One of the effective methods for studying control systems is modeling- development of models that allow making objective decisions in situations that are too complex for a simple causal assessment of alternatives. Despite the fact that many models of the studied socio-economic systems are so complex that it is often impossible to do without a computer, the concept of modeling is simple. According to Shannon, "a model is a representation of an object, system, or idea in some form other than the whole itself." An organization chart, for example, is a model that represents its structure. The main characteristic of the model can be considered a simplification of the real life situation to which it is applied. Since the form of the model is less complex and irrelevant data is eliminated, the model enhances the manager's ability to solve problems. There are a number of reasons to use a model instead of trying to interact directly with the real world:

the complexity of many organizational situations: since the real world of an organization is extremely complex and the actual number of variables related to a particular problem far exceeds the ability of any person, then comprehend it
possible by simplifying the real world through simulation;

Difficulties associated with conducting experiments in real life, in particular the need for significant costs, including material ones;

· Orientation of management to the future: it is impossible to observe a phenomenon that does not yet exist and, perhaps, will never take place; modeling is currently the only systematic way to see futures and determine the potential consequences of alternative solutions.

Types of models and the process of their construction

A model is a system located between the researcher and the subject of his research. There are the following types of models: physical (a model of a building, device, machine), mathematical (a system of formulas, identities and inequalities that describes a process, phenomenon), logical (a system of concepts that describes a phenomenon, process, object), models of socio-economic formations, models of structures, methods, etc.

Let's consider the main ones.

Physical model represents what is being explored with the help of an enlarged or reduced description of an object or system at one scale or another. According to Shannon, the distinguishing characteristic of a physical model (sometimes referred to as a portrait model) is that it looks like a "simulated integrity". An example of a physical model is a drawing of a factory drawn to a specific scale. Such a physical model simplifies visual perception and helps to establish whether a particular equipment can physically fit within its allocated space. Automotive and aviation companies always make physical thumbnails of new vehicles to test certain characteristics.

analog model represents an object under study - an analogue that behaves like a real object, but does not look like it. An example of an analog model is a diagram of the organizational structure of an enterprise. By building it, management is able to easily imagine the chains of passage of commands and the formal dependence between individuals and their activities. The analog model is a simpler and more effective way of showing the complex relationships of the structure of a large organization than compiling a list of relationships between all employees.

In the mathematical model (also called symbolic) uses symbols to describe the properties or characteristics of objects or events. An example of a mathematical model as a means of helping to solve exceptionally complex problems is A. Einstein's well-known formula Ε = me2. If A. Einstein could not build this mathematical model, in which symbols replace reality, it is unlikely that physicists would have even a remote idea about the relationship between matter and energy. Mathematical models are the type of models most often used in organizational decision making.

The main stages of the process of building models:

· formulation of the problem;

· model building;

· validation of the model;

· application of the model.

Formulation of the problem - the most important stage of building a model that can provide the correct solution to the management problem. The use of mathematics or a computer is of no use unless the problem itself is accurately diagnosed. A. Einstein noted that the correct formulation of the problem is even more important than its solution. Huge amounts of money are spent every year to find elegant and thoughtful answers to the wrong questions.

When building a model the developer must define the main goal of the model, the output standards, or the information that is expected to be obtained in order to help management solve a particular problem. In addition to setting the main goals, the developer must determine what information is required to build the model. Another important factor that needs to be taken into account when building a model is cost. A model that is worth more than the whole problem it solves will certainly not contribute to the achievement of the organization's goals.

One aspect validating the model- determination of the degree of conformity of the model to the real world. The developer must determine whether all the essential components of the real situation are built into the model. The more fully the model reflects the real world, the higher its potential as a means of assisting the manager in making an effective managerial decision. Another aspect of validating a model is to determine to what extent the information it provides helps the manager solve the problem. A good way to test a model is to try it out on situations from the past.

After checking for validity model is ready to use. According to Shannon, no model "can be considered successfully built until it is accepted, understood and put into practice." This is obvious, but often this stage of building models is one of the most difficult. According to the results of the study, only about 60% of management science models were used to the full or almost to the full extent - due to the fact that managers show fear or misunderstanding.

Modeling (in the broadest sense)- the main method of research in all fields of knowledge, in various fields of human activity.

Modeling in scientific research has been used since ancient times. Modeling elements have been used from the very beginning of the emergence of the exact sciences, and it is not by chance that some mathematical methods bear the names of such great scientists as Newton and Euler, and the word "algorithm" comes from the name of the medieval Arab scientist Al-Khwarizmi.

