Application of computer modeling in the learning process. Using simulations for teaching in computer science. Description of experimental work

R. P. Romanski

Technical University, Sofia, Bulgaria

Introduction

To develop computer technology and improve the architectural organization of computer systems (CS), continuous training and self-improvement of computer specialists and students is necessary. When conducting this training, it is necessary to combine forms of traditional training with opportunities for self-study, distance learning, practical development of projects and implementation of research experiments. A significant role in training in the field of computer science is played by the use of modern methods for studying architectural organization and analyzing the system performance of computer systems. In this sense, the use of modeling methods in the process of studying the basic structures of various CSs and the organization of computer processes allows us to develop a suitable mathematical description of the object under study and create software for performing computer experiments [Romanski, 2001, Arons, 2000]. Analysis of experimental modeling results [Bruyul, 2002] allows us to evaluate the main characteristics of the system and the performance of the studied CS.

The use of modeling in the process of studying CS allows one to study the features of the architecture and the organization of calculation and control. This can be done on the basis of a model experiment, the organization of which involves designing a computer model as a sequence of three components (conceptual model, mathematical model, software model) and implementing this model in a suitable operating environment. This paper examines the possibility of using different methods for studying CS in the process of studying them and, in particular, the application of modeling principles to study ongoing processes, as well as analyzing the system performance of CS. The main goal is to define a general computer modeling procedure as a sequence of interrelated stages and present the main stages of the modeling research methodology. To do this, the next part presents the general formalization of computer information processing and the features of computer computing as an object of study. The application of modeling principles in the process of studying CS is associated with the methodological organization of training in the traditional, distance, or distributed sense.

Computer systems as an object of study and research methods

One of the main objectives of specialized training courses in the field of computer systems and performance research is to train future and current computer designers, computer hardware developers and computer users in the correct use of technological capabilities for modeling and measuring system performance. These capabilities are used both in the process of assessing the effectiveness of new computer projects, and for conducting a comparative analysis of existing systems. During the training process, the task is to clarify the sequence of research stages and the possibility of processing experimental results to obtain adequate estimates of performance indices. This task can be clarified depending on the specific area of computer training and the features of the principles of computer information processing under consideration.

Rice. 1. Information support for computer processing.

In general, computer processing is concerned with the implementation of certain functions to transform input data into final solutions. This defines two levels of functional transformation of information (Fig. 1):

mathematical transformation of information is the actual processing of data in the form of mathematical objects and is represented by a generalized function f:D®R, which depicts the elements of the data set D in the elements of the result set R;

computer implementation of processing - represents a specific implementation f*:X®Y of the mathematical function f depending on computer and software equipment based on a suitable physical representation of real information objects.

As a result, we can write a generalized functional model of computer processing r = f(d)ºj 2 (f*[ 1(d)]), where functions j 1 and j 2 are auxiliary for encoding and decoding information.

When considering CS as an object of study, we must keep in mind that computer processing consists of processes, each of which can be represented in the form of a structure I = , where: t is the initial moment of the process; A - defining attributes; T - process trace. The last component of the formal description defines the time sequence of events e j for a given process to access elements of the system resource S=(S 1, S 2, ..., S n). The sequence of time stages and the load of the system resource make it possible to determine the profile of the calculation process (Fig. 2).

Rice. 2. Approximate profile of a computer process.

Supporting various processes during the organization of computer processing forms the system load of the computer environment. For each moment (t =1,2,...) it can be represented by the vector V(t)=Vt= , the elements of which express a free (v j =0) or occupied (v j =1) device S j єS (j=1,2,...,n).

When studying CS, it is necessary to determine a set of basic system parameters that reflect the essence of computer processing, as well as to develop a methodology for studying the behavior of a system resource and ongoing processes. As the main system parameters (performance indices), you can study, for example, the workload of each element of the system resource, the total system load of the computer system, response time when solving a set of problems in multiprogram mode, the degree of stability (resilience) of equipment, the cost of computer processing, the efficiency of scheduling parallel or pseudo-parallel processes, etc.

A typical course in the field of analysis and research of CS performance should discuss the main theoretical and practical problems in the following areas:

opportunities to study the performance of computer equipment and the efficiency of computer processes;

application of effective research methods (measurement, modeling);

technological features of measuring system parameters (benchmark, monitoring);

technological features and organization of modeling (analytical, simulation, etc.);

methods for analyzing experimental results.

All this is connected with the use of this research method and the selection of suitable tools. In this sense, in Fig. Figure 3 presents an approximate classification of methods for studying CS and processes. Three main groups can be identified:

Software mixtures - represent mathematical dependencies for assessing processor performance based on the coefficients of application of individual operating classes. Allows you to estimate the processor load by statistical analysis after executing typical programs.

Counting methods - allow you to obtain reliable information about the course of computer processes based on the direct registration of certain values of the available CS parameters. To do this, it is necessary to use or develop a suitable counting tool (monitor) and organize the execution of the counting experiment. It should be noted that modern operating systems have their own system monitors, which can be used at the software or firmware level.

Modeling methods are used when there is no real experimental object. The study of the structure or ongoing processes in the CS is carried out on the basis of a computer model. It reflects the most important aspects of the behavior of structural and system parameters depending on the goal. To develop a model, it is necessary to choose the most suitable modeling method that allows you to obtain maximum adequacy and reliability.

Rice. 3. Classification of methods for studying CS and processes.

The traditional learning process involves a core course of lectures combined with a set of classroom exercises and/or laboratory workshops. In the field of computer science, when studying the organization of computer systems and the principles of computer process control (at a low and high level), as well as when analyzing system performance, there is often a need to develop computer models while performing laboratory tasks in the classroom or when independently implementing projects. To successfully complete these practical works and to obtain the necessary practical skills, it is necessary to determine the sequence of stages and present the technological features of developing models. This will allow students to acquire the necessary knowledge about the development of adequate and reliable computer models for research, evaluation and comparative analysis of system performance of different computer architectures. As a result, a generalized procedure for carrying out modeling is further proposed, as well as a methodological scheme for model research of CS and processes.

Computer modeling procedure for studying CS and processes

Using Simulation for Computer Science Education

R. P. Romanski

Technical University, Sofia, Bulgaria

Introduction

Computer systems as an object of study and research methods

Rice. 1. Information support for computer processing.

As a result, we can write a generalized functional model of computer processing r = f(d)ºj 2 (f*[ 1(d)]), where functions j 1 and j 2 are auxiliary for encoding and decoding information.

