Classification of Models in Pedagogy

Sapronov Vitalii Aleksandrovich Senior Lecturer, Department of Pedagogy of the Educational and Scientific Complex of Psychology of Official Activity, Moscow University of the Ministry of Internal Affairs of the Russian Federation named after V.Ya. KIKOT 52 Sovetskaya str. 10, office 46, Golitsyno, Moscow region, 143040, Russia poligraf-sharikov88@yandex.ru

Introduction to the problem

The rapid development of the scientific and technical industry, “informatization” and “digitalization” of society, expressed in the need to process large amounts of information, the use of opportunities in the process of obtaining, analyzing and storing automated technical means and specialized software, places increased demands on the technical literacy of specialists in the field of management, stimulate the implementation of measures to optimize the educational process in universities in order to increase its effectiveness.

Qualitative changes in education and upbringing are preceded by a preparatory stage, which includes an analysis of the situation, a search for solutions to the problem and the formation of an idea for upcoming changes, implemented in the form of a model. When building a model of the process under study, researchers may have questions: “what should the model be and what properties should it have?”, “what information should I carry and in what form should I display?”, “how to characterize the proposed model without revealing its content and features?”, “is there a need for a model at all when studying the pedagogical process, or is it possible to do without it?”. We will try to understand these questions and answer them.

A brief overview of the research

F.I. Peregudov and F.P. Tarasenko convince us of the need for a preliminary study of the properties of the process (object, system) precisely on the model: “The most important organizing element of professional activity is the goal–the image of the desired future, i.e. the model of the state, the realization of which the activity is aimed at. Modeling is an obligatory, inevitable action in any expedient activity, permeates and organizes it, is not a part, but an aspect of this activity” ^{[8, p. 36]}; Yu.V. Kurnosov and P.Yu. explain their significance. Konotopov: “Models are used as systems that replace specified fragments of reality – computational and logical operations are performed on them, expressing the relationships and dependencies identified at the previous stages, the values of the selection criteria are determined, providing the possibility of comparing alternative strategies” ^{[5, p. 140]}.

Thinking about the requirements for the model being developed led to the understanding that the model should be:

- adequate to the goals and conditions of operation;

- more effective than the current model of a fragment of reality;

adaptively mobile, flexible, with effective feedbacks.

It will be easier to classify models if you narrow down the search area and consider only those that are appropriate to use in pedagogy when evaluating the effectiveness of the educational process, reflected in:

- the level of formation of personal qualities of students, their knowledge, skills, skills (competencies);

- the use of the latest technologies and teaching methods, the possibilities of modern learning tools, telecommunications and communications;

- continuous professional improvement of teaching staff;

- evaluation of the effectiveness of auxiliary systems for supporting the pedagogical process (monitoring and control over the activities of teachers, quality management of education, etc.).

In the process of searching for a “true” classification of models, it is important to avoid repeated “discoveries”, erroneous interpretations and definitions, and substitution of established concepts with “copyrights”. The work uses subjectively neutral, without explicit specifics of the activity, but the most accurate and exhaustive interpretations. The analysis of scientific papers devoted to models and modeling in pedagogy contributes to the formation of the material.

“A model is some kind of intermediate auxiliary system (natural or artificial, material or abstract) with the following basic properties:

- is in objective accordance with the cognizable (studied) object;

- replaces the given object in a certain respect;

- at the same time provides information about the object obtained on the basis of the study of this model and the corresponding rules of the model –object transition (prototype)” ^{[5, P. 144]}.

“A model is a set of logical, mathematical or other objects, connections and relationships that display with the necessary or maximum achievable degree of similarity a certain fragment of reality to be studied, as well as a description of all the essential properties of the object being modeled” ^{[7, p. 360]}.

“A model is a representation: targeted; abstract or real, static or dynamic; coherent; finite, simplified, approximate; having, along with the unconditionally true, conditionally true and false content; manifested and developing in the process of its creation and practical use" ^{[8, p. 62]}.

“The model is a system representation of the original" ^{[8, p. 62]}.

The formulations proposed by the authors together give a clear idea of the object of the reasoning, are exhaustive in content and eliminate the need to clarify them or offer their own version.

To understand the essence of the classification of models, the formation and justification of one's point of view, let us turn to the scientific works of research teachers devoted to this topic.

A.M. Novikov and D.A. Novikov propose to consider a typology of models based on the following principles:

- compliance with the properties of the object under study (physical, functional, dynamic, topological and other models);

- implementation features (theoretical, full-scale, semi-natural, simulation models) (Figure 1).

