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Документ A Markov Chain Representation of the “5 E’s” Instructional Treatment(СумДПУ імені А. С. Макаренка, 2019) Voskoglou Michael Gr.; Воскоглой Майкл Гр.Formulation of the problem. The socio-constructive theories of learning have become very popular during the last decades for teaching mathematics. The “5 E’s” is an instructional model based on the principles of social constructivism that has recently become very popular, especially in school education, for teaching mathematics. Each of the 5 E's describes a phase of learning which begins with the letter "E" – Engage, Explore, Explain, Elaborate, Evaluate. Depending on the student reactions, there are forward or backward transitions between the three middle phases (explore, explain, elaborate) of the 5E’s model during the teaching process. The “5 E's” model allows students and teachers to experience common activities, to use and build on prior knowledge and experience and to assess their understanding of a concept continually. Materials and methods. Probabilistic methods of analysis are used. Results. The mathematical representation of the “5 E’s” model is attempted by applying an absorbing Markov chain on its phases. A Markov Chain (MC) is a stochastic process that moves in a sequence of steps (phases) through a set of states and has a one-step memory. A finite MC having as states Si the corresponding phases Ei, i = 1, 2,…, 5, of the “5 E’s” instructional model is introduced. A classroom application is also presented illustrating the usefulness of this representation in practice. The following application took place recently at the Graduate Technological Educational Institute of Western Greece for teaching the concept of the derivative to a group of fresher students of engineering. Conclusions. The Markov chain representation of the “5 E’s” model provides a useful tool for evaluating the student difficulties during the teaching process. This is very useful for reorganizing the instructor’s plans for teaching the same subject in future.Документ A Method of Studying Students Work in the EDraw Max Environment(СумДПУ імені А. С. Макаренка, 2020) Базурін Віталій Миколайович; Bazurin Vitalii MykolaiovychThe article describes the components of the methodical system of teaching students to work in the EDraw Max environment. EDraw Max Graphics Editor is one of the best tools for building a home plan and designing engineering communications. In the process of studying EDraw Max graphic editor, student-builders develop such competence as the ability to solve professionally-important tasks using ICT tools. The article describes the requirements for students who start studying EDraw Max, used methods and means of training, types of training exercises, topics of laboratory work. Formulation of the problem. The rapid development of information and communication technologies has led to the fact that they are included in many spheres of professional human activities, including construction. It is difficult to imagine the design of modern buildings and structures without the use of computer graphics. The state standard of the specialty "Construction and Civil Engineering" defines one of the professional competencies "the ability to use modern means of computer technology for the solution of applied problems". Materials and methods. State standard analysis, curriculum analysis, graphical editor functionality analysis, synthesis, generalization and systematization. Results. The proposed topic of work was tested during 2017-2018 in the process of training students of specialty 015.01 "Vocational education. Construction". Learning outcomes are positive. Students completed most of the laboratory work. The use of EDraw Max was more effective than AutoDesk AutoCad. Conclusions. The use of the EDraw Max graphic editor in the course of "Information and Communication Technologies" is fully justified.Документ A Note on the Graphical Representation of the Derivatives(2017) Воскоглой Майкл Гр.; Voskoglou Michael Gr.In the article at hands an alternative definition of the concept of the derivative is presented, which makes no use of limits. This definition is based on an old idea of Descartes for calculating the slope of the tangent at a point of a curve and holds for all the algebraic functions. Caratheodory extended this definition to a general definition of the derivative in terms of the concept of continuity. However, although this definition has been used successfully by many German mathematicians, it is not widely known in the international literature, nor it is used in the school book texts. After presenting Caratheodory’s definition, the article closes by describing methods for calculating the derivative at a point of a function y = f(x) with the help of a suitably chosen table of values of f(x), and for designing of the graph of the derivative function f΄(x) given the graph, but not the formula, of f(x). These methods are based on the graphical representation of the derivative, which should be reclaimed better in general for teaching purposes.