Gradually, modeling captured all new areas of scientific knowledge: technical design, construction and architecture, astronomy, physics, chemistry, biology and, finally, social sciences. However, the modeling methodology has long been developed by individual sciences independently of each other. There was no unified system of concepts, a unified terminology. Only gradually the role of modeling as a universal method of scientific knowledge began to be realized. The 20th century brought great success and recognition in almost all branches of modern science to the modeling method. In the late 1940s and early 1950s, the rapid development of modeling methods was due to the advent of computers (computers), which saved scientists and researchers from a huge amount of routine computational work. Computers of the first and second generations were used to solve computational problems, for engineering, scientific, financial calculations, for processing large amounts of data. Starting from the third generation, the field of application of computers also includes the solution of functional problems: it is database processing, management, and design. A modern computer is the main tool for solving any modeling problems.

Here are the basic concepts related to modeling ,,.

Object (from lat. objectum - subject) of research- everything that human activity is aimed at.

Model (object - original)(from Latin modus - "measure", "volume", "image") - an auxiliary object that reflects the patterns, essence, properties, features of the structure and functioning of the original object that are most essential for the study.

The original meaning of the word "model" was associated with the art of building, and in almost all European languages ​​it was used to denote an image or prototype, or a thing similar in some respect to another thing.

Currently, the term "model" is widely used in various fields of human activity and has many semantic meanings. This tutorial deals only with models that are tools for gaining knowledge.

Modeling- a research method based on replacing the original object under study with its model and working with it (instead of the object).

Modeling theory- the theory of replacing the original object with its model and studying the properties of the object on its model.

As a rule, some system acts as an object of modeling.

System- a set of interrelated elements united to achieve a common goal, isolated from the environment and interacting with it as an integral whole, and at the same time showing the main system properties. 15 main system properties are singled out, among which are: emergence (emergence); wholeness; structuredness; integrity; subordination to the goal; hierarchy; infinity; ergaticity.

System properties:

1. Emergence (emergence). This is a system property, according to which the result of the behavior of the system has an effect that is different from the “addition” (independent connection) in any way of the results of the behavior of all the “elements” included in the system. In other words, according to this feature of the system, its properties are not reduced to the totality of properties of the parts of which it consists, and are not derived from them.

2. The property of wholeness, purposefulness. The system is always considered as something whole, integral, relatively isolated from the environment.

3. structured property. The system has parts that are expediently connected to each other and to the environment.

4. Integrity property. In relation to other objects or with the environment, the system acts as something inseparable into interacting parts.

5. The property of subordination to the goal. The whole organization of the system is subordinated to some goal or several different goals.

6. property of hierarchy. A system can have several qualitatively different levels of structure that cannot be reduced to one another.

7. property of infinity. The impossibility of complete knowledge of the system and its comprehensive representation by any finite set of models, in particular, descriptions, qualitative and quantitative characteristics, etc.

8. Ergatic property. A system having parts may include a person as one of its parts.

Essentially, under modeling the process of building, studying and applying models of an object (system) is understood. It is closely related to such categories as abstraction, analogy, hypothesis, etc. The modeling process necessarily includes the construction of abstractions, and inferences by analogy, and the construction of scientific hypotheses.

Hypothesis- a certain prediction (assumption) based on experimental data, observations of a limited scope, conjectures. The hypotheses put forward can be tested in the course of a specially designed experiment. When formulating and testing the correctness of hypotheses, analogy is of great importance as a method of judgment.

by analogy called a judgment about any particular similarity of two objects. A modern scientific hypothesis is created, as a rule, by analogy with scientific provisions tested in practice. Thus, the analogy connects the hypothesis with the experiment.

The main feature of modeling is that it is a method of indirect cognition with the help of auxiliary substitute objects. The model acts as a kind of tool of knowledge, which the researcher puts between himself and the object, and with the help of which he studies the object of interest to him.

In the most general case, when building a model, the researcher discards those characteristics, parameters of the original object that are not essential for studying the object. The choice of characteristics of the original object, which are preserved and included in the model, is determined by the goals of modeling. Usually, such a process of abstracting from non-essential parameters of an object is called formalization. More precisely, formalization is the replacement of a real object or process by its formal description.

The main requirement for models is their adequacy to real processes or objects that the model replaces.

In almost all sciences about nature, animate and inanimate, about society, the construction and use of models is a powerful tool of knowledge. Real objects and processes are so multifaceted and complex that the best (and sometimes the only) way to study them is often the construction and study of a model that reflects only some facet of reality and therefore many times simpler than this reality. Centuries-old experience in the development of science has proved in practice the fruitfulness of this approach. More specifically, the need to use the modeling method is determined by the fact that many objects (systems) are either impossible to directly study, or this study requires too much time and money.

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Modeling method.

At present, the modeling method is widely used in pedagogical research.

Modeling is a method of creating and examining models. The study of the model allows you to get new knowledge, new holistic information about the object.