When considering the CS as an object of study, one must keep in mind that computer processing consists of processes, each of which can be represented in the form of a structure I = , where: t is the initial moment of the occurrence of the process; A - defining attributes; T - process trace. The last component of the formal description defines the time sequence of events e j for a given process to access elements of the system resource S=(S 1, S 2, ..., S n). The sequence of time stages and the load of the system resource make it possible to determine the profile of the calculation process (Fig. 2).

Rice. 2. Approximate profile of a computer process.

Supporting various processes during the organization of computer processing forms the system load of the computer environment. For each moment (t =1,2,...) it can be represented by a vector V(t)=Vt= , the elements of which express a free (v j =0) or occupied (v j =1) device S j єS (j=1 ,2,...,n).

A typical course in the field of analysis and research of CS performance should discuss the main theoretical and practical problems in the following areas:

opportunities to study the performance of computer equipment and the efficiency of computer processes;

application of effective research methods (measurement, modeling);

technological features of measuring system parameters (benchmark, monitoring);

technological features and organization of modeling (analytical, simulation, etc.);

methods for analyzing experimental results.

Rice. 3. Classification of methods for studying CS and processes.

Computer modeling procedure for studying CS and processes

The main task of computer modeling in the study of CS and processes is to obtain information about performance indices. Planning a model experiment during the learning process is carried out based on the following stages:

collection of empirical data for specific values of basic system parameters;

structuring and processing of empirical information and development of a functional diagram of the model;

determination of a priori information and definitional areas of operating parameters for the development of a suitable mathematical model of the original object;

implementation of model experiments, accumulation of model information and its subsequent analysis.

A generalized formalized model research procedure for organizing a model experiment is shown in Fig. 4.

Rice. 4. Model research procedure.

The initial goal is determined by the need to study a real object (system or process). The main steps of the procedure are as follows:

Defining the basic concept of building a model by decomposing an object into subsystems and introducing an acceptable degree of idealization for certain aspects of the behavior of system processes.

Mathematical formalization of the structure and relationships in the studied object based on a suitable formal system.

Mathematical description of the functioning of a real system and development of a suitable functional model depending on the purpose of the simulation.

Implementation of a mathematical model using the most appropriate modeling method.

Description of the created mathematical model using a suitable software environment (specialized or universal).

Performing experiments based on the created model and subsequent processing and interpretation of model information to assess the parameters of the research object.

The main methods of computer modeling are as follows:

Analytical methods - use mathematical tools to describe the components of a real system and ongoing processes. Based on the chosen mathematical approach, a mathematical model is usually constructed as a system of equations that allows easy programming, but implementation requires high accuracy of formulations and accepted working hypotheses, as well as significant verification.

Simulation (imitation) methods - the behavior of a real object is imitated by a software simulator, which in its operation uses a real workload (emulation) or a software model of the workload (simulation). Such models allow the study of complex systems and obtaining reliable results, but they are performed in time and this determines the main advantage of the method - significant consumption of computer time.

Empirical methods are quantitative techniques for recording, accumulating and analyzing information about the functioning of a real object, on the basis of which it is possible to build a statistical model for its study. Typically, linear or nonlinear equations are used to represent the relationship of selected parameters (for example, from a set of primary factors) and to calculate statistical characteristics.

The main task of computer modeling is to create an adequate model, with the help of which the structure of the system under study and the ongoing processes can be fairly accurately represented. The development of a computer model includes three successive levels - a conceptual model (an ideological concept for structuring a model), a mathematical model (an image of a conceptual model using a mathematical formal system) and a software model (a software implementation of a mathematical model with a suitable language environment). At each level of computer modeling, it is necessary to check the adequacy of the model to ensure the reliability of the final model and the accuracy of the results of model experiments. The specifics of the individual stages of the modeling procedure determine the approaches and means of assessing adequacy used. These features found a place in the developed computer modeling methodology, which is presented below.

Model research methodology

In the process of computer modeling, regardless of the method used, it is possible to determine a generalized matodological scheme for a model study (Fig. 5). The proposed formalized methodological sequence includes several main phases, presented below. Basically, it represents an iterative procedure for obtaining the necessary reliability of the developed computer model based on the formulation of the initial model hypothesis and its sequential modification. This approach is successful when studying complex systems, as well as in the absence of sufficient a priori information for the object under study.

Formulation stage

At the first stage of model development, it is necessary to accurately and clearly define the object of modeling, the conditions and hypotheses of the study, as well as the criteria for assessing model effectiveness. This will allow us to develop a conceptual model and define it in abstract terms and concepts. Typically, an abstract description defines the initial principles of model construction (basic approximations, definitional domains of variables, performance criteria and types of expected results). At this stage the following sub-stages can be defined:

Definition and analysis of the task. Includes a clearly defined nature of the research problem and planning of the necessary activities. Based on the analysis of the problem, the scope of expected actions and the need for decomposition of the task are determined.

Clarification of the type of initial information. This information allows us to obtain correct output modeling results and therefore it is necessary to ensure the necessary level of reliability of the estimates.

Introduction of assumptions and hypotheses. This is necessary when there is not enough information to implement the model. Assumptions replace missing or complete data. Hypotheses refer to the type of possible results or the environment for the implementation of the processes under study. During the modeling process, these hypotheses and assumptions can be accepted, rejected, or modified.

Determination of the main content of the model. Based on the applied modeling method, the features of the real object, the task and the means for solving it are reported. The results of this substage include the formulation of the basic concept of the model, a formalized description of real processes, and the selection of a suitable approximation.

Determination of model parameters and selection of performance criteria. At this substage, primary and secondary factors, input influences and expected output reactions of the model are determined, which is especially important for achieving the required accuracy of the mathematical description. Clarification of efficiency criteria is associated with the definition of functional dependencies for assessing the system response when changing model parameters.

Abstract description of the model. The general formulation phase of the conceptual model ends with the abstraction of the model in a suitable medium of abstract terms - for example, as a block diagram, as a Data Flow Diagram, as a graphical diagram (State Transition Network), etc. This abstract representation allows one to easily construct a mathematical model.

Rice. 5. Methodological scheme of the model study.

Stage "Design"

Designing a computer model is associated with the development of a mathematical model and its software description.