Документ Algorithms and Elementary Functions: Two Sides of the Same Fundamental Notion(СумДПУ імені А. С. Макаренка, 2016) Субботін І.; Subbotin I.; Білоцький Н.; Bilotskyi N.An elementary function is one of the foundational notions of calculus course. However, many calculus textbooks do not provide students with a clear definition of the elementary function or simply avoid it completely. The current paper offers a simple and rigor approach of introducing the notion of an elementary function via linear algorithms.Документ Application of Fuzzy Relation Equations to Assessment of Analogical Problem Solving Skills(СумДПУ імені А. С. Макаренка, 2018) Воскоглой Майкл Гр.; Voskoglou Michael Gr.Analogical reasoning is a very important part of the human cognition in general for creativity and scientific discovery and in particular it is a very useful method for solving mathematical problems by retrieving from the memory similar problems solved in the past and adapting their solutions for use with the target problem. On the other hand, the student assessment is an essential task of Education, because, apart of being a social need and demand, it helps the instructors in designing their future plans for a more effective teaching procedure. However, frequently an instructor is not sure about the exact grade corresponding to each student’s performance. Therefore, the student assessment is characterized by a degree of vagueness and/or uncertainty. Consequently, fuzzy logic, due to its property of characterizing the ambiguous real life situations with multiple values, becomes a reach resource of assessment techniques to be applied in such vague cases. In this work fuzzy relation equations are used as a tool for evaluating student analogical problem solving skills. The fuzzy relation equations are obtained by the composition of binary fuzzy relations, which are fuzzy sets defined on the Cartesian product of two crisp sets. The compositions of binary fuzzy relations are conveniently performed in terms of the membership matrices of them. The same elements of the membership matrices are used in these compositions as would be used in the regular multiplication of matrices, but the product and sum operations are here replaced with the min and max operations respectively. The notion of fuzzy relation equations was first proposed by Sanchez in 1976 and later was further investigated by other researchers. A classroom application and other suitable examples are also presented in this article illustrating our results. Further, the present work is connected to our earlier research efforts on utilizing several other fuzzy Logic techniques as tools for the assessment of the student performance.Документ Basic Education and Fundamental Ideas – Clear Combination of Mathematical Structures(СумДПУ імені А. С. Макаренка, 2020) Шмельцер Неллі; Schmelzer Nelli; Кляйне Міхаель; Kleine MichaelFormulation of the problem. At present, the focus on competence is an important part of discussions about mathematics lessons. In such discussions, particular attention is given to basic mathematical education. In this article, we substantiate the importance of mathematical competence in mathematical work and introduce mathematical work as a modeling cycle. The focus is on the processes of transforming reality into mathematics. In particular, transformational processes contribute to a better mathematical understanding of students and thus contribute to improving the quality of teaching of mathematics. Materials and methods. In order to achieve our goals, we use in this article an empirical methods and general methods of scientific cognition: benchmarking to clarify different views on a problem and determining the direction of research, systematization and generalization to formulate conclusions and recommendations, summarize the author's pedagogical experience and observations. Results. In Chapter 1.2, we describe the process of mathematical work at different stages, using the example of a typical problem. The above example is intended to clearly disclose the processes of thinking and work according to the theoretical model proposed in Chapter 1.1. It should also not be assumed that in a general situation, mathematical work can be comprehensively described by the example that we are studying. However, a competency-oriented teaching methodology is used to help students develop new strategies and heuristics to work with mathematics as a science. In order for students to develop their mathematical competence, mental models are called, which we call fundamental ideas. The construction of such cognitive structures is called the formation of fundamental ideas. This process is characterized by fixing the meaning of the new terms in terms of known factual connections, constructing mental objects that describe the term, and applying this objects to new contexts. Training involves both extending and changing existing foundational ideas as well as building new ideas. Accordingly, in Chapter 2.1 we use an example of probability to illustrate how various aspects of probability can be understood in terms of such a fundamental concept and how the development of fundamental ideas can occur. Significant in this article is a new approach that focuses on competence with a modeling cycle and a basic conception of foundational ideas. Conclusions. The approach developed emphasizes the importance of considering mathematical work as a process and linking the individual levels of foundational ideas to a basic concept. The use of the proposed structure enables teachers to more effectively identify, interpret, and appropriately remove misunderstood students' basic mathematical ideas.