In the process of developing a model of a fragment of reality, it is necessary to have a clear understanding of its purpose – the formation of model characteristics is carried out in accordance with the goals of modeling with the expression of specificity in the form of a detailed implementation of the necessary functions. The structural structure, content and operational component of the model, its visualization and degree of formalization, together with individual properties reflecting the peculiarities of the model's application, must comply with certain norms or rules of model construction, be adapted for comfortable and effective work with it by a human specialist or a specialized tandem operator and an automated system.

1. Model functions:

- a descriptive function that allows, by abstracting from external influences, to describe and explain the observed phenomena and processes with acceptable simplifications, to answer the question “why is this happening?”;

- a predictive function implemented to predict the future properties and conditions of the effective functioning of simulated objects, processes, systems, answers the question “what happens if ...?”;

- a normative (regulatory) function that sets the final result of modeling and the permissible limits of correction of the studied fragment of reality or reality itself in order to achieve the desired result. If the function is implemented correctly, we can get an answer to the question “how should it be?” (Figure 2).

2. Requirements for model properties:

- inertia. Characterizes the necessary and sufficient degree of consistency of the created model with the environment in which it is to function. The model should have a mechanism of interrelationships with this environment (operating conditions), which allows to assess the nature and dynamics of impacts on the studied fragment of reality, check the adequacy of the behavior of its model under specified conditions and, if necessary, make changes either to the model or to the specified conditions;

- simplicity. A model in pedagogy is usually developed for specific goals and objectives, to describe the functioning of an object or process in certain conditions. It is extremely difficult, resource-intensive and generally impractical to take into account all the variability of real situations and try to implement a universal functional suitable for “all occasions” in the model of the studied pedagogical process (unless we are talking about modeling a system with artificial intelligence or a virtual learning environment). The degree of simplicity of the model is determined by the human factor: the simplicity of the customer's perception of the descriptive and operational components of the model, its functional flexibility, an unambiguous and understandable reaction to external influences, as well as the convenience of obtaining and processing the results of research on a fragment of reality is important;

- adequacy. If the model is sufficiently complete, accurate and true, then it is considered adequate. It is not enough at all, but precisely to the extent that allows you to achieve your goal ^{[6, p. 198]}.

An alternative approach to the classification of Y.M. Plotinsky's models, based on their distinction by sequence and periodization of construction, is considered by most researchers (Figure 3). The author suggested that the life cycle of the model and, accordingly, the first stage of modeling begins during the observation of an object, when a person forms a mental image in his head – a cognitive model of this object. In the process of forming a model, the researcher sets himself quite certain questions that are most relevant to him at that moment, to which he will seek answers, and the knowledge acquired along the way will remain unnoticed and will not be perceived by him, therefore, at the stage of mental formation of the model, everything unnecessary is deliberately cut off from an infinitely complex reality in order to obtain more a compact and concise description of the object ^{[9, p. 88]}.

 The next stage of modeling is the visualization of the formed mental image. To collect and analyze information about the functioning of an object, identify relationships with the external environment and other objects, a cognitive model from a mental image in the form of text, special signs, drawings, diagrams, etc. is transferred to an information carrier as a meaningful model.

A meaningful model, in the development of which theoretical concepts, constructs or points of view of a given subject area of knowledge are used, Yu.M. Plotinsky proposes to call a conceptual model. Conceptual models are embodied either in a purely verbal form or in a mixed verbal-visual representation and, depending on functional features, are divided into logical-semantic, structural-functional and causal. The elements of the logical-semantic model in this case are all statements and facts included in the verbal description of the object (models are visualized as a formal description of a system of concepts characteristic of the field of knowledge); structural and functional models consider the object as a system comprising functional components, elements and subsystems interconnected by structural relationships describing interdependence and the subordination of objects, the logical and temporal sequence of the processes of their interaction (visualized in the form of diagrams, algorithms, diagrams, etc.); causal models are used to explain and predict the behavior of an object, focused on describing the dynamics of the processes under study, while interacting processes can be spaced in time relative to each other (presented mainly in verbally).

The third stage of modeling is understood as the creation of a formal model that makes it possible to comprehend the essence of the phenomena and processes under study, to identify and confirm the alleged relationships and patterns. Using formal analysis tools will allow you to obtain the most accurate data about the model, obtain new, non-obvious results, and refine previously formed meaningful and cognitive models. The formalization of the model is carried out using a mathematical descriptive apparatus (mathematical models) or using specialized software (computer models).

A.I. Ponomareva and A.V. Suvorova systematized the ideas about the distinctive properties of various models of substitution of fragments of reality and proposed a simplified scheme of the typology of models (Figure 4).