A mathematical model is a representation of the structure of the object under study and the ongoing processes in a suitable mathematical form Y=Ф(X, S, A, T), where: X is a set of external influences; S - set of system parameters; A - reflects functional behavior (functioning algorithms); T - operating time. Thus, the behavior (reaction) of object Y models a set of functional influences Ф, representing analytical dependencies (deterministic or probabilistic). In this sense, a mathematical model is a description of an abstract model by means of a selected mathematical system, evaluating accepted hypotheses and approximations, initial conditions and defined research parameters. When developing a mathematical model, it is possible to apply known mathematical formulas, dependencies or mathematical laws (for example, probability distributions), as well as combine and supplement them. The most common theoretical mathematical systems for modeling purposes provide the opportunity to present a mathematical model in graphical form - Petri nets, Markov chains, queuing systems, etc. Based on the criteria determined at the previous stage, the created mathematical model must be evaluated in order to achieve the required degree of reliability and adequacy, and after that you can approve or discard it.

A software model is an implementation of a mathematical description in a program language - for this purpose, suitable technical and technological means are selected. In the process of software implementation, a logical structural and functional diagram of the model is developed on the basis of a mathematical model. To build this diagram, you can use traditional block diagrams, or graphical tools that are presented in a specialized modeling environment - such as in GPSS (General Purpose Simulation System). The software implementation of the model is a software development task and in this sense is subject to the principles of programming technology.

Stage "Clarification"

The actions of this stage are intended to fully validate the designed model and establish its adequacy. An assessment of the current adequacy at previous stages is essential for their effectiveness. In this sense, the process of refining the model should be considered as a set of distributed actions at all previous stages of computer modeling. In general terms, the refinement stage can be represented as an iterative procedure (Fig. 6), allowing for consistent modification of the initial version of the model being developed.

Rice. 6. Iterative procedure to refine the model.

The main purpose of checking model reliability is to determine the level of accuracy of correspondence when representing the processes of a real object and the mechanism for recording model results. In general terms, a computer model represents a collection of individual components and in this sense it is especially important to properly plan adequacy checks.

Execution stage

This is the stage of implementation of the created model (solution using a numerical method or execution in time). The most important goal is to obtain maximum information for minimal computer time. There are two sub-steps:

Planning a model experiment - determining the value of controlled factors and the rules for registering observed factors when executing the model. The choice of a specific experimental design depends on the stated goal of the study when optimizing the execution time. To obtain an effective design, statistical methods are usually used (complete design, single-factor design, randomized design, etc.) to remove the joint influence of observed factors and estimate the acceptable experimental error.

Implementation of the experiment - preparation of input data, computer implementation of the experimental plan and storage of experimental results. The experiment can be implemented as follows: control modeling (to check the performance and sensitivity of the model and estimate the modeling time); working modeling (actual implementation of the developed experimental plan).

Stage "Analysis and interpretation of model results"

When implementing a model experiment plan, information (modeling results) is accumulated, which must be analyzed to obtain an assessment and conclusions about the behavior of the object under study. This determines two aspects - the choice of methods for analyzing experimental information and the application of suitable methods for interpreting the obtained estimates. The latter is especially important for the formation of correct research conclusions. In the sense of the first aspect, statistical methods are usually used - descriptive analyzes (calculation of boundary values of parameters, mathematical expectation, dispersion and mean square error; determination of stratification for a selected factor; calculation of a histogram, etc.); correlation analysis (determining the level of factor relationship); regression analysis (study of causal relationship in a group of factors); analysis of variance (to establish the relative influence of certain factors based on experimental results).

The results of the analysis of model data can be presented in numerical or tabular form, using graphical dependencies, diagrams, histograms, etc. To select suitable graphical tools, the analysis method used is essential, as well as the subjective skills of the experimenter for formatting the experimental results.

Conclusion

The main goal of organizing each model experiment is to implement effective modeling. It is associated with computer time - a significant amount of processing in the model increases the cost of modeling and reduces efficiency. Rapid model validation and achievement of convergence are essential for the effectiveness of the study. For each real system, it is often necessary to create many different models that differ in the method of decomposition and level of detail, modeling method, software implementation tools, etc. In the process of choosing the optimal option, only assessing accuracy and adequacy is insufficient. From a variety of convergent models, you need to choose the most effective option that will spend the least amount of time on implementation.

To achieve sufficient efficiency of the model, the applied language of software implementation is also essential, as well as the completeness of the formal system of abstract representation of the conceptual model, simplicity of description terms, development of an optimal plan, etc. The use of universal software systems is characterized by the absence of specific language operators and therefore they are suitable primarily for analytical modeling. To implement simulation models, it is advantageous to use specialized language environments.

Bibliography

[Bruyul 2002] Bruyul A. SPSS: the art of information processing. Analysis of statistical data. St. Petersburg: DiaSoft, 2002, - 608 p.

[Romanski, 2001] Romanski R. Mathematical modeling and study of stochastic time characteristics of computer data processing processes // Information technologies. - Moscow, Russia, 2001, No. 2, - P. 51 - 55.

Arons H., van Asperen E. Computer assistance for model definition // Proceedings of the 32nd Winter Simulation Conference. - Florida, USA, December 2000. - P. 399-408.

Benveniste A., Fabre E., Haar St. Markov nets: probabilistic models for distributed and concurrent systems // IEEE Transactions on Automatic Control. November 2003, vol. 48, No. 11. - P. 1936-1950.

Butler J.E., Brockman J.B. A Web-based learning tool that simulates a simple computer architecture // ACM SIGCSE Bulletin. June 2001, vol. 33, No. 2. - P. 47-50.

Crosbie R. E. A model curriculum in modeling and simulation: Do we need it? Can we do it? // Proceedings of the 32nd Winter Simulation Conference. December 2000. -P. 1666-1668.

Fabre E., Pigourier V. Monitoring distributed systems with distributed algorithms // Proceedings of the 41st IEEE Conference on Decision and Control. - vol. 1. 10-13 December 2002 - P. 411-416.

Ibbett R.N. WWW Visualization of Computer Architecture Simulations // Proceedings of the 7th Annual Conf. on Innovation and Technology in Computer Science Education. June 2002. - P. 247.

Lilja D.J. Comparing Instructional Delivery Methods for Teaching Computer Systems Performance Analysis // IEEE Trans. on Education. February 2001, vol. 44, No. 1, - P. 35-40.

Music G., Zupancic B., Matko D. Petri net based modeling and supervisory control design in Matlab // Proceedings of the IEEE Conference EUROCON 2003 "Computers as a Tool". - vol. 1. 22-24 Sept. 2003. - Slovenia. - P. 362-366.

