics" and are based on Einstein and Debye classical models. This approach is based on the assumption that in dielectric crystals heat is transferred due to the phonons (Debye model) and thermal diffusion between the thermally activated neighboring quantum mechanical oscillators directly from site to site on a time scale of one-half of the oscillation period (Einstein model). In term of this consideration the thermal conductivity of molecular crystals are simulated in the framework of thermal conductivity model where heat is transferred by low-frequency phonons with taking into account phonon–rotation coupling, and above the phonon mobility edge by "diffusive" modes. For this purpose the theoretical temperature dependences of the isochoric thermal conductivity have been calculated numerically in the interval near or over the Debye temperature and compared with experimental results for solid C₆H₁₂, CHCl₃ and CH₂Cl₂. Using simple molecular crystals as an example it is shows the dualism of the nature of heat transfer processes in the temperature region of the order of the Debye temperature and above. The obtained results will be useful for implementation in the educational process in the study course "Solid State Physics" in particular for understanding the features of heat transfer in the high-temperature range of dielectric crystals existence.

Time has come to form a new education system. This is confirmed by the UNESCO initiative on the future of education for 2050 and thereafter and provides an opportunity to understand how education can shape the future of humanity and the planet. Today, the development of ICT, artificial intelligence, digital platforms and information growth are agents of change in the educational process. The amount of information in the world doubles every day; information-oriented society (a community connected to each other and the world through information and technology) is being formed. Open information systems, global educational networks, interacting digital resources, developing digital educational and information resources provide an opportunity to improve the quality of education. In view of this, special information educational resources are developed in accordance with the trends of science, regional context, individual characteristics and needs of students. In recent years, STEM education has been actively developing both in the world and in Ukraine. This contributes to students' involvement into STEM disciplines, and young people's choosing engineering professions. This article substantiates the feasibility of developing a system of visualized teaching cases in Physics. A classification of educational cases is proposed. The paper describes the experience of development and introduction of visualized cases using a combination of Google-services and digital computer measuring system Einstein in the process of teaching Physics as a STEM-discipline. The method of organization of classes with the help of digital computer measuring complex Einstein in the context of situational teaching of Physics is suggested. The article also presents the analysis of the results of implementation of the system of visualized Physics teaching cases into educational process on the basis of Physics and Educational Technologies Laboratory of Kherson State University.

As a complement to the traditional elements of the physics laboratory, alternative strategies are sought that allow the experimentation of mechanical oscillations and improve the understanding of these phenomena by university students. Smartphones have very high quality built-in sensors, which in the particular case of the gyroscope allows to carry out oscillator experiments with excellent results. Two experiments that were implemented with the gyroscope integrated into a smartphone are shown. Appropriate setups are suggested to make these experiments.

The development of pedagogical-psychological theories causes an increase in the number of examined factors (cognitive and non-cognitive). One of the non-cognitive factors is the family environment, so the paper deals with determining the connection between success in physics and mathematics and family functioning. In the research, 80 seventh and eighth-grade elementary school students participated. The constructed questionnaire included eight dimensions of family functioning: cohesion, flexibility, disunity, networking, chaos, rigidity, family communication, and family satisfaction. Results showed that students whose parents are married achieve significantly higher scores on all four mentioned scales. The children whose parents are divorced achieved the lowest marks. Also, the dimensions of communication and family satisfaction are rate as good. The chaotic component was influenced by parents' level of education, where the highest value was expressed by students whose parents are at the primary school level. This component proved to be important for students' achievements in mathematics. Achievements in physics were influenced by the level of cohesion, whose increase also caused a higher student achievement. Family environment is an important factor determining students' development, functioning, and school success, so it is important to monitor its impact and train teachers to work with students from dysfunctional families.

In many studies, special attention is paid to examining how students acquire scientific concepts and use scientific terminology. Proper understanding of scientific concept is in direct correlation with the quality of students' knowledge. The knowledge composed of irregularly adopted concept leads to misconceptions. The aim of the research was to examine how students of biology understand certain scientific concepts in physics that are relevant to their profession. Also, it is examined their intrinsic motivation for physics using a standardized questionnaire. This research was conducted in February 2016. The research results pointed that students do not understand some basic concepts related to physics, but students' motivation for learning physics is on a medium level.