The essential features of the model are: visibility, abstraction, an element of scientific fantasy and imagination, the use of analogy as a logical method of construction, an element of hypotheticality. In other words,the model is a hypothesis expressed in visual form.

An important property of the model is the presence of creative imagination in it. Concepts, paradigms, various scenarios, business and cognitive games, etc. can become forms of modeling, say, the educational process.

The process of creating a model is quite laborious, the researcher, as it were, goes through several stages.

First - a thorough study of the experience associated with the phenomenon of interest to the researcher, the analysis and generalization of this experience and the creation of a hypothesis underlying the future model.

Second - drawing up a research program, organizing practical activities in accordance with the developed program, making adjustments to it prompted by practice, clarifying the initial research hypothesis taken as the basis of the model.

The third - Creation of the final version of the model. If at the second stage the researcher, as it were, offers various options for the constructed phenomenon, then at the third stage, on the basis of these options, he creates the final sample of the process (or project) that he is going to implement.

In pedagogy, modeling is successfully used to solve important didactic problems. For example, a teacher-researcher can develop models for: optimizing the structure of the educational process, activating the cognitive independence of students, a student-centered approach to students in the educational process.

The modeling method opens up the possibility of mathematization of pedagogical processes for pedagogical science. Mathematization of pedagogy has a huge epistemological potential. The use of mathematical modeling is most closely associated with an ever deeper knowledge of the essence of educational phenomena and processes, and a deepening of the theoretical foundations of research.

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In everyday life, in production, in research, engineering or any other activity, a person is constantly faced with solving problems. All tasks according to their purpose can be divided into two categories: computing tasks whose purpose is to determine a certain quantity, and functional tasks designed to create a certain apparatus that performs certain actions - functions.

For example, designing a new building requires solving the problem of calculating the strength of its foundation, supporting structures, calculating the financial costs of construction, determining the optimal number of employees, etc. To increase the productivity of builders, many functional machines have been created (functional tasks have been solved), such as an excavator, a bulldozer, a crane, etc.

Computers of the first and second generation were used mainly for solving computational problems: carrying out engineering, scientific, and financial calculations. Starting from the third generation, the field of application of computers also includes the solution of functional problems: this is database maintenance, management, and design. A modern computer can be used to solve almost any problem.

Human activity and, in particular, problem solving are inextricably linked with the construction, study and use of models of various objects, processes and phenomena. In his activity - in the practical sphere, artistic, scientific - a person always creates a certain cast, a substitute for the object, process or phenomenon with which he has to deal. It can be a painting, a drawing, a sculpture, a layout, a mathematical formula, a verbal description, etc.

object(from lat. objectum - subject) is called everything that opposes the subject in his practical and cognitive activity, everything that this activity is aimed at. Objects are understood as objects and phenomena, both accessible and inaccessible to human sensory perception, but having a visible effect on other objects (for example, gravity, infrasound or electromagnetic waves). Objective reality, which exists independently of us, is an object for a person in any of his activities and interacts with him. Therefore, an object should always be considered in interaction with other objects, taking into account their mutual influence.

Human activity usually goes in two directions: study properties of the object for the purpose of their use (or neutralization); creation new objects with useful properties. The first direction relates to scientific research and has a great role in their conduct. hypothesis, i.e. prediction of the properties of an object with insufficient knowledge of it. The second direction relates to engineering design. In this case, the concept plays an important role. analogy– a judgment about any similarity between a known and a projected object. The analogy may be complete or partial. This concept is relative and is determined by the level of abstraction and the purpose of constructing an analogy.

Model(from Latin modulus - sample) of any object, process or phenomenon is called a substitute (image, analogue, representative) used as an original. The model gives us a representation of a real object or phenomenon in some form different from the form of its real existence. For example, in a conversation we replace real objects with their names, words. And from the replacement name in this case the most basic thing is required - to designate the necessary object. Thus, from childhood we are faced with the concept of “model” (the very first model in our life is a nipple).

The model is a powerful tool of knowledge. The creation of models is resorted to when the object under study is either very large (model of the solar system) or very small (model of the atom), when the process proceeds very quickly (model of an internal combustion engine) or very slowly (geological models), the study of the object can lead to its destruction (training grenade) or the creation of a model is very expensive (architectural model of the city), etc.

Each object has a large number of different properties. In the process of building a model, the main, most significant, properties, those that interest the researcher. This is the main feature and the main purpose of the models. Thus, under model some object is understood that replaces the real object under study with the preservation of its most essential properties.

There is no such thing as just a model, “model” is a term that requires a qualifying word or phrase, for example: a model of an atom, a model of the Universe. In a sense, a picture of an artist or a theater performance can be considered a model (these are models that reflect one or another side of the human spiritual world).