Pandey S., Ramamritham K., Chakrabarti S. Monitoring the dynamic Web to respond to continuous queries // Proceedings of the 12th International Conference on World Wide Web. - Hungary, May 2003, - P. 659-668.

Pockec P., Mardini W. Modeling with queues: an empirical study // Proceedings of the Canadian Conference on Electrical and Computer Engineering. - vol. 1. 13-16 May 2001. - P. 685-689.

Romansky R. et al. An Organization of Informational Network InfoNet for Distributed e-Learning // Proceedings of the 3rd International Conference on Computer Systems and Technologies (e-Learning). 20-21 June 2002. Sofia, Bulgaria. - P. IV.4-1 - IV.4-6.

Sargent R.G. Verification and validation of simulation models // Proceedings of the 2003 Winter Simulation Conference. - vol. 1. 7-10 December 2003. - P. 27-48.

Stahl, I. GPSS: 40 years of development // Proceedings of the 33rd Winter Simulation Conference. December 2001. - P. 577-585.

Ye D, Xiaofer Xu, Yuliu Chen. Integrated modeling methodology for virtual enterprises // Proceedings of the 10th Conference on Computers, Communications, Control and Power Engineering. - vol. 3. October 2002. - P. 1603-1606.

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Rozova Natalia Borisovna. The use of computer modeling in the learning process: 13.00.01, 13.00.02 Rozova, Natalia Borisovna The use of computer modeling in the learning process (On the example of studying molecular physics in a secondary school): Dis. ...cand. ped. Sciences: 13.00.01, 13.00.02 Vologda, 2002 163 p. RSL OD, 61:03-13/523-2

Introduction

Chapter 1. Models and simulation in science and teaching 14

1.1 Models and modeling in modern science 14

1.2 Application of models in the process of teaching schoolchildren 26

1.3 Computer simulation in teaching 33

Chapter 2. Psychological and pedagogical foundations of computer training 50

2.1 Psychological and pedagogical aspects of computer training 50

2.2 Features of educational activities and their management based on computer training 58

Chapter 3. Methodology for organizing and conducting physics lessons in the 10th grade of a secondary school when studying the topic “Molecular Physics” using computer modeling 74

3.1 Analysis of the state of computer modeling in the section “Molecular Physics” 74

3.2 Characteristics of the experimental program for computer simulation of the dynamics of many particle systems and the possibility of its use in the educational process 83

3.3 Methodology for organizing and conducting physics lessons in grade 10 when studying the section “Molecular Physics” based on an experimental program 92

4.1 Objectives of the experiment and organization of its implementation 128

4.2 Analysis of the results of the pedagogical experiment 140

Conclusion 147

Introduction to the work

One of the most important areas of social development is education. Education “works” for the future; it determines the personal qualities of each person, his knowledge, abilities, skills, culture of behavior, worldview, thereby creating the economic, moral and spiritual potential of society. Information technologies are one of the main tools in education, so developing a strategy for their development and use in education is one of the key problems. Consequently, the use of computer technology is acquiring national importance. Many experts believe that at present the computer will make it possible to make a qualitative breakthrough in the education system, since the teacher has a powerful teaching tool in his hands. Usually there are two main directions of computerization. The first aims to ensure universal computer literacy, the second - to use the computer as a means of increasing the effectiveness of learning.

In the education system, two types of activities are distinguished: teaching and educational. N.F. Talyzin and T.V. Gabay proposed to consider the role of a computer in teaching from the point of view of the function that it performs.

If a computer performs the function of managing educational activities, then it can be considered as a teaching tool that replaces a teacher, since the computer models educational activities, asks questions and responds to the student’s answers and questions like a teacher.

If a computer is used only as a means of educational activity, then its interaction with students is carried out according to the “computer user” type. In this case, the computer is not a teaching tool, although it can impart new knowledge. Therefore, when they talk about computer training, they mean the use of a computer as a means of managing educational activities.

Despite the fact that there is not yet a unified classification of training programs, many authors distinguish the following five types among them: training, mentoring, problem-based learning, simulation and modeling, and games. Computer models have the highest rank among the above. According to V.V. Laptev, “a computer model is a software environment for a computational experiment, combining, on the basis of a mathematical model of a phenomenon or process, means of interactive interaction with the experimental object and the development of a means of displaying information... Computer models are the main object for computational physics, the distinctive method of which is a computational experiment, just as the distinctive method of experimental physics is a full-scale experiment.” Academician V.G. Razumovsky notes that “with the introduction of computers into the educational process, the capabilities of many methods of scientific knowledge increase, especially the modeling method, which allows one to sharply increase the intensity of training, since during modeling the very essence of phenomena is highlighted and their commonality becomes clear.”

The current state of computer training is characterized by a large set of training programs that vary significantly in quality. The fact is that at the initial stage of computerization of schools, teachers who used computer training created their own training programs, and since they were not professional programmers, the programs they created were ineffective. Therefore, along with programs that provide problem-based learning, computer modeling, and so on, there is a large number of primitive training programs that do not affect the effectiveness of training. Thus, the teacher’s task becomes not the development of training programs, but the ability to use ready-made high-quality programs that meet modern methodological and psychological-pedagogical requirements.

One of the main criteria for the didactic significance of modeling programs is the ability to conduct research that was previously impossible in a school physics classroom. In the content of school physics education there are a number of sections in which a natural experiment only qualitatively describes the phenomenon or process being studied. The use of computer models would make it possible to conduct a quantitative analysis of these objects.

One of these sections of school physics is molecular physics, the state of computer education in which we will analyze. By studying it, students encounter a qualitatively new form of motion of matter - thermal motion, in which, in addition to the laws of mechanics, the laws of statistics also apply. Natural experiments (Brownian motion, diffusion, interaction of molecules, evaporation, surface and capillary phenomena, wetting) confirm the hypothesis of the molecular structure of matter, but do not allow us to observe the mechanism of the physical processes occurring. Mechanical models: Stern's experiment, Galton's board, installation for demonstrating gas laws make it possible to illustrate Maxwell's law of the distribution of gas molecules by speed and to obtain experimentally the relationships between pressure, volume and temperature necessary for deriving gas laws.

The use of modern electronic and electronic computer technology can significantly supplement the design and conduct of the experiment. Unfortunately, the number of works on this topic is very small.