The article is devoted to the study of STEM education. It is one of the important directions of educational reform of the XXI century and can be implemented through the integration of formal and non-formal education. The authors of the paper study the ecosystem of formal and non-formal STEM education. Researchers have identified the main characteristics of this ecosystem such as the harmonious combination of formal and informal components of STEM learning, increasing the motivation of students to STEM sciences, constant updating of educational programs and professional development programs for teachers; use of non-formal education approaches; constant connection with external communities of STEM professionals; building partnerships between schools and non-formal institutions. The authors have developed the main components of the model of functioning of the educational STEM centre as an education ecosystem. In particular, they are educational research, assessment (evaluation), research projects, innovative teaching methods, programs for training, undergraduate education, teacher training, mentoring, services, communications, cooperation, infrastructure, connection, networking. To assess the extent of the impact of various forms of formal and non-formal learning activities on the results of the implementation of STEM education, an expert survey was conducted. The results of the survey are systematized, illustrated with the help of infographics, statistically significant relationships between individual parameters of the proposed model are established. To test this model in practice, an experiment was conducted. It lasted from 2016 to 2020. Researchers have confirmed the hypothesis that STEM education gives the best results due to a combination of formal and non-formal levels. Therefore, their STEM centre promotes STEM education among the general public, training and retraining of educators involved in STEM, development of STEM competencies of pupils and students.

The article considers the problem of STEM education in the context of improving the quality of science and mathematics literacy of pupils. The results of the monitoring study conducted by the "OsvitAnalityka" Analytical Center of Borys Grinchenko Kyiv University in cooperation with the Kyiv City Educational Agency and the Ukrainian Center for Educational Quality Assessment are presented. The state of formation of science and mathematical literacy of pupils as the ability to apply knowledge to solve practical problems for the implementation of STEM education has been established. Examples of practice-oriented integrated tasks in geography, chemistry, biology and physics that reveal the possibilities of STEM education are given. The success of the implementation of individual tasks, which involved subject integration and the use of knowledge in practice is analyzed. The most important factors influencing the quality of STEM education are highlighted: professional level of teachers, material and technical and educational-methodical support, motivation of pupils, practice-oriented content of education. As a result of the monitoring study, recommendations were prepared for general secondary education institutions for further implementation of STEM education.

Recently, attention is paid to conceptual aspects of STEM or particular usage of specific tools during STEM. This paper is devoted to systemize all digital tools used during STEM classes. It is proposed to systemize all equipment into instrumental, computer simulation, and modern ones (VR, AR, and AI and 3d-modelling). It is proved the dominant role of computer simulation and modern instruments during providing STEM classes due to their simplicity and absence of necessity of expensive equipment usage. Using any of the described tools do not guaranty providing STEM, but they can be used as an element of the STEM didactic approach.

The modern informational society poses new challenges to the education system, and one of the ways to solve them is STEM education, which has become one of the popular learning trends. The solution of the set tasks encourages not only the growth of the economic indicators, but also the general stable development of society with a careful attitude to resources, both material and immaterial. The practitioners are the leaders in high-tech changes of the education system, that is why they are the ones who can implement the STEM approach in the most effective way. This is important because the scientific component of technology is evolving over time and, accordingly, the skills of employees that are needed are changing, too. And the STEM approach in education, in turn, is the best to meet this requirement. The professional development of practicing teachers means to update knowledge in the field and acquire new teaching methods and technologies. Thus, in addition to professional necessity, professional development of practicing teachers is of innovative importance. The proposed certificate program of advanced training aims to develop students' skills to implement STEM education in a scientifically sound and critical way; widely use interdisciplinary interaction; to introduce methods and means of STEM education in professional activity. The target audience of the program is future and practicing teachers of general and professional higher education.

Relevance of the selected research topic is due to its development results aiming to resolve contradictions between society's needs for personality-oriented training of Physics and Mathematics basics at comprehensive secondary school and the inadequate basic (necessary and sufficient) conditions to provide this in primary grades. Teachers also lack for a systematic and scientifically substantiated practice of immersing their students into the didactic fairytale environment. The research primarily aims to reveal the author's conceptual vision of the essence and principles of didactic fairy tale designing in order to convert it into a basic tool of Physics and Mathematics training to 1st – 4th grade pupils.

The project announced by the authors is focused on the smart systems of open science, the issues of elaboration of methodological, methodic, and organizational support for the use of these emerging ICT in teaching and research, increasing the level of ICT competence of educators, including teachers. Given the significant pedagogical potential and novelty of existing approaches to the use of smart learning systems meaning first of all the cloud-based adaptive open science systems, their design and use in educational institutions, these issues still need theoretical and experimental research, refinement of approaches, models, methods and techniques, possible ways of implementation. In the process of studying leading experience, the following advantages of using the cloud-based services for teachers' training were identified: resource savings, access mobility, elasticity, and others. The cloud-based methodological system for educational personnel training at different levels was proposed and considered: for the training of students for the Master level for educational sciences; for the in-service teachers' training. The methods and tools of smart systems design and implementation were considered and evaluated. The recommendations and suggestions for the advisable ways for smart systems of open science introduction into the learning process were provided.

The article presents an analysis of the phenomenon of "clip thinking" in the educational and cognitive activities of students of natural and physical-mathematical educational profile. The involvement of clip thinking in the initial stage of cognition in comparison with rational and theoretical thinking is theoretically substantiated. An empirical verification of the originality of cognitive processes of students of natural and physical-mathematical educational profile in the situation of comparing traditional linear (textual) and hypertextual way of presenting information is established. Deficiency of cognitive processes characteristic of clip thinking for results is revealed, which is characterized by characteristics of mental (theoretical) level of cognition. Therefore, the next stage of cognition should be the understanding of information through the mechanisms of comparison, generalization, categorization and re-synthesis.

