Modern Education
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Publications of Mayer Robert Valerievich
Modern Education, 2019-2
Mayer R.V. - The Physical Field concept and peculiarities of its application in formation of the scientific worldview in students mindset pp. 75-81


Abstract: The object of this research is the process of studying the gravitational, electromagnetic and other physical fields. The goal is to analyze the formation of the “physical field” concept, which is the core of conceptual field incorporating the “gravitational”, “electric”, “magnetic”, “electromagnetic”, “nuclear forces” and others, from the perspective of didactics and cognitive linguistics; determine the imagery-perceptual component of the concept, its structure and key cognitive qualities; examine the specificities of their representation of the courses of “Physics”, “Concepts of Modern Natural History”, and “Natural Science Worldview”. The following methods were used in the course of this research: 1) analysis of the definitions of concept, determination of the key cognitive qualities; 2) studying the sensual and visual image formed in a student’s mindset; 3) semantic and cognitive analysis of academic texts; 4) building of the semantic model. The result of quantitative analysis of the various textbooks established that the conceptualization of “physical field” first and foremost suggests the examination of the following cognitive qualities: “physical field – form of matter”, “gravitational field”, “field of gravity”, “electric and electrostatic filed”, “magnetic field”, “electromagnetic field, and “field worldview (concept, theory)”.
Modern Education, 2016-4
Mayer R.V. - On evaluation of difficulty of educational text in natural scientific disciplines pp. 56-64


Abstract: This article is dedicated to the question of evaluation of didactical difficulty of the educational text. The author introduces the notion of didactical difficulty as the characteristic proportional to time that is required for digestion of information presented in the text. The universal criteria of evaluation of difficulty of the notions on various natural scientific disciplines are being proposed. It is substantiated that didactical difficulty of the studied in school questions is defined by the diversity and abstractness of the qualitative and mathematical models. The author analyzes the modern textbooks on environmental studies, geography, biology, physics, and chemistry, as well as performs their pairwise comparison with each other. The article examines the two methods of determination of the didactical difficulty of educational texts: 1) through calculation of the number of scientific terms and consideration of their difficulty using the computer; 2) by means of pairwise comparison of various texts with each other. The scientific novelty consists in proposition of the criteria of assessment of the didactical difficulty of scientific notions, as well as analysis of the results of expert evaluation of the textbooks from the perspective of difficulty of the qualitative and quantitative models.
Modern Education, 2015-4
Mayer R.V. - Rotation of theoretical and practical activities as an effective method of education: Results of imitation modelling pp. 145-155


Abstract: The subject of this research is a computer model of a student based on the following hypotheses: 1) in the course of studying the student acquires new knowledge, and the unsubstantiated knowledge transforms into substantiated; 2) the efforts applied by a student depend on the disparity between the requirement of the teacher and the knowledge of the student; 3) with increase in speed of presentation of new material, the coefficient of the transfer rate in the “teacher-student” communication channel decreases. The article examines the methodology that consists in splitting the theoretical and practical material into several parts and their alternation. The scientific novelty lies in the following: 1) the author suggests the new computer model of a student that takes into account the transformation of the surface knowledge into deep knowledge, and the nonlinear dependencies of a student from the teacher, and the coefficient of the transfer rate of communication channel from the speed of presentation of new material; 2) by the means of imitation modelling it is demonstrated that the alternate studying of theory and practice leads to a greater result.
Cybernetics and programming, 2015-2
Mayer R.V. - Numerical method of the solution of a boundary problem for the oscillating membrane pp. 59-67


Abstract: The article considers the simple method of the numerical solution of the two-dimensional wave equation which allows to simulate the following phenomena: 1) propagation and reflection of waves; 2) change of wavelength upon its transition from one environment to another; 3) an interference of waves from several coherent sources; 4) formation of a standing wave; 5) rounding by a wave of obstacles, diffraction of waves; 6) the forced oscillations of an elastic plate; 7) free oscillations of an elastic plate of any form; 8) self-oscillations of an elastic plate. The method of mathematical modeling, a method of the numerical solution of the differential equations in private derivatives, and also a method of color mapping of two-dimensional fields on the screen are used. Novelty of work: the article presents two simple computer programs written in Free Pascal, allowing to simulate rather big set of the phenomena connected about distribution of waves in two-dimensional environments and oscillations of an elastic plate. The given programs can be used in studying numerical methods and bases of computer modeling.
Modern Education, 2015-1
Mayer R.V. - Computer Two-Component Probability Model for Studying Academic Disciplines pp. 42-52


Abstract: The article is devoted to the solution of the main task of the mathematical learning theory which is to define the level of knowledge of a student studying a discipline. The researcher states that all the acquired academic knowledge can be conditionally divided into the two categories: 1) ephemeral knowledge that is easily forgotten, and 2) time-proof knowledge (skills) developed through multiple repetitions of the academic material that is slowly forgotten. The given simulation model also takes into account the dependence of the ratio of knowledge acquisition and time a student spends on studying the material on the overall level of student's actual knowledge. To achieve the objectives of the research, the researcher has used the methods of the analysis and synthesis of complex systems, mathematical and computer simulation. The scientific novelty of the research is caused by the fact that the researcher proves that it is possible to create a two-component probability model for studying an academic discipline and this model may include: 1) probability of a student studying a new issue or repeating the material; 2) increasing share of time-proof knowledge as a result of a growing number of repetitions; 3) reduction of time spent on studying a particular material while repetitions of the material grow; 4) growing ratio of knowledge acquisition while the overall quantity of knowledge and/or knowledge of this particular material multiply. The given model allows to monitor the dynamics of student's growth of overall knowledge and his knowledge of a particular discipline.
Cybernetics and programming, 2014-6
Mayer R.V. - On the use of computational experiments in the study of physics pp. 74-84