The work describes the use of a computer to demonstrate the dependence of the speed of molecules of various gases on temperature, the calculation of changes in the internal energy of a body during evaporation, melting and crystallization, as well as the use of a computer in processing laboratory work. Here is a description of the lesson on determining the efficiency of an ideal heat engine based on the Carnot cycle.

The methodology for setting up an experiment using electronic and electronic computer technology was described by V.V. Laptev. The experimental design looks like this: measured quantities - sensors - analog-to-digital converter - microcalculator MK-B4 or Yamaha computer. Based on this principle, a universal electromechanical installation was designed for studying gas laws in the school physics course.

In the book by A.S. Kondratyev and V.V. Laptev “Physics and Computer”, programs have been developed that analyze in the form of graphs the formula for the Maxwellian distribution of molecules by speed, the use of the Boltzmann distribution to calculate the height of rise and the study of the Carnot cycle.

I.V. Grebenev presents a program that simulates heat transfer through the collision of particles of two bodies.

In the article “Modeling of laboratory work of a physical workshop” V.T. Petrosyan and others contain a program for simulating Brownian motion of particles, the number of which is determined by experiment.

The most complete and successful development of the section of molecular physics is the educational computer course “Open Physics” of the Scientific Center for Physics LLP. The models presented in it cover the entire course of molecular physics and thermodynamics. For each experiment, computer animation, graphs, and numerical results are presented. The programs are of good quality, user-friendly, and allow you to observe the dynamics of the process when changing input macroparameters.

At the same time, in our opinion, this computer course is most suitable for consolidating the material covered, illustrating physical laws, and independent work of students. But the use of the proposed experiments as computer demonstrations is difficult, since they do not have methodological support, and it is impossible to control the time of the ongoing process.

It should be noted that to date, “no established view has been developed on a specific instruction: where and when a computer should be used in the learning process, no practical experience has been gained in assessing the impact of a computer on the effectiveness of training, there are no established regulatory requirements for the type, type and parameters of hardware educational software."

Questions about methodological support for pedagogical software were raised by I.V. Grebenev. “The most important criterion for the effectiveness of computer learning should probably be considered the possibility of students obtaining new, important knowledge on a subject in dialogue with a computer, through such a level or with such a nature of cognitive activity that is impossible with machine-free learning, provided, of course, that their pedagogical effect and is worth the investment of teacher and student time.”

This means that in order for the use of computers to bring real benefits, it is necessary to determine where the existing methodology is imperfect and to show which properties of the computer and how they can increase the effectiveness of learning.

Analysis of the state of computer modeling indicates that:

1) computer modeling is represented by a small number of programs in general and in particular those that simulate physical processes based on the principles of molecular kinetic theory (MKT);

2) in programs modeling based on MCT, there are no quantitative results, but only a qualitative illustration of a physical process;

3) in all programs there is no connection between the microparameters of the particle system and its macroparameters (pressure, volume and temperature);

4) there is no developed methodology for conducting lessons using computer modeling programs for a number of physical processes of MCT.

This determines the relevance of the study.

The object of the study is the learning process in a secondary school.

The subject of the study is the process of using computer modeling in teaching physics in a secondary school.

The purpose of the study is to study the pedagogical possibilities of computer modeling and develop methodological support for the use of computer modeling programs based on the material of a school physics course.

Based on the purpose of the study, the following tasks were set in the work:

1) conduct a holistic analysis of the possibilities of using computer simulation in the learning process;

2) determine the psychological and pedagogical requirements for educational computer models;

3) analyze domestic and foreign computer programs that simulate physical phenomena and give a real learning effect;

4) develop a computer modeling program based on the material of the physical content of secondary general education (section “Molecular Physics”);

5) check the use of an experimental computer modeling program and evaluate its didactic and methodological results.

Research hypothesis.

The quality of knowledge, skills and information culture of students can be improved if, in the process of teaching physics, computer modeling programs are used, the methodological support of which is as follows:

Adequately to the theoretical foundations of computer modeling in the learning process, the tasks, place, time, and form of using educational computer models are defined;

There is variability in the forms and methods of managing students’ activities;

Schoolchildren are taught the transition from real objects to models and back.

The methodological basis of the study consists of: systematic and activity-based approaches to the study of pedagogical phenomena; philosophical, cybernetic, psychological theories of computer modeling (A.A. Samarsky, V.G. Razumovsky, N.V. Razumovskaya, B.A. Glinsky, B.V. Biryukov, V.A. Shtoff, V.M. Glushkov and others); psychological and pedagogical foundations of computerization of education (V.V. Rubtsov, E.I. Mash-bits) and the concept of developmental education (L.S. Vygotsky, D.B. Elkonin, V.V. Davydov, N.F. Talyzina, P.Ya. Galperin).

Research methods:

Scientific and methodological analysis of philosophical, psychological, pedagogical and methodological literature on the problem under study;

Analysis of the experience of teachers, analysis of one’s own experience of teaching physics in high school and physics methods at a university;

Analysis of modeling computer programs for molecular physics by domestic and foreign authors in order to determine the content of the program;

Modeling of physical phenomena in molecular physics;

Computer experiments based on selected modeling programs;

Questioning, conversation, observation, pedagogical experiment;

Methods of mathematical statistics.

Research base: schools No. 3, 11, 17 of Vologda, Vologda State Natural Mathematics Lyceum, Faculty of Physics and Mathematics of Vologda State Pedagogical University.

The research was carried out in three stages and had the following logic.

At the first stage (1993-1995), the problem, purpose, objectives and hypothesis of the study were determined. Philosophical, pedagogical and psychological literature was analyzed in order to identify the theoretical foundations for the development and use of computer models in the learning process.

At the second stage (1995 - 1997), experimental work was carried out within the framework of the problem being studied, and methodological developments were proposed for the use of computer modeling programs in physics lessons.

At the third stage (1997 - 2000), an analysis and generalization of experimental work was carried out.

The reliability and validity of the results obtained is guaranteed by: theoretical and methodological approaches to the study of the problem of computer modeling in teaching; a combination of qualitative and quantitative analysis of results, including the use of mathematical statistics methods; methods adequate to the purpose and subject of the study; scientifically based requirements for the development of a computer modeling program.

The latter requires some explanation. We have developed a program for modeling the dynamics of systems of many particles, the calculation of the movement of which is based on the Verlet algorithm used by H. Gould and J. Tobochnik. This algorithm is simple and gives accurate results even over short periods of time, and this is very important when studying statistical patterns. The original interface of the program allows you not only to see the dynamics of the process and change the system parameters, recording the results, but also makes it possible to change the time of the experiment, stop the experiment, save this frame and begin subsequent work on the model from there.