The study of objects, processes or phenomena by constructing and studying their models to determine or refine the characteristics of the original is called modeling. Simulation can be defined as the representation of an object by a model in order to obtain information about this object by experimenting with its model. The theory of replacing original objects with a model object is called modeling theory. The whole variety of modeling methods considered by modeling theory can be divided into two groups: analytical and simulation modeling.

Analytical modeling consists in building a model based on describing the behavior of an object or system of objects in the form of analytical expressions - formulas. With such modeling, an object is described by a system of linear or non-linear algebraic or differential equations, the solution of which can give an idea of ​​the properties of the object. Analytical or approximate numerical methods are applied to the obtained analytical model, taking into account the type and complexity of the formulas. The implementation of numerical methods is usually assigned to computers with high computing power. However, the application of analytical modeling is limited by the complexity of obtaining and analyzing expressions for large systems.

Simulation modeling involves the construction of a model with characteristics that are adequate to the original, based on any of its physical or information principles. This means that external influences on the model and the object cause identical changes in the properties of the original and the model. With such modeling, there is no general analytical model of large dimensions, and the object is represented by a system consisting of elements that interact with each other and with the outside world. By setting external influences, it is possible to obtain the characteristics of the system and analyze them. Recently, simulation modeling has been increasingly associated with the modeling of objects on a computer, which allows you to interactively explore models of objects of various nature.

If the simulation results are confirmed and can serve as a basis for predicting the behavior of the objects under study, then the model is said to be adequate object. The degree of adequacy depends on the purpose and criteria of modeling.

The main goals of modeling:

7. Understand how a particular object works, what is its structure, basic properties, laws of development and interaction with the outside world (understanding).

8. Learn to manage an object (process) and determine the best methods of management for given goals and criteria (management).

9. Predict the direct and indirect consequences of the implementation of the specified methods and forms of impact on the object (forecasting).

Almost any modeling object can be represented by a set of elements and relationships between them, i.e. be a system interacting with the external environment. System(from the Greek. system - the whole) is a purposeful set of interconnected elements of any nature. External environment is a set of elements of any nature existing outside the system that influence the system or are under its influence. With a systematic approach to modeling, first of all, the purpose of modeling is clearly defined. Creating a model of a complete analogue of the original is a laborious and expensive task, so the model is created for a specific purpose.

Once again, we note that any model is not a copy of the object, but reflects only the most important, essential features and properties, neglecting the rest of the characteristics of the object, which are insignificant within the framework of the task. For example, a model of a person in biology can be a system striving for self-preservation; in chemistry, an object consisting of various substances; in mechanics, a point with mass. One and the same real object can be described by different models (in different aspects and for different purposes). And the same model can be considered as a model of completely different real objects (from a grain of sand to a planet).

No model can completely replace the object itself. But when solving specific problems, when we are interested in certain properties of the object under study, the model turns out to be useful, simple, and sometimes the only research tool.

MODELING AS A METHOD OF PEDAGOGICAL RESEARCH

E.N. Zemlyanskaya

Annotation. The article is devoted to the disclosure of the functions and content of the modeling method. The definition of the model is given, approaches to the multidimensional classification of scientific models are revealed. Particular attention is paid to the problem of the relationship between the model and the original and the construction of the research process based on models. The possibilities of the method are revealed, as well as the gnostic functions of the models. The features of scientific models and modeling in pedagogy are revealed.

Key words: model, original, modeling, research, gnostic functions of models, method, pedagogical theory.

summary. The article is dedicated to the disclosure of functions and content of modeling method. It also defines the model and reveals a multidimensional approach to the classification ofscientific models. Special attention is paid to the problem of the relation between the original model and the research process and the creation of research process on the basis of models. The article reveals the possibilities of the method, as well as Gnostic function models (reflective, concretizing, interpretive, explanatory, predictive). Ratures of scientific models and modeling in pedagogy come to light.

Keywords: model, original, modeling, research, gnostic function models, methods, pedagogical theory.

Increasing the role of pedagogical theory is a necessary condition and the most important requirement for the transfer of educational institutions to the development mode. Achieving a new quality of education at school is impossible without a teacher conducting research activities, the foundations of which are laid in higher education. Modeling is one of the methods of pedagogical research, which, unfortunately, is superficially familiar to teachers. The article is devoted to the disclosure of the functions and content of this research method; It is intended primarily for students, graduate students performing research in the field of pedagogy.

In the context of our problem, it is important to distinguish between modeling as a research method, on the one hand, and the use of models as a teaching method, on the other. The latter has its origins in the principle of visibility. Analogous models and methods of their construction and use in the educational process were given great importance by many didactic teachers: V.P. Vakhterev, N.P. Kashin, K.D. Ushinsky, and

A.P. Anoshkin (1998), S.I. Arkhangelsky (1980), S.P. Baranov, Yu.V. Vardanyan (1990), V.P. Mizintsev (1977), Yu.I. Kulyutkin (1981), D. Tollingerova (1994), A.I. Shcherbakov (1988) and others.