Документ Computer Models for Polygonal Numbers Investigation and Their Use in Mathematical Education(СумДПУ імені А. С. Макаренка, 2016) Гризун Л. Е.; Hryzun L. E.Urgent needs of society to raise level of mathematical education and falling students’ motivation to learn mathematics as well as insufficient using of its cognitive power in the educational process actualizes necessity to propose relevant didactic mechanisms, to apply computer technologies and make mathematical concepts serve educational purposes. In this context the phenomenon of polygonal numbers represents really bright example of both cognitive resource of math and its application to didactics and real life. According to the aims of the work, there were obtained and represented some relations among flat polygonal numbers based on their properties investigation; binary algebraic operations on the sets of polygonal numbers of various angularity were determined and algebraic properties of the polygonal numbers sets as algebraic systems were investigated; author’s computer models of polygonal numbers were built in GeoGebra environment and the ways in which these and other results might be used in mathematical education were determined.Документ Computer Models Using in Terms of the Realization of Holistic Approach to School Mathematics Learning(СумДПУ імені А. С. Макаренка, 2019) Білоусова Людмила Іванівна; Гризун Л. Е.; Bilousova Liudmyla Ivanivna; Hryzun L. E.Analysis of the problems of contemporary mathematical education reveals necessity of improvements of the learning approaches. Being complicated integrative science, Mathematics nowadays tends to become a bridge between various subject areas, which causes greater importance of deep understanding of mathematical basics. On the other hand, learning Mathematics appears to be really complicated for schoolchildren, as it operates by the system of concepts with high level of abstraction. Formulation of the problem. Thus, according to the studies, it seems to be necessary to implement holistic educational ideas into Mathematics teaching. It can help to form students' concentrated conceptual mathematical knowledge and facilitate their using. However, in order to apply effectively holistic approach we need to arm teachers with proper didactic aids. On balance, computer models development and their implementation for holistic learning of mathematical objects seem to be vital for contemporary education. The aim of the paper is to represent the authors' complex of computer models and their didactic facilities as for the abstract mathematical concepts mastering by schoolchildren. It is also covered the role of the models and recommendations for their classroom using in terms of holistic approach to school Mathematics learning. Materials and methods. Analysis of the number of studies enables us to cover theoretical basics as for the peculiarities of mathematical objects mastering by students, the difficulties which might happen during their learning, and instruments that can facilitate them. During the research, the set of theoretical, empirical, and modelling methods were applied. Theoretical background for the computer models elaboration made comprehensive analysis of the current mathematical curriculum, demands to the final requirements to the pupils' knowledge and skiils, and learning of related subject areas, held by the authors beforehand. In order to meet the main principles of holistic approach to mathematical education it is also necessary to reveal key mathematical objects, establish connections between them, and build chains of proper internal and transdisciplinary links. Results. The results of the theoretical analysis were used at the design of the authors' complex of computer models which can be implemented in terms of the realization of holistic approach to school Mathematics learning. The complex of the computer models embraces some groups of models directed on the facilitating the mastering of a number of abstract mathematical concepts. The process of the models elaboration is covered in the paper as well as the models functionality and didactic support to them. The potential of the elaborated complex of computer models as for their implementation in terms of holistic approach to Mathematics school learning is proved and analyzed. Conclusions. It seems to be relevant to predict positive influence of the computer models implementation on the forming of trainees' holistic system of knowledge and skills. Elaboration of proper methodology of its diagnosing and estimation might be a prospect of our further research.