The system under study consists of particles whose speeds are set randomly and which interact with each other according to the laws of Newtonian mechanics, and the interaction forces between molecules are displayed by the Lennard-Johnson curve, that is, the program contains a model of a real gas. But by changing the initial parameters, it is possible to bring the model to an ideal gas.

The computer modeling program we presented allows us to obtain numerical results in relative units, confirming the following physical laws and processes:

a) the dependence of the interaction force and potential energy of particles (molecules) on the distance between them;

b) Maxwell's velocity distribution;

c) the basic equation of molecular kinetic theory;

d) Boyle-Mariotte and Charles laws;

e) Joule and Joule-Thomson experiments.

The above experiments can confirm the validity of the method of statistical physics, since the results of the numerical experiment correspond to the results obtained on the basis of the laws of statistics.

A pedagogical experiment confirmed the effectiveness of the methodology for conducting lessons using computer modeling programs.

Scientific novelty and theoretical significance of the study:

1. A comprehensive description of computer modeling used in the learning process (philosophical, cybernetic, pedagogical) has been carried out.

2. Psychological and pedagogical requirements for computer educational models are substantiated.

3. The method of computer simulation of the dynamics of many particles was used, which made it possible, for the first time in a school course of molecular physics, to create a computer model of an ideal gas, which makes it possible to demonstrate the relationship between the microparameters of the system (velocity, momentum, kinetic, potential and total energy of moving particles) with macroparameters (pressure, volume, temperature).

4. Based on computer modeling programs in physics methods, the following numerical experiments were carried out: the basic equation of molecular kinetic theory was obtained; the relationship between temperature and the kinetic energy of translational motion of particles (molecules) is shown; Joule and Joule-Thomson experiments for ideal and real gases were simulated.

The practical significance of the study lies in the fact that the selected content and developed computer modeling programs can be used in secondary schools to conduct numerical experiments on a number of issues in molecular physics. A methodology for conducting lessons in molecular physics using modeling computer programs has been developed and experimentally tested. The materials and results of the study can also be used in the process of teaching students at pedagogical universities and improving the qualifications of physics and computer science teachers.

Approbation of the main materials and results obtained during the study was carried out

At the international electronic scientific and technical conference (Vologda, 1999);

At the interuniversity scientific and practical conference “Social aspects of youth adaptation to changing living conditions” (Vologda, 2000);

At the second regional scientific and methodological conference “Modern technologies in higher and secondary vocational education” (Pskov, 2000);

At the sixth All-Russian scientific and practical conference “The problem of educational physical experiment” (Glazov, 2001);

When teaching physics in secondary schools in the city of Vologda, in classes on methods of teaching physics with students of the Vologda State Pedagogical University, at seminars for graduate students of the Vologda State Pedagogical University and teachers of the department of general physics and astronomy.

The following are submitted for defense:

1. Theoretical approaches to the use of computer modeling in the learning process and its methodological support.

3. Methodology for organizing and conducting physics lessons in the 10th grade of a secondary school when studying the topic “Molecular Physics” based on a computer modeling program.

Structure of the dissertation.

The structure of the dissertation is determined by the logic and sequence of solving the assigned problems. The dissertation consists of an introduction, four chapters, a conclusion, and a bibliography.

Models and simulation in modern science

Currently, models and simulation, as one of the methods of understanding the world around us, are widely used in science, technology and teaching.

The term “model” comes from the Latin word modulus, which means measure, pattern, norm. A person’s holistic view of the world in most cases is reflected in his consciousness in the form of a certain physical model.

In modern philosophy the following definitions of the concepts of model and simulation are given.

“A model (French modele) in the logic and methodology of science is an analogue (scheme, structure, sign system) of a certain fragment of natural or social reality, a product of human culture, conceptual and theoretical education, etc. - the original model. This analog serves to store and expand knowledge (information) about the original, its properties and structures, to transform or manage it. From an epistemological point of view, a model is a “representative”, “substitute” of the original in knowledge and practice. The results of processing and studying the model under certain conditions, clarified in logic and methodology, and specific to various areas and types of models, are transferred to the original. “Modeling is a method of studying objects of knowledge on their models; construction and study of models, real-life objects and phenomena (organic and inorganic systems, engineering devices, various processes - physical, chemical, biological, social) and constructed objects to determine or improve their characteristics, rationalize the methods of their construction, control them, etc. P." . Depending on the type of models, subject and sign modeling are distinguished. In subject modeling, research is carried out on a model that reproduces certain geometric, physical or functional characteristics of the original. For example, in analog modeling, mechanical, acoustic, hydrodynamic and other phenomena are studied using energy models, since the functioning of the model and the original is described by the same differential equations.

“In symbolic modeling, models are diagrams, drawings, formulas proposed in some alphabet (natural or artificial language), etc.” . Modeling is one of the important methods of cognition, therefore it belongs to the epistemological category. The results obtained from studying models can be transferred to the original if the model reflects the properties of the original.

This classification is based on the method of reproducing the properties of the original in the model. All models are divided into two classes: material and ideal. Material models include models that exist objectively and are created by man to reproduce the structure and essence of the process or phenomenon being studied.

For spatially similar models, a prerequisite is geometric similarity to their original, because they reflect the spatial properties and relationships of an object. This group includes various layouts, models of technical devices, crystal lattices, etc.

In physically similar models, the similarity of its physical nature with the original and the identity of the laws of motion are necessary. Such models differ from the nature they depict only by changing the spatial or time scale. This group includes operating models of various technical devices, for example, electric motors and generators, ships, airplanes, etc.

Mathematically similar models of the functioning of research objects must be described by the same mathematical equations and, as a rule, do not have physical and geometric similarity with the original. Mathematical models include analog, structural, digital, and cybernetic models.

Psychological and pedagogical aspects of computer training

In recent years, domestic and foreign psychologists have paid attention to the role of students' individual characteristics in the learning process. The search for ways to preserve and further develop the child’s individuality, his potential, and abilities led to the development of concepts for the individualization of education. Promoting the implementation of educational programs by each student by means of individualization, preventing student failure; the formation of general educational skills based on the zone of proximal development of each student; improvement of educational motivation and development of cognitive interests; the formation of personal qualities: independence, hard work, creativity - the essence of individualization of learning. The main advantage is that individualization allows you to completely adapt the content, methods and pace of a child’s educational activity to his characteristics, monitor his actions at every stage of solving a problem, make timely adjustments to the activities of the student and teacher, adapt them to the constantly changing but controlled situations on the part of the student and the teacher. All this allows the student to work economically, control the expenditure of his energy, and achieve better results.