B.V. Davydov substantiated training models

whether, revealing the specifics of visualization due to theoretical training, and D.B. Elkonin considered the child's modeling of certain aspects of reality as a general principle of assimilation. These and other educators have developed principles for constructing and using training models in teaching, they have been classified, and psychological and pedagogical conditions and patterns have been identified.

Modeling as a method of cognition (research) is associated with the use of analogy - a conclusion about the similarity of objects in a certain respect based on their similarity in a number of other respects. The essence of this method lies in the fact that not the object itself is directly investigated, but its analogue, a substitute - a model, and then the results obtained during the study of the model are transferred to the object itself according to special rules.

Modeling as a method of scientific research is less familiar to teachers, although in almost every dissertation of recent years for the degree of doctor or candidate of pedagogical sciences, we can see the task of “develop a model of some process, phenomenon”. Let's turn to the research process and try to answer the following questions: What is the meaning of modeling in research? Its functions? What is fundamentally new can give the use of this method in comparison with others? Is the model just a convenient form of presenting the results of scientific research or is it an independent object of study? What is the structure of the M&S research process? Is the model built in the dissertation the ultimate goal and scientific result, or is it just a means of further scientific research?

The problem of modeling is one of the most important methodological problems brought to the forefront of the development of a number of natural sciences of the 20th century, especially physics, chemistry, and cybernetics. It was with the emergence of the latter that the question of the method of cognition with the help of models arose with particular acuteness, raising in turn questions about the epistemological nature of models, their functions, and the place of models among other means of cognition. Summarizing methodologically the new methods of modern science that came from the natural sciences, the model as a means of cognition and an important epistemological category has now taken a firm place in psychological and pedagogical science. Conceptual ideas about the model approach to the study of reality, a theoretical understanding of models and methods of modeling in pedagogy are given by many scientists: Yu.K. Babansky, V.P. Bespalko, A.A. Bratko, T.A. Ilina, L.B. Itelson, N.V. Kuzmina, A.N. Leontiev, Yu.O. Ovakimyan and others.

Model definition. Model - from the Latin "modus, modulus", which means "measure, image, way." Its original meaning was associated with the art of building and in almost all European languages ​​it was used to refer to a model or thing similar to another. Even now, in everyday life, a model is understood as copying certain external properties of an object, most often its spatial forms (“ship model”, “knowledge model”).

In modern science, there has been a departure from the initial understanding of the model as an image, sample, prototype, analogy. A deeper interpretation of the word "model" suggests that the focus is on modeling the hidden internal properties of the object,

Teacher ^

that is, the ability of the model to display, reproduce and thereby replace the object of study with an essential feature of the model is considered. Such models exist only in the description and, as a rule, do not need to be made in the form of certain physically tangible objects. Example. Speaking about the model of the atomic nucleus, a modern physicist does not assume that we are talking about a demonstration of a model made of wood, metal, plastic, which can be held in hands, measured, weighed, twisted, etc. Under the model, he understands the totality of scientific hypotheses about the structure of the nucleus, allowing not only to correctly describe and interpret what is already known about this object, but also to predict new facts that have not yet been discovered by science.

From the above example, it is clear that the modeling of any object, phenomenon, process in a similar sense is the fixation of one or another level of knowledge of this object, which makes it possible to describe its structure and functioning, as well as to describe its behavior with some degree of approximation. Therefore, it is often said that such models are information models, thereby emphasizing that we are talking about information about a given object that is at our disposal.

In the modern sense, a model is such a mentally represented or materially realized system that, displaying or reproducing the object of study, is able to replace it in a certain respect so that its study gives us information about this object. At the same time, not every image can be called a model, but only one that, on the one hand,

fixes precisely the general relation of a certain system, on the other hand, ensures its further study. The similarity between objects by random (insignificant) features cannot be considered a model. Therefore, one should distinguish between modeling and only the image of the external features of the objects under study.

Modeling in pedagogical science is sometimes understood as the process of creating a model, which seems to us not entirely correct, too narrow an interpretation. It is more correct to consider scientific modeling as a method of studying various objects on their models. Let's explain our idea.

Modeling as the creation of a model is only a part of the process of cognition or the process of research1. The created model must be fixed in some way. At the same time, it must be borne in mind (and we will demonstrate this in a further presentation) that the information model fixed in one way or another is unable to give a greater number of conclusions about the behavior of the modeled object than those conclusions that were put into it from the very beginning, that is, it is static . To move to dynamic modeling, a dynamic model, it is necessary to take a number of manipulations, intellectual actions with this model, to transform the information contained in it. This is what true modeling is, which is its own and is a method of scientific knowledge.