Документ Current Problems and Future Perspectives of Mathematics Education(СумДПУ імені А. С. Макаренка, 2018) Воскоглой Майкл Гр.; Voskoglou Michael Gr.From the origin of mathematics as an autonomous science two extreme philosophies about its orientation have been tacitly emerged: Formalism, where emphasis is given to the axiomatic foundation of the mathematical content and intuitionism, which focuses on the connection of the mathematical existence of an entity with the possibility of constructing it, thus turning the attention to problem-solving processes. Although none of the existing schools of mathematical thought, including formalism and intuitionism, have finally succeeded to find a solid framework for mathematics, most of the recent advances of this science were obtained through their disputes about the absolute mathematical truth. In particular, during the 19th and the beginning of the 20th century, the paradoxes of the set theory was the reason of an intense “war” between formalism and intuitionism, which however was extended much deeper into the mathematical thought. All these disputes created serious problems yo the sensitive area of mathematics education, the most characteristic being probably the failure of the introduction of the “New Mathematics” to the school curricula that distressed students and teachers for many years. In the present work current problems of mathematics education are investigated, such as the role of computers in the process of teaching and learning mathematics, the negligence of the Euclidean Geometry in the school curricula, the excessive emphasis given sometimes by the teachers to mathematical modeling and applications with respect to the acquisition of the mathematical content by students, etc. The future perspectives of teaching and learning mathematics at school and out of it are also discussed. The article is formulated as follows: A short introduction is attempted in the first Section to the philosophy of mathematics .The main ideas of formalism and intuitionism and their effects on the development of mathematics education are exposed in the next two Sections. The fourth Section deals with the main issues that currently occupy the interest of those working in the area of mathematics education and the article closes with the general conclusions stated in the fifth Section that mainly concern the future perspectives of mathematics education.Документ Cинергетичний підхід у підготовці до професійної мобільності майбутніх фахівців(2017) Рідкодубська А. А.; Ridkodubska A. A.Стаття присвячена аналізу процесу професійної підготовки майбутніх працівників соціальної сфери в рамках синергетичного підходу. Сучасна наука використовує нову методологію міждисциплінарності, комплексності, системності. В якості універсальної основи для підготовки майбутніх працівників соціальної сфери до професійної мобільності виступає синергетичний принцип. Зроблено висновки стосовно формування професійної мобільності майбутніх соціальних працівників в рамках синергетичного підходу про те, що цей процес є динамічним, системним, який характеризується єдністю цілей, інноваційних технологій за рахунок впровадження патернів нового мислення, які містять у собі нове знання про механізми і процеси самоорганізації та саморозвитку відкритих нелінійних систем. В статті виділено ряд умов, за реалізації яких можлива самоорганізація освітніх систем, їх цілеспрямований саморозвиток: відкритість системи, постійний притік інформації із соціуму; відносно колективно узгоджену поведінку суб’єктів освітнього процесу; перехід від нестійкого до стійкого стану; нелінійність, багатоваріантність розвитку, що переконує у необхідності його використання при підготовці майбутніх працівників соціальної сфери.Документ Cовершенствование математической подготовки бакалавров компьютерных наук при освоении дисциплины физическое воспитание(СумДПУ імені А. С. Макаренка, 2016) Кравченко В. І.; Kravchenko V. I.Неможливість підготовки висококваліфікованих фахівців у галузі інформаційних технологій без безперервного вдосконалення математичних знань і скорочення обсягів аудиторних занять з дисциплін математичного циклу, що проводяться профільною кафедрою, спонукає випускаючу кафедру комп'ютерних інформаційних технологій шукати резерви для підвищення рівня математичної підготовки студентів за рахунок інтенсифікації навчального процесу шляхом тісної взаємодії з кафедрою фізичного виховання, здійснюваного проведенням міжкафедральної комплексної самостійної роботи. Досліджується предметна область діяльності викладача кафедри фізичної культури щодо формування здорового способу життя у студентів і співробітників ВУЗу. Виділяється основний бізнес- процес, що полягає у визначенні, обліку і контролі оздоровчо – фізичних навантажень студентів з допомогою проби Руф'є – Діксона, індексів маси тіла, добової калорійності харчування, на підставі яких розробляються інформаційна та математична моделі. З використанням методології функціонального моделювання SADT проводиться алгоритмізація основного бізнес-процесу і створюється маюче практичну спрямованість автоматизоване робоче місце викладача – спеціаліста по фізкультурі і спорту. Робоче проектування АРМа для визначення, обліку і контролю оздоровчо – фізичних навантажень студентів або співробітників ВУЗу здійснюється як додаток баз даних за допомогою вільно розповсюджуваної мови програмування Web-розробок – Ruby із застосуванням фреймворку Ruby on Rails.Документ Cуб'єктивні та об'єктивні характеристики звуку(2017) Воронкін О. С.; Voronkin O. S.