The technology of individualization of learning covers all parts of the educational process - goals, content, methods and means. The characteristics of individualized learning are humanistic in their philosophical basis; development factors: bio-, socio- and psychogenic; the management principle is the “tutor” system, the approach to the child is humane and personal, organizational forms are academic, individual and group; The predominant method is programmed, self-development, creative. One of the options for individualizing learning is developing ideas for adaptive learning. It takes into account both age and individual characteristics of students. Adaptations can be based on information gathered from each student's learning experience or pre-programmed. An adaptive system, programmed in advance, usually implements training according to a branched program, where, depending on the nature of the error made, it is indicated what auxiliary influences are issued. Adaptive learning systems, as a rule, take into account: a) the correctness of the answer, b) the reasons that caused difficulties in completing educational tasks.

The development of technology and the development of various types of technical devices make it possible to combine the capabilities of individualized learning technology with the use of modern computer technology.

Computer-based learning, based on flexible and rapid adaptation to the individual characteristics of each student, is able to prevent the occurrence of psychological discomfort, decreased self-esteem, and decreased educational motivation, since it is able to take into account the individuality of the student as much as possible.

L.V. Shenshev describes three options for adaptive learning. The first option is the concept of maximum adaptability of the English cyberneticist G. Pask. The second is the theory of partial adaptability of the American psychologist N. Crowder. The third is B. Skinner's concept of minimal adaptability. The authors of adaptive learning theories are similar in assessing the reasons for the low effectiveness of traditional learning and in choosing to eliminate these reasons. The concepts of adaptive learning impose certain requirements on the educational process:

1. Prompt adaptation to the individual characteristics of students, taking into account the pace of learning, diagnosing the causes of difficulties, timely adjustment of educational material.

2. Continuous and targeted management of the student’s affective and motivational sphere, stabilization of his condition. 3. Maintaining continuous dialogue, stimulating student activity.

4. Automation of training.

Fulfillment of the listed requirements is easier to attribute to computer training, since the teacher is not able to simultaneously adapt to different students, while the machine is impartial, patient and tireless.

The above-mentioned concepts of adaptive learning quickly came into mass practice, giving rise to a fashionable craze for educational devices and computer programs. Amateurish and primitive in their pedagogical capabilities, they ignored the basic idea of taking into account individual characteristics and stabilizing the positive emotional mood of students. In connection with this state of affairs, the effectiveness of computer training is called into question. Modern arguments in favor of the use of computers repeat the conclusions of the developers of adaptive learning. This includes the importance of taking into account the dynamics of learning, and the automation of learning, allowing the teacher not to be distracted by organizational tasks.

Analysis of the state of computer modeling in the “Molecular Physics” section

In the first and second chapters, we examined the issues of using computer modeling in teaching from the perspective of epistemology, pedagogy and psychology, and also determined their place and functions. The use of computer models in teaching physics makes it possible to show the importance of modeling as a method of understanding the world around us, promotes the formation of abstract thinking, the development of cognitive interest, and mastery of elements of information culture. At the same time, in order to more fully realize such advantages as the possibility of individual learning, guidance of educational activities, clarity, and imitation properties of computer models, it is necessary to identify that section of physics in which the use of computer modeling will give a real learning effect, and to determine methodological techniques for including it in the lesson .

The difficulty of studying the course “Molecular Physics and Thermodynamics” in a basic secondary school is that here students encounter a qualitatively new form of motion of matter - thermal motion, in which, in addition to the laws of mechanics, the laws of statistics also apply. In addition, natural experiments (Brownian motion, diffusion, interaction of molecules, evaporation, surface and capillary phenomena, wetting) only confirm the hypothesis of the molecular structure of matter, but do not allow us to observe the mechanism of the physical processes occurring. Mechanical models: Stern's experiment, Galton's board, installation for demonstrating gas laws make it possible to illustrate Maxwell's law of the distribution of molecules by speed and to obtain experimentally the relationships between pressure, volume and temperature necessary to derive gas laws. The effectiveness of a lesson can be increased by expanding and improving a demonstration or laboratory experiment using a computer (we mentioned the importance of computer models in the study of physics in). Such software tools for conducting a demonstration experiment in the school course of molecular physics and thermodynamics are available, although in small quantities. We have done a review of a number of works in, and here we will present an analysis of all the computer programs known to us used in the study of molecular physics and thermodynamics.

The use of modern electronic and electronic computer technology can significantly improve the design and conduct of the experiment. It describes the use of a computer to demonstrate the dependence of the speed of molecules of nitrogen, hydrogen, argon and air on temperature, the calculation of changes in the internal energy of a body during melting and crystallization, during evaporation and for the gaseous state, as well as the use of a computer when processing the results of laboratory work.

The same book describes a lesson on determining the efficiency of an ideal heat engine based on the Carnot cycle. The model of the Carnot cycle was a computer, which programmatically implements adiabats and isotherms on the monitor screen, graphically representing the Carnot cycle.

The experimental technique using electronic and computer technology was described by V.V. Laptev. He used the versatility of the electrical signal, which not only contains the necessary information, but can also be processed by electronic computing technology. Therefore, it is necessary to convert all non-electrical quantities involved in the experiment into electrical ones using primary converters - sensors, at the output of which an electrical analog signal appears, usually in the form of electrical voltage. Laptev V.V. and collaborators developed and manufactured several sensors for measuring illumination, temperature and time. Sensor signals can be recorded using pointer or digital measuring instruments. In order to use digital electronic computers when processing experimental results, it is necessary to convert the analog signal into a digital one using an analog-to-digital converter, using the appropriate microcircuits for this. Thus, the experimental design looks like this: measured quantities - sensors - analog-to-digital converter - MK-64 microcalculator or Yamaha computer. Based on this principle, a universal electromechanical demonstration installation was designed for studying the physics of gas laws in a school course. The values of pressure, volume and temperature measured in the experiment are recorded in turn on a demonstration digital indicator and fed to the computer data bus, which displays graphs of all possible relationships between pressure, volume and temperature on the display screen. After plotting the graphs, the numerical values of these quantities are entered into the computer's RAM and can be displayed on the display screen in the form of a table of experimental data and used for quantitative calculations. Thus, students have the opportunity to observe the quantitative and qualitative characteristics of gas processes simultaneously.