Classification of scientific models. One of the classifications, continuing the above thought, is based on differences in the way an object is displayed. Models can therefore

1 Cognition is a creative activity of the subject, focused on obtaining reliable knowledge about the world. Research is the process and result of scientific activity aimed at identifying general facts, connections and patterns of the process or its aspect under study.

be: material (material, real) and mental (ideal, imaginary). The first group of models is models, dummies (space-like), as well as physically and mathematically similar objects. Model real experiments are possible with them, they exist objectively. It is clear that pedagogical models mainly belong to the second group (see table). This group of models is represented by all kinds of mental formations, which are built according to certain rules and laws based on considerations dictated by the studied objects and observed facts. They acquire a material form and are expressed in the form of a drawing, diagram, drawing. All transformations with such a model, in contrast to the models of the first group - material ones, are carried out by the researcher in his mind. They are the basis and component of thought experimentation.

Like any complex concept, models provide for a multidimensional classification. So, there are stochastic and uniquely determined models; discrete and continuous; simple and complex; schematic and detailed. Based on the target orientation of the created

Classification of models according to

models and from the nature of the side of the object that is being modeled, they are divided into structural and functional. In the first case, the structure of the object is studied, in the second - its behavior (the functioning of the processes occurring in it, etc.). It is clear that the distinction between structural and functional modeling acquires a clear meaning in pedagogical science.

In general, it can be argued that a unified classification of types of models is impossible due to the ambiguity of the concept of “model” in various branches of science [for more details, see, for example: 3].

1) if it demonstrates behavior similar to the behavior of the original, performs similar functions;

2) if, based on the study of the behavior and structure of this model, it is possible to discover new features or properties of the original that are not explicitly contained in the original factual material.

The ratio of the model and the original. Modeling significantly expands the possibilities of any research, as it makes it possible to study

the way the object is displayed

No. Class of models Characteristics / examples

1 Material

1.1 Space-like Models

1.2 Physically similar Possessing mechanical, dynamic, kinetic and other physical similarities with the original

1.3 Math-like Analogue, digital, functional

2 Mental (ideal)

2.1 Figurative Hypothetical, analogues, idealizations, representations

2.2 Symbolic Schemes, graphs, maps, drawings, graphs, structural formulas

2.3 Mixed Other sign systems

Lecturer XXI 3 / 2013

the processes and phenomena of interest to us on models, followed by transferring the result of the study to the prototype. Thus, modeling consists in reproducing the characteristics of some object on another, specially created for study, which is called a model. Therefore, the question arises about the relationship between the model and the original. By "original" we mean objects, phenomena, processes of the real environment.

The meaning of modeling lies in the possibility of obtaining information about the original by transferring to it the knowledge gained in the study of the corresponding model. The decisive factor here is human thinking, which is capable of abstraction.

The modeling process requires the establishment of certain specific relationships between the original and the model, on the basis of which it is possible to study certain aspects of the object under study. It is clear that the model cannot contain all the properties of the studied original, because otherwise it becomes identical to it, and therefore is able to provide information about it exactly as much as the original. Consequently, modeling as a process of creating a model involves the selection of some properties of the object and the neglect, rejection of others. Thus, replacing the phenomenon under study with a model, one should indicate in respect of which properties the model should be isomorphic to the phenomenon under study, and indicate its essential features.

In addition, not only the ease of perception of those properties and relations that the isomorphic

original model, but also the ease of handling these properties. This circumstance makes it possible to organize the study of the model in the process of model or mental experimentation, and the data obtained in this case can serve as messages for conclusions about the original.

Sometimes researchers present the original with a system of specific models, which together reflect the structure, function, purpose, and application of the original in practice. The usefulness of this kind of representation lies in the comprehensive disclosure of the cause-and-effect relationships of the phenomenon under study. Collected from the standpoint of a systematic approach, such a set of models, ways of expressing and transforming them, in fact, is a holistic scientific theory of the object under study.

Model based research process. The scientific modeling method consists of the following main steps:

1) heuristic - formulating a system model based on accumulated facts, hypotheses, theories about the process under study;

2) cognitive - manipulation of the model and obtaining certain conclusions with its help, knowledge of essential features in the process of a thought or model experiment;

3) pragmatic - transferring the findings to a real system (original), in the setting of an experiment to verify the correctness of the conclusions;

4) explanatory - reformulation of the model in the light of the results of such verification.

These stages also represent a model experiment - a laboratory study of the object under study on its

2 Isomorphism is a one-to-one correspondence.

material models. It is clear that model experimentation has its own specifics in comparison with conventional experimentation: the role and specific weight of theoretical research tools is increasing.