The authors note that the differences between the types of models have a certain degree of conditionality: each specific model characterizing a real object or the directions of its change can be complex and combine various formats for representing those relationships and trends that the modeling subject considers necessary to display with its help. It is often impossible to describe a complex system using models of only one type, moreover, there may be a need to form a whole set of models (including those belonging to various groups identified within the framework of the proposed typology), each of which describes only one of the elements of the system ^{[11, p. 233]}.

F.I. Peregudov and F.P. Tarasenko focus our attention on the importance of models in the organization of any human activity and mention the lack of a single algorithm for working with models suitable for all cases, referring to the specifics of modeling:

- the model functions in a cultural environment, and the specific environment of each model may be so different that the experience of working with the model cannot be transferred to another without changes;

- the requirements for the model are contradictory: the completeness of the model contradicts its simplicity, the accuracy of the model contradicts its dimensionality, efficiency contradicts the cost of implementation. Much of the model depends on which compromise is chosen between these conflicting criteria.;

- from the very beginning, it is impossible to foresee all the details of what will happen in the future with any model. Modeling is designed to eliminate uncertainty, but there is uncertainty about what exactly needs to be eliminated. The initial goals may later turn out to be incomplete ^{[8, p. 56]}.

The authors do not provide a single typology or classification of models, but distinguish them by features:

- according to the orientation of the main information flows circulating between the subject and the world around him – to cognitive and pragmatic;

- according to the method of embodiment – into abstract (ideal) and material (material);

- by displaying changes in the state of a fragment of reality – into static and dynamic;

- based on the similarity of the model with the original – on the model of direct, indirect and conditional similarity (Figure 5).

 The essence of research in pedagogy, for the most part, consists in the search and analysis of contradictions between the desired and the actual, the nomination and verification of hypotheses about the proposed forms and methods of resolving contradictions in order to increase the efficiency of the functioning of the object, process, system.

Yu.V. Kurnosov, P.Yu. Konotopov classify models according to the level of formalization and step–by–step advancement in the hierarchy of knowledge about the studied fragment of reality, and attribute the hypothesis - a harbinger of the path to obtaining new knowledge - to the initial level of the hierarchy, which corresponds to verbal (conceptual) models (Figure 6). Based on this, it can be assumed that in pedagogy, the main type of models being developed is verbal, which is explained by quite understandable reasons:

- the formalism of the verbal model is easily perceived by a wide class of consumers;

- the synthesis of a verbal model can also be carried out by a specialist who does not have special skills in the field of building formal models;

- verbal models have the highest expressive ability and are often used as a tool for integrating formal models and the results of their application.

 At the same time, a verbal model is not necessarily an exclusively text document, it can contain quantitative characteristics, structuring elements (tables, diagrams and graphs), etc. ^{[5, pp. 152-154]}.

Additionally, the authors recommend distinguishing models by specific characteristics:

1. The similarity of the model to fragments of the real world (physical, functional, dynamic and topological).

2. According to the degree of formalization (the model of a fragment of reality can be considered as a set of models placed one into another, while the interpretation model, which serves as a kind of interface between a fragment of reality and the consumer, is an outer shell, and the essential model of the object under study is enclosed inside). In this case, the interpretation model is significant as a tool for formalizing knowledge about an object in order to transform it into a form suitable for human or software processing, and the degree of knowledge formalization will depend on the purpose of the model.

3. According to the degree of detail. The detail of the model is determined on the one hand by the specifics of the task, and on the other by the specifics of the studied fragment of reality and depends on the degree of influence of related factors:

- model assignments and research objectives;

- selectivity of the study (the system or process as a whole or their individual aspects are being investigated);

- completeness of knowledge about the fragment of reality to be modeled;

- observability conditions (continuous, discrete);

- characteristics of the operating environment of the studied object (process) and parameters of disturbing influences;

- the time available for the synthesis of the model and the production of calculations;

- accuracy characteristics of the tools and methods used for data collection and processing, model construction and implementation ^{[5, pp. 144-152]}.

Concluding the analysis of the works devoted to models and modeling, we note that it is difficult to build a unified typology of models, and it is not possible to take into account all the classification features of models in a single scheme. One of the ways to solve the problem is to abandon the development of a unified typology of models in favor of a multi-level descriptive classification according to the main features (Table 1).

The results of the work and their discussion

The reason for writing the article was the need to characterize the developed model of the formation of personal qualities in students, using the generally accepted classification of models as a basis. The search for a single generally accepted classification was not successful, but it prompted an analysis and generalization of the information available on this issue, which is reflected in the proposed version of the classification. In this capacity, its version seems to be quite viable, made according to the principle of a universal decimal classifier and combining models into groups according to specific characteristics with an accompanying conceptual apparatus given to understand the characteristics of each type of model. This form of presentation allows you to introduce, change and supplement classification categories in accordance with the tasks to be solved and the specifics of the activity.