Стаття розкриває матеріали відкритої лекції на тему «Характеристики звуку», підготовленої та прочитаної в Комунальному закладі «Сєвєродонецьке обласне музичне училище ім. С. С. Прокоф’єва» у межах навчальної дисципліни «Фізика». Розглядаються об’єктивні (інтенсивність, частота, амплітудно-частотний спектр) і суб’єктивні (гучність, висота, тембр) характеристики звуку, досліджується зв’язок між ними. Спрощено розкриваються фізичні особливості будови слухового аналізатора людини та механізму сприйняття звуку людиною. Показано доцільність використання сукупності апаратних і програмних засобів під час вивчення зазначеної теми. Акцентовано увагу на застосуванні методу комп’ютерного моделювання акустичних явищ і процесів з метою покращення фахової підготовки студентів вищих навчальних закладів культури і мистецтв I-II рівнів акредитації. Робиться висновок, що посилення міждисциплінарних зв’язків фізики, математики, біології та музичного мистецтва дозволяє студентам розвивати уміння виокремлювати головне у навчальному матеріалі, порівнювати, узагальнювати, робити висновки, розвивати спостережливість, логічне мислення, пам’ять та увагу.Документ Cучасні вимоги до математичної підготовки майбутніх фахівців морської галузі відповідно до міжнародних стандартів(2017) Доброштан О. О.; Dobroshtan O. O.У статті відображені результати дослідження щодо основних тенденцій сучасної вищої морської освіти у світі. Встановлено, що в умовах переходу на нові показники якості освіти математична підготовка майбутніх фахівців морської галузі має бути орієнтована на формування готовності і здатності курсантів використовувати математичні знання і вміння до розв’язання професійних завдань, бажання та готовність застосування ІКТ до розв’язання задач навчального, прикладного та професійного змісту. Розкрито роль математичної підготовки майбутніх судноводіїв у вищому навчальному закладі морського профілю. Розглянуті особливості викладання курсу вищої математики з урахуванням міжнародних стандартів ІМО (International Маritime Organization). Проаналізовано рівень математичної підготовки у вищих морських навчальних закладах України та світу. Досліджено відповідність рівня математичної підготовки курсантів Херсонської державної морської академії до міжнародних стандартів підготовки фахівців морської галузі.Документ Didactics of Digital Century: Issues and Trends of E-Learning Development(СумДПУ імені А. С. Макаренка, 2020) Каменєва Тетяна Миколаївна; Kamenieva Tetiana MykolaivnaFormulation of the problem. Revolutionary changes in society and education due to intensive implementation of new digital technologies suggest the revision of the traditional understanding of didactics as a science of teaching. Particularly, the widespread Web 2.0 applications have the capacity for educational institutions to extend the possibilities of e-learning. Such active approaches to learning as the professional communities’ creation, the use of cloud computing, the development of mobile communications, thanks to which a large number of users have the opportunity to collect and visualize data, are becoming increasingly widespread. Consequently, development of pedagogy, which is aimed at educational goals of a higher level, is a driver of innovations in educational systems. Technologies and new modes of content delivery open up wonderful opportunities to rethink completely the teaching process. However, the traditional understanding of didactics does not meet the requirements of the digital society with the rapid development of digital technologies. This contradiction suggests that it is necessary to develop an orderly theoretical basis for e-learning ― e-Didactics. Currency of the paper is conditioned by the problems of developing the theoretical basis of elearning – electronic Didactics (e-Didactics), which corresponds to the modern conceptual understanding of the role of digital technologies in the educational process. Particular attention is paid to trends in the development of educational technologies and factors that oppose their introduction into the higher education sector. The objectives of the research are to (1) consider the way technology is changing educational process in the sector of high education, leading to the emergence of a new pedagogy, (2) examine recent tendencies in the development of educational technologies that will have the most significant impact on future educational processes in higher education. Materials and methods. The process of scientific and pedagogical research was carried out using the methods of investigation. In particular, there were: analysis of scientific and educational literature on scientific research problem; comparative analysis of scientific data, generalization and systematization of pedagogical approaches concepts and practical experience of digital technologies, social media, and mobile devices implementation in teaching process, modelling of the didactic system of e-learning. Results. The results of the research in terms of its objectives are: a) the key distinctions of e-Didactics from the traditional didactics were represented; b) instructional strategies, teaching methods and digital tools as a direction for the further development of edidactics have been generalized; c) the most promising pedagogical approaches and trends which are contributing to the introduction of digital pedagogy into the higher education sector have been discussed. Conclusions. The realization of the specific opportunities provided by digital technologies for education requires the transition of the didactic system of e-learning to a higher level of complexity, the use of new organizational forms and methods. The results of the research should be of help for educators, methodologists and instructors in the system of professional development of higher education, as well as for all those willing to master the new didactic approaches.