Research process based

modeling is an iterative3 process. The four stages outlined above are cyclically repeated each time at a higher level of generalization. At the same time, after each iteration, the researcher gains new knowledge about the original.

The modeling process is shown in the diagram, where the solid arrow characterizes the direct impact on the object, the dashed arrow characterizes the relation of the model to the original.

Thus, the research scheme original - model - original begins with a primary idea of ​​the object, is corrected on the basis of the model, its validity is confirmed again by examples of reality, but at a higher level of abstraction. At the same time, the stage of ascent to the original after the formation and correction of the model is the most important aspect of the study, since it contributes to the knowledge of reality, its patterns and interdependencies, predicting the behavior of the object under study in the context of the consequences of decisions.

In the context of research activities, it is important to keep in mind two circumstances.

First of all. Modeling, displaying the properties of the original that are essential from the point of view of the purpose of the study and digressing from the rest, necessarily involves the use of abstraction and idealization. From the level of these

abstractions and idealizations depends on the whole process of transferring knowledge from the model to the original. In this case, it is appropriate to single out models of different levels: potential feasibility; real feasibility (even in the distant future); practical expediency (the transfer of knowledge from the model to the original is desirable for solving specific practical problems) [see, for example: 4].

Secondly. The model cannot be identical to the original - then why is it? If the subject of modeling is complex systems, the behavior of which depends on a significant number of interrelated factors of various nature, then such systems are displayed in various models. At the same time, some of the models may be close to each other, while others may be significantly different. Therefore, a situation where mutually complementary or contradictory models are created can take place. In the course of the development of science and the emergence of models of a deeper level, the contradictions that have arisen are eliminated. This circumstance is extremely important for pedagogical research.

The question of the truth and falsity of models. The question of the relationship between the model and the original naturally raises the question of whether the model corresponds or not to the original. In this case, we can talk about the truth or falsity of the model. Truth or falsity are inherent in models, since they are always determined by a certain level of scientific knowledge, and also due to the presence or absence of isomorphism of the model to the process under study. At the same time, in relation to some properties of the original, the model can

3 Iterative process - approaching the end point based on a sequence of small steps - iterations.

Teacher XX

Researcher

Scheme. Simulation-Based Research Process

be isomorphic, and then it is true, in relation to others it is not isomorphic, and then there is no question of truth.

The question of the relationship between absolute and relative truth in the model can be resolved as follows. No model can give an absolutely complete and absolutely accurate reflection of the original, since this follows from the very definition of the model as a simplified image that does not have isomorphism with the object at all levels of abstraction and in all respects. However, scientific models contain elements of absolute truth in the form of relative truth (Yu.A. Gastev). Indeed:

The nature of any model is historically transient due to the continuity and unlimitedness of the process of cognition;

The model always contains elements of conventionality, scientific fantasy and author's arbitrariness;

The model is partial, not comprehensive.

But that's what makes models a method of scientific inquiry.

Method capabilities. The fundamental feature of the modeling method that distinguishes it from others

1. Of particular importance is the modeling method in cases where the empirical picture of the phenomenon under study is incomplete, not detailed. Modeling allows you to synthesize the existing knowledge about the object, to identify unexplored aspects that are important for the study.

2. Psychological and pedagogical objects differ from objects of a different nature by their extraordinary complexity. Individual phenomena under study (for example, mental processes) do not appear to the researcher in an explicit form, but are of a hidden or indirect nature. Such processes are sometimes difficult to study without disturbing them. These processes are multifaceted, they depend on many random and subjective factors. The expediency of studying these processes on the basis of model experimentation is due to the fact that it makes it possible to isolate for study the internal, essential dependencies of the phenomenon, while abstracting from the "noise" - distracting, non-essential properties of the original.

3. Modeling is considered as the highest and special form of visibility. It helps to systematize knowledge about the phenomenon or process under study, to predict the ways of description and cognition, outlines the structure of connections between the components, opens up the possibility for a deeper insight into the essence of the phenomenon, for management

them, to identify ways to improve the characteristics of the phenomena and processes under study. The psychological function of the model, therefore, is that it serves as an external support for internal actions.

4. Modeling is a universal research method. It can be applied both at the theoretical level of research to build a theory or mastery, and at the empirical level by organizing an experiment. In addition, the uniqueness of the method lies in the fact that it allows you to transfer the identified theoretical provisions into practice and vice versa, include the noticed practical facts in the existing theory, thus ensuring a stable organic connection between theory and practice. Therefore, the modeling method cannot be confidently attributed to either theoretical or empirical research methods.

Principles of modeling as a method of scientific research.