 Table 1 – Classification of mofels in pedagogy 

 As an example of the application of this classification, we will give a description of the model of the pedagogical process presented in the work “Formation of professionally important qualities in students of universities of the humanities by means of teaching technical disciplines” in two ways:

1. Verbal:

- in relation to the original in the process of activity – cognitive;

- according to the method of embodiment – ideal, descriptive;

- according to the form of presentation (degree of formalization) – verbal;

- by reflecting the state of the simulated object – static.

2. Digital code: 11.211.31.41.

Thus, the model receives the characteristic: “cognitive, ideal, descriptive, verbal, static model of the pedagogical process” or “model of the pedagogical process 11.211.31.41".

They are mentioned in the works, but due to the functional similarity with other models (or rather the obvious lack of originality), the presence of controversial points in the issues of application in pedagogy, the following types of models were not reflected in the proposed classifier:

An analog model is made by analogy (similarity) with something. Any model is an analogue and is defined as a system representation of the original, which is an analogue of the process (object) under consideration. The similarity or similarity with the original in the classifier is characterized by the term “similarity”, which has gradations of similarity: direct similarity, indirect similarity and conditional similarity.

Hierarchical, network, relational models are models of data representation, their relationships in the form of graphs or relationships supported by database management systems. The use of the description of objects (subjects) in pedagogy, the processes of education and upbringing in educational organizations is questionable.

A scale model is a feature of the implementation of a material model of an object. It is applicable in the educational process as a means of teaching.

Full–scale, semi-natural, quasi-natural models are varieties of material models, which are characterized by varying degrees of involvement of the studied real objects in modeling. As a rule, they are used in modeling physical processes and determining the capabilities of existing equipment using simulator devices (substitutes) and specialized software. It is difficult to characterize the model of the pedagogical process in this way as an open system due to the structural complexity, dynamism and abundance of direct, indirect and inverse object connections of the original.

An experimental model is a reduced or enlarged copy of the projected object, made in order to determine its properties. It refers to material models, and is applicable in the educational process when conducting research as a means of teaching.

The pedagogical model is a general characteristic of the model by field of application, does not disclose the features of the construction and properties of the model, does not have classification features.

Meaningful, structural and functional models are the conditional division of models according to the subject of modeling: the content of a pedagogical object, its structure and pedagogically significant functions, respectively. The model of the pedagogical process (object) a priori has a structure, content and assumes its functioning, therefore, the models in the proposed classification will have only a semantic emphasis in description and display.

An educational model is a model of a process or object used for educational purposes for students to work with it. It is advisable to attribute these models to learning tools, and not to modeling tools.

A factor model is a model containing two basic concepts of factor analysis: a factor (a hidden variable) and a load (a correlation between an initial variable and a factor). The factors must be independent and unambiguous, directly affect the optimization parameter, and be determined operationally. It is used to determine the relationships between variables and reduce the number of variables needed to describe the data.

The formal model is a common name for formalized models, it is the result of the evolution of knowledge about the system, the formalization (organization, ordering) of information about the object under study, provides predictable accuracy and high objectivity of research results. Formal models include mathematical (analytical, statistical), logical-linguistic (logical, semiotic) and other models.

A chromatic model is a full-color image model expressed in the natural language of concepts, with fixed relationships between concepts and displaying their meaningful and semantic connections. The model is a visualized representation of knowledge and finds application as a learning tool.

Conclusions

Modeling is an obligatory, inevitable process in any expedient activity, models are used as systems that replace specified fragments of reality – computational and logical operations are performed on them, expressing the relationships and dependencies identified at previous stages, the values of the selection criteria are determined, providing the possibility of comparing alternative strategies.

Modeling in pedagogy is focused on models-goals, models-ideals, which pedagogical practice strives for. Such an operationally defined (modeled) goal requires a system of control action and adjustment of intermediate results. To do this, they build models-slices of pedagogical reality, which make it possible to determine the dynamics of the results of the educational process and help develop corrective solutions. When studying the effectiveness of the pedagogical process as an open system, such monitoring and corrective measures are especially important, as is the correct formalization of the simulated reality.

A model characterizing a real object or the directions of its change can be complex and combine various formats for representing those relationships and trends that the modeling subject considers necessary to display with its help. A complex system is often impossible to describe using models of only one type, moreover, there may be a need to form a whole set of models, each of which describes only one of the elements of the system.

Due to the structural complexity, dynamism, abundance of interrelations of the studied objects (processes), the lack of a single integrated approach to the classification of models and the variety of their characteristics, a single universal classification of models satisfying the needs of all research teachers can be created only if regulatory regulation is applied (creating a single reasonably replenished database) in this field of knowledge.