Документ Fundamental form of Motion of Matter and Traditional Problematic Issues of Physics(СумДПУ імені А. С. Макаренка, 2015) Сусь Б. А.; Sus B. A.; Сусь Б. Б.; Sus B. B.In the article it is shown that there is a continuous transition from one form (substance) to another (the field) as a fundamental form of motion of matter. The basis of this oscillatory process is known in the theory of relativity as the ratio W = c2×m which is suitable to understand as the law of conservation of matter. Proposed approach makes it possible to remove a number of fundamental traditional problematic issues of physics related to the dual nature of matter.Документ Fuzzy Numbers as an Assessment Tool in the Apos/Ace Instructional Treatment for Mathematics(СумДПУ імені А. С. Макаренка, 2016) Воскоглой Майкл Гр.; Voskoglou Michael Gr.У статті використовується комбінація методів трикутних нечітких чисел (TFNs) та центру тяжіння (COG) як техніки дефазифікації для оцінки знань і навичок студентів універистету у процесі навчання математики у рамках APOS/ ACE.Документ Innovative Culture in the Mainstream Development of the Modern Society: Theoretical Analysis(СумДПУ імені А. С. Макаренка, 2019) Козлов Дмитро Олександрович; Kozlov Dmytro OleksandrovychFormulation of the problem. The article deals with the concepts: tradition and innovation; historical analysis of their interaction in the field of education is conducted. In any era, traditions were reworked, rethought, and applied to their own ends and only those that were in harmony with the style and culture of society were preserved. Some elements of the old traditional system have survived, adapting to new circumstances, changing their functions or joining the new system as elements. It can’t be spoken of traditions as something solid and unchanging; in fact, there is a continuous process of changing and transforming some traditions and dying of others, transforming some innovations into traditions. This is the basic logic behind the interaction between tradition and innovation. Thus, the concepts of "tradition" and "innovation" are dialectically interrelated. Tradition exists as a basis for innovation, and innovation is the basis for the tradition origin. Materials and Methods. Solving the highlighted aim, a set of methods of scientific research adequate to them were used, theoretical: a comparative analysis of innovative culture in the mainstream development of the modern society; a systematic analysis of innovative culture as an integrative personality quality of the future manager of the educational institution. The article analyzes the theoretical foundations of the concepts of "tradition - innovation" as two sides of the educational process. The traditions analysis and innovations has been carried out based on the approaches considered to these concepts, taking into account development over time, depending on the particular circumstances of the society's development. Results. The concepts of "tradition" and "innovation" are dialectically interrelated. Tradition exists as a basis for innovation, and innovation is the basis for the origin of tradition. The article reveals the essence of innovative culture and its place and significance in the modern society development. The interrelation between person’s innovative culture and the innovative culture of society is analyzed and the main development tasks of effective innovative culture are highlighted. Conclusions. The category "innovative culture" is one of the corporate culture directions of the general secondary education institution. The essence definition and the category content" person’s innovative culture" is offered, its main tasks in providing an innovative favorable environment are defined. The article attempts to answer the question of what should be the process of pedagogical support of innovative activity of future heads of secondary educational institutions, in order to effectively influence the innovative practice results taking into account its peculiarities.