1. Visibility - the obvious expressiveness of the model: constructive, iconic, symbolic, pictorial, functional.

2. Certainty - a clear allocation of essential aspects of the object of study and non-essential.

3. Objectivity - the independence of research findings from the personal beliefs of the researcher.

Gnostic functions of models. The scientist's idea of ​​the possible functions of models in the process of cognition contributes to goal-setting in his research.

1. Reflective. The essence of the model is not in copying the object, but in describing its behavior, while the model is secondary in relation to the original. A model is a consciously created

epistemological image of an object used for the purpose of its cognition. Therefore, the importance of modeling in the processes of simplification, idealization, in the abstraction of potential feasibility is great. It allows you to mentally imagine and analyze the so-called limiting cases that are not actually realized, to draw conclusions that can be verified experimentally.

2. Concretizations. A model is a way of concretizing the studied aspects of an object. This is achieved on the basis of detailing abstract constructs, as well as by building additional models. Thus, mental models help connect the abstract and the concrete dialectically.

3. Interpretation. This function of models is realized in two aspects: a model as an interpretation of a formal theory; model as an interpretation of observed phenomena. When using models as an interpretation of processes and phenomena, they make it possible to give at first a hypothetical, and after an experimental verification, an explanation of the observed facts. Thus, in the process of iterative modeling, a transition is made from an interpretive model to an explanatory model. Thus, the model, on the one hand, implements the theory, on the other hand, homomorphically reflects reality.

4. Explanatory. This function lies in the fact that a model causal explanation is built on the basis of the similarity of the phenomenon being explained with the phenomenon that has already received a reliable causal explanation. Noticing the external similarity in something of two phenomena, the researcher makes an assumption about similar cause-and-effect relationships. Model-based explanation is thus built on the following

century teacher

scheme: (1) describes the model, its causal laws; (2) describes the rules for translating information obtained on the model into information about the original; (3) the probabilistic nature of the model causal explanation is fixed, as if in contrast to the missing causal relationships in the original.

5. Prognostic. This important cognitive function of models is to serve as an impulse, a source of new theories. It often happens that a theory initially appears in the form of a model that gives an approximate, simplified explanation of the phenomenon. In the process of modeling, new ideas and concepts may arise, that is, the model acts as a working hypothesis for the subsequent study.

pedagogical models. Models related to pedagogical sciences represent a fragment of a certain natural and (or) social reality, a product of human culture. At the same time, functional models reflect pedagogical phenomena, for example, a model of a school as a management system, and pedagogical processes, for example, a model of the activity of a curator of a student group.

Structural models are more often represented by personality models as guidelines for educational purposes - a model of a teacher, a model of a student, etc. At the same time, a personality model is understood as a diagnostic description with all possible completeness of all aspects, properties and qualities of a person that are essential for life in the modern world. For example, the term “teacher model” should be understood in this sense. The teacher model is a mental image of the original ideal professional, including qualification characteristics.

teristics and professiogram. It is obvious that the teacher's model does not include all of his qualities, but only essential ones. This is a standard that is quite appropriate to use in characterizing a teacher, it is advisable to use it in a scientific study of the teaching profession, however, for specific practical activities, its use, obviously, has limitations.

LIST OF SOURCES AND LITERATURE

1. Shtoff V.A. Modeling and philosophy. - M.: Nauka, 1966.

2. Slastenin V.A., Frumkin M.L. Teaching students to solve pedagogical problems // Soviet Pedagogy. - 1984. - No. 7.

3. Anoshkin A.P. Fundamentals of Modeling in Education: Textbook. - Omsk: OmGPU Publishing House, 1998.

4. Gastev Yu.A. Model // Philosophical Encyclopedia. - T. 3. - M., 1964.

5. Babansky Yu.K. Problems of improving the effectiveness of pedagogical research. - M.: Pedagogy, 1982.

6. Biryukov B.V., Geller E.S. Cybernetics in the Humanities. - M., 1973.

7. Bratko A.A. Modeling of the psyche. -M., 1969.

8. Gastev Yu.A. On epistemological aspects of modeling // Logic and methodology of science. - M., 1967.

9. Davydov V.V. Types of generalizations (psychological and pedagogical problems of the construction of educational subjects). - M., 1972.

10. Zemlyanskaya E.N. Socialization of younger schoolchildren in the process of economic preparation. - M.: MPGU, 2006.

11. Kan-Kalik V.A., Nikandrov N.D. Pedagogical creativity. - M.: Higher school, 1990.

12. Kochergin A.N. The role of modeling in the process of cognition // Some patterns of scientific knowledge. - Nsb., 1964.

13. Kuzmina N.V. Methods of research of pedagogical activity. - L., 1970.

14. Mizintsev V.P. Application of models and modeling methods in didactics. -M.: Knowledge, 1977. ■