Forming and increasing motivation for educational activities is the main condition for the training of future designers. Important components in the process of training student designers will be three-dimensional modeling methods, which can activate motivated activity. Knowledge of three-dimensional modeling methods is becoming, today, a necessary component in a designer’s qualifications, since not a single issue related to the design of design objects can be solved without knowledge of three-dimensional modeling methods.

Three-dimensional modeling is one of the most important areas of human activity, as it is often used in design. For example, when designing a new design for household products, as well as in the design of small architectural forms and other objects. Without the use of three-dimensional modeling methods, it is practically impossible to solve a single constructive issue related to the design, modification or modernization of a technological object.

In the future activities of the future designer, three-dimensional modeling methods can be used: in the basic principles of style and shape formation of interior products, furniture and decorative items; in architectural elements and building structures; in small plastic items; in the construction of ornamental compositions; in decorative and applied arts when performing visualization of carvings, paintings, inlays, mosaics, forging, etc.

The goal of teaching three-dimensional modeling is to study three-dimensional objects, which will allow the development of spatial and abstract thinking. Studying the ways and methods of displaying these models will contribute to the development of design skills and graphic image culture. Model building tasks will influence the expression of initiative and ingenuity. Tasks involving images of an original object will have a positive impact on the development of creative abilities.

At the same time, the designer’s professional environment places new demands on his activities, and the state determines the image of the graduate, formulating its requests for his education in the form of competencies. This dynamic forces us to look for new educational resources based on computer technology.

The practice of computerizing the learning process has clearly shown that with the help of computer technologies it is possible to significantly increase the effectiveness of teaching in all disciplines that are provided for in the curriculum of the “Design” training direction. The use of a computer allows you to obtain the compactness of any artistic and graphic information, in a visual and easily perceptible form, to evaluate the various aspects of the displayed objects and phenomena, including conducting their detailed and qualitative analysis.

The introduction of computer technology will improve the process of teaching 3D modeling. The effectiveness of the professional training of students depends on how thoughtfully and competently, from a pedagogical point of view, this training is organized. The use of computer technology in teaching three-dimensional modeling allows us to consider the computer as a teaching tool.

Three-dimensional computer modeling is, first of all, visualization of projects. This is the work with materials, cameras and lighting necessary to achieve a realistic three-dimensional project. By studying three-dimensional computer modeling, design students gain both general knowledge, skills and abilities, as well as applied ones, namely, the ability to use three-dimensional modeling to convey design ideas.

In three-dimensional modeling, computer technologies are conveniently used to demonstrate various constructions and modeling operations in space. In this case, the teacher will have the opportunity to display on the display screen those models, objects and graphic images that he needs to conduct classes.

The practical use of computer 3D modeling in the educational process of designers dictates the need to create an updated model of the educational environment that has a positive effect on the development of their artistic and creative activity, which is the main component of the professional competencies of the future designer.

All illustrative material of the three-dimensional modeling course can be presented, during the learning process, on the display screen. Moreover, this illustration must be created dynamically, using all the visual capabilities of the computer. Unlike other traditional technical means, computer technology will allow the teacher to manage the demonstration process. For example, when constructing a three-dimensional object, all actions will be sequentially described on the computer screen and such a “live picture” will compare favorably with a still illustration, since the teacher will be able to control this demonstration process. Thus, it is possible to show that a similar process of sequential constructions can be carried out for any object, accompanying all educational material with clear practical examples.

Three-dimensional computer modeling is one of the most complex areas in computer technology today and can be widely used in the process of developing design projects. It requires a special level of development of artistic and creative activity and spatial thinking, since all objects and characters are modeled and placed in virtual space. The design process is accompanied by an active transition from one projection window to another, from one observation point to another. To describe the three-dimensional space of the scene and the objects located inside it, the coordinate method is used. The use of this technology as a means of training future designers allows not only to increase the degree of visibility, but also to establish an individual pace for students to master educational material. Thanks to working with three-dimensional graphics, the teacher has the opportunity, in a short period of time and with minimal effort, to show a block of information in the form of three-dimensional visual aids on a certain topic, which entails better digestibility of the material being studied and saves a significant part of the teaching time that could be spent on performing the practical part of the studied material.

The capabilities of new technical means increase creative potential and creative requests, contribute to the development of artistic and creative activity, and expand the sense of the possible. Only creative perception and human needs generate and support technological capabilities. This means that a system of practical tasks in 3D computer modeling should encourage students not only to master a rich toolkit, but also to generate artistic tasks that require creative exploration of this toolkit.

1. Modeling of objects.

2. Modeling of the environment.

3. Architectural modeling.

4. Character modeling.

The system of tasks in the experimental group was divided into three types depending on the level of complexity: basic, advanced, high.

The first type of tasks is basic. This type of assignment focuses on learning the basic tools and operations of computer programs. Tasks of the first type are provided for all four blocks, but differ in the level of complexity and methods of completion. They lead students to solving more complex problems, since all the actions that a student performs when performing this type of task contribute to the development of abilities such as figurative memory, imagination, etc.

Tasks with an increased level of complexity, belonging to the second type, involve independent selection of tools and an algorithm for performing modeling of a three-dimensional object or scene. When completing tasks of this type, the student develops the ability to independently apply the acquired knowledge in practice, at the same time, these tasks stimulate the development of intuition and flexibility of thinking, and increase independence.

The third type of tasks are tasks with a high level of complexity. In the process of completing them, it was necessary to consider several options for completing the task and provide a fairly wide visual range. Tasks of the third type assumed the development of such abilities as originality, flexibility of thinking, spatial imagination, etc. The tasks assumed variability and independence in the search for modeling methods.

The introduction of computer technologies into the learning process today is one of the most important reserves for increasing the efficiency of the educational process and self-education of students. Compared to traditional educational and methodological complexes, computer-based educational complexes have a number of advantages, such as: multimedia and hypertext organization of training sessions; redundancy and variability of the content of theoretical material; the use of multimedia objects that allow the use of different types of information perception; high degree of interactivity. In the learning process, where computer technologies are the means, it is possible to increase the professional and cognitive motivation of students through the use of multimedia technologies, such as: animation fragments, sound and music, various computer graphics, hypertext; as well as multivariate practical tasks of varying levels of difficulty.

Models and simulation in modern science

Psychological and pedagogical aspects of computer training

Analysis of the state of computer modeling in the “Molecular Physics” section

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