Abstract: The author reviews a problem of use of educational computational experiments in the study of physical phenomena. By educational computational experiment author means experiment on the mathematical model of the object carried out with the aid of a computer for the purpose of learning. A set of simplified versions of educational computational experiments adapted to the conditions of learning form a System of educational computational experiments. The article analyzes the examples of the use of educational computer experiment for: 1) for the study of the magnetization of a ferromagnet, calculation of the magnetization curve and hysteresis loop; 2) study of chaotic oscillations of a Dafing pendulum, occurrence of bifurcation in changes in the profile of the potential well, study of Poincaré section and the evolution of the phase volume. The authors apply mathematical and computational methods (simulation) modeling, which involves the construction of a mathematical model and building a software simulating the phenomenon under study based on the numerical solution of the corresponding to its’ system of equations. The novelty of the work is in the proposed four simple computer programs in Pascal, allowing: 1) obtain the magnetization curve and hysteresis loop for a ferromagnet in a changing magnetic field; 2) simulate the oscillation of the Dafing pendulum; 3) study the transition of oscillator into the chaotic regime at a change of the potential well; 4) get a Poincaré section and to study the evolution of the phase volume for Dafing pendulum.
Modern Education, 2014-4
Mayer R.V. - Optimization of Time Required to Learn Elements of Educational Material of Different Importance: Computer Simulation pp. 51-63


Abstract: Different elements of the educational material have different importance for learning the following topics and passing the final tests. By using the method of expert evaluation, it is possible to define how important this or that element is. The subject of the present research is the process of learning a sequence of topics of different importance. Some important topics require more time to be learnt while other topic that are not important should be even ignored. The present article is devoted to the problem of optimization of time required to learn particular elements of educational material of different importance in order to achieve the best learning efficiency. To achieve the aforesaid objectives, the author has used the methods of systems analysis, mathematical and computer simulation, algorithmization adn programming. The scientific novelty of the research is caused by the following: 1) for the first time in the academic literature the author raises the problem of optimization of time required to learn educational material of different importance; 2) the author has carried out a number of simulation experiments to define the best time distribution in the process of learning topics of difference importance; 3) based on the results, the author describes the rules for the best time distribution and efficient learning of topics of different importance. 
Cybernetics and programming, 2014-4
Mayer R.V. - Computational experiments in studying of wave processes in linear and nonlinear media pp. 57-65


Abstract: The course of physics in colleges and universities includes various wave processes: reflection and transmission of the pulse through the interface between two media, interference, wave propagation in a dispersive medium, the formation and interaction of solutions. Here it is important to combine theoretical and practical approaches to studying of these phenomena with computer models, allowing creating visual image of the phenomenon and analyzing its behavior in different conditions. The subjects of the study are the simple computer models and computational experiments helping to show the wave processes in the one-dimensional linear and nonlinear media. The experiments require mathematical and computer modeling, building a mathematical model, creating software simulating the studied phenomenon based on the numerical solution of the corresponding system of equations. The novelty of the work is in the fact that the author presents three simple computer programs written in Pascal, simulating pulse propagation in one-dimensional medium, its reflection from the boundary between two media, and its passage of the second medium, the wave propagation in a dispersive medium, the formation of different solutions and their interactions. The analysis of the results of computer modeling allows to state that the use of such computational experiments based on the simulation of a one-dimensional medium by a system of coupled springing or simple pendulums or solving the sine-Gordon equation really allows to study the wave processes at a higher level and to form interest in physics and information technologies. 
Modern Education, 2014-2
Mayer R.V. - Computer Model of the Society and Using This Model For Studying Social and Economic Processes pp. 22-30


Abstract: The article is devoted to the problem of creating a simulation computer model of the economic and demographic development of the society and using sucha model for studying the basics of computer modelling of social and economic processes. The subject of research is the method of teaching university students hwo to use computer modelling for studying social systems. The simulation model of the society offered by the author of the article explains how to build the structural model of the modern society, create the mathematical model, develop the algorithm and write a program. The author of the article also analyzes the results of modelling different situations (sustainable development, crisis and crisis recovery). In order to create the simulation computer model of the society, the author of the article used the following methods: the systems analysis method, mathematical model method, simulation modelling method, algorithmic and programming methods. Methodological grounds for developing the teaching method under review included modern didactic and methodological principles lying in the basis of computer sciences, programming and computer modelling. The scientific importance and novelty of the research is the following: 1) the researcher developed a simple training computer model of the demographic and economic development of the society; 2) the researcher carried out the analysis of possible applications of the model when studying the basics of computer modelling of social and economic processes; 3) the researcher also provided the source program which makes it easier for university teachers to use this model. 
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