The paper deals with the pedagogical aspects of blended learning implementation in the educational process of undergraduates majoring in computer science. Certain peculiarities of blended learning for foreign language teaching have been presented. The design principles of a blended course for one term as well as the practice of its functioning have been discussed. The blended English for Specific Purposes course for computer science students with the focus on critical thinking skills formation and development has been introduced. One specific profession-related theme studying within the blend has been described. The experience of applying authentic demonstration videos in the English language as contents of tasks for critical thinking skills enhancing has been propounded. Practical aspects of carrying out a 30 multiple-choice question test for determining the undergraduates' critical thinking skills level have been presented.

The paper studies the issue of increasing the ICT competency of a Maths teacher. The study analyzes the concept of ICT competency of a Maths teacher and considers the possibilities of its formation in different countries. One of the ways to increase the ICT competency of a Maths teacher is to use the "Personal e-learning environment of the Maths teacher" online course. The authors describe the model of the developed course, which is based on the ADDIE model and takes into consideration the key activities of a teacher. The experiment, conducted among master's students majoring in "Secondary education. Mathematics" showed the positive effects of the developed course on the level of their ICT competency. The redistribution of the percentage of the students towards normative and high levels of ICT competency formation was observed.

Nowadays, there are a lot of psychological and pedagogical research aimed to explore students' individual characteristics and how to take them into account in educational process, as well as to develop new teaching techniques. In this study, we focus on future IT specialists' internal motivation to continue education and training, internal motivation for professional activity as a software engineer, and reflective skills. We consider the impact of psychological and learning training on educational motivation and reflective skills of university students. We present pedagogical technique which involves motivational training, training exercises, and learning training. In particular, we give a brief description of author's learning training on "NoSQL databases: MongoDB and ASP.NET MVC". The results of pedagogical experiment conducted to evaluate effciency of this technique are presented. In experimental work 405 higher education students majoring in 121 Software Engineering, 122 Computer Science, 123 Computer Engineering took part. Based on statistical processing of empirical data, we made a conclusion about potency of our technique.

The article presents the results of an empirical study of computer addiction of student youth in the context of personal self-realization by parameters: motivation to succeed, volitional self-regulation, development of emotional intelligence. The aim of the article is to analyze the manifestations of computer addiction as a new way of personal self-realization, to empirically investigate the relationship of individual psychological factors of self-realization of personality by parameters: motivation to succeed, volitional self-regulation, development of emotional intelligence with subjective assessment of computer addiction by the student youth. Psychodiagnostic methods were used: test for Internet addiction of K. Young; Shostrom's personal orientation (short form) in the modification of E. Jones and R. Crandall; N. Hall's emotional intelligence test, a questionnaire to study the motivation to succeed of T. Ehlers; questionnaire "Study of volitional self-regulation" by A. Zverkov and E. Eidman. The study allowed to obtain significant correlations between computer dependence and the level of self-actualization, volitional self-regulation and its components, self-management of emotions as a component of emotional intelligence. Virtual space for the younger generation in modern conditions serves as a means of meeting those significant needs that are frustrated in real conditions. In particular, personal self-realization in student youth is transferred to cyberspace through new hobbies, acquaintances and attributions of their own "I". Thus, computer addiction in this study was considered as a new way of personal self-realization of student youth, which is still treated mainly as a form of deviant behavior. Self-realization on the Internet for modern youth is a significant area of personal self-realization in general, which under favorable conditions complements self-realization in reality, and under adverse conditions replaces self-realization in reality. Taking into account these points will allow to build a system of psychological work with different levels of computer addiction of student youth in the context of their personal self-realization.

By surveying 95 students studying design and technology in the light industry, the problems in mastering upcycling technologies were explored, and ways to overcome them were outlined. The analysis of existing problems is carried out at three levels - personal perception of upcycling, the formation of relevant skills and knowledge and lack of experience in scaling personal expertise to a business startups level. All respondents are roughly divided into those who practice upcycling frequently and those who do it occasionally. Another 15% of respondents did not decide on their preferences. Respondent attitude, control of behaviour, and behavioural intentions are the most influential factors that encourage upcycling. The influence of social factors, perceived habits and the presence of facilitating conditions is more moderate. Interviewed students have a poor understanding of the benefits of upcycling. Competence for creativity, which is key to mastering upcycling techniques, is absent in educational and professional programs in technology and design. Several examples of possible changes in curricula from 4 disciplines aimed at the formation of creativity are given. The main reasons that complicate the scaling of acquired skills and knowledge in developing business startups with upcycling are analysed. An example of a designed startup is given.