Документ Innovative Technology for Mastering Mathematical Concepts and Mathematical Terms(2020) Ковачева А. К.; Kovacheva A. K.This article presents pedagogical experience in the use of numerical and verbal crossword puzzles in a math-lesson in primary school. They are one of the many enigmatic tools that find a place in learning, but their effective application requires extensive pedagogical experience. The technology for the realization of crossword puzzles is very plentiful and the teacher can choose the most suitable one for his students. The idea of their application is to support the learning process on the one hand by providing students with a higher level of understanding, more lasting memorization, and application of mathematical knowledge in practice, and on the other hand diversification and enrichment of teaching methods and tools. For students to acquire skills for applying the acquired mathematical knowledge in practical situations, it is first necessary to master a stable level of theoretical knowledge - a condition that depends primarily on the work of the teacher. The success of a teacher is the result of the variety of tools and methods he applies in his work and the ability to present them to students in a way that will intrigue and provoke them. The review of the existing textbooks, collections, and books for the math teacher shows that the number of mathematical crossword puzzles in them is very small and they are only numerical. The analysis of the teaching practice shows that the possibilities of these tools are underestimated, on the one hand, due to the lack of ready-made crossword puzzles, and on the other hand the unpreparedness of the trainers to adequately apply the crossword puzzles in a real learning environment. Our goal is to arouse interest, increase the activity and motivation of students by applying numerical and verbal crossword puzzles in the math lesson. This pedagogical experience was tested by an experimental study, the results of which show that the proposed and applied numerical and verbal crossword puzzles in the teaching of EG (experimental group) seventh-graders contribute to improving the results of mathematics education at the end of 7th grade. Proof of this is not only the experiment conducted within the study but also the results achieved by the NEE (National External Evaluation) in June 2020 of EG.Документ Interactive Demonstration with Multiple Representation іn Learning оf Magnetic Field Concepts(СумДПУ імені А. С. Макаренка, 2017) Фатмар'янти Сіска Деси; Fatmarianty Siska Desy; Супармі A.; Suparmi A.; Сарванто; Sarvanto; Ашаді; AshadiМетою даного дослідження є підтвердження ефективності використання інтерактивної демонстрації з різними зображеннями для підвищення розуміння студентами понять теорії магнітного поля. Вибірка з 62 студентів вибирається випадковим чином з числа учнів старших класів. Результати тесту показали, що розподіл учасників є нормальним. В експериментальному класі навчання проводилося з використанням інтерактивної демонстрації з різними зображеннями, в той час як у контрольних класах навчання проводилося традиційно. Результат дослідження показує, що (1) навчання із використанням інтерактивних демонстрацій з з різними зображеннями є більш ефективним в плані підвищення у студентів розуміння понять теорії магнітного поля в порівнянні з традиційним навчанням; (2) використанням різних способів зображення допоможуть школяреві мінімізувати труднощі, повязані з векторним добутком та використанням правила буравчика, орієнтації векторів. Модель навчання розглядається в якості альтернативи на заняттях з метою навчання учнів формулювати їх відповіді різними способами при вивченні абстрактних понять.Документ Interdisciplinary Problems as one of the Ways of Implementation of Practical-Oriented Approach in Teaching of General Physics of Future Teachers of Labor Education and Technologies(СумДПУ імені А. С. Макаренка, 2018) Базурін Віталій Миколайович; Bazurin Vitalii MykolaiovychGeneral physics is one of the fundamental disciplines studied by future teachers of labor education and technology. An important factor influencing the motivation of students to study general physics is a practice-oriented approach. The main means of learning at the same time are practical-oriented tasks, including tasks of interdisciplinary nature. The article proposes the topics and contents interdisciplinary tasks of general physics for students of the specialty 014.10 "Secondary education. Labor training and technology”. The author proposes a set of tasks on the main topics studied by future technology teachers: kinematics, dynamics, dynamics of solids, dynamics of liquids and gases, conservation laws, thermodynamics, laws of direct and alternating current, optics. The developed tasks belong to the main topics in physics, which are studied by future teachers of labor studies and technologies: kinematics, dynamics, dynamics of solids, dynamics of liquids and gases, conservation laws, the basis of thermodynamics, the laws of constant and alternating current, geometric optics. The content of the developed tasks is organically linked with the content of such disciplines as resistance of materials, technical mechanics, thermal and hydraulic machines, technological workshops, tractors and cars. The developed interdisciplinary tasks are important for increasing the motivation of students to study general physics, since they ensure compliance with such a didactic principle, as a connection between theory and practice. The prospect of further research in this direction is to develop a system of practical-oriented tasks in general physics as well as an experimental verification of their impact on the motivation and success of the students.