On methodological aspects and tasks of pedagogy and education development

For a long time, the functioning of the education system is largely determined by two main points – the setting of goals and the means of achieving them. Ya.A. Komensky substantiated the relevance of each of them in his essay "Exit from the school labyrinths, or the Didactic machine, in accordance with the mechanical method, designed so that in matters of teaching and learning not to linger in place, but to go forward." Before his intervention in the situation, it looked like this: “They teach in order to teach, and learn in order to learn, (...) there is never seen certainty that the goal of the work will be achieved or that it is precisely the set goal that has been solicited” [1, from. 175]. According to Komensky, this approach did not correspond to the needs of economic, state and church life, therefore, in order to meet these needs, the goals of education must be described with greater certainty, as well as to find “means precisely adapted to achieve these goals, and 3) firm rules to use these means in this way, so that it was impossible not to achieve the goal” [1, p. 189]. In formal terms, the “didactic machine” of Komensky was built to solve problems assigned mainly from the outside, but its equipment was favorable for both teachers and students.

Suffice it to mention his classroom-lesson system, one of the elements of which consisted in organizing education in groups of pupils close in age and level of training. This gave a significant and obvious economic effect, since it allowed the teacher to conduct classes with a group of students in almost the same way as with one of them. This circumstance is an implicit reason that the classroom-lesson system of teaching persists, despite being heavily criticized.

An even more significant role in the system of Komensky is played, in our opinion, by his teaching method, based on the constant application of analysis and synthesis. “No matter what nook and cranny you find yourself in,” writes Komensky, – analysis will not allow anything to escape your attention (which is the basis of any kind of scholarship). And the synthesis from the gorges of theory will again lead you into [spacious] fields of action” [1, p. 109]. The analysis, which is constantly used by both the teacher in presenting the material and to the students and the students in their comprehension, contributes to the development of the student's thinking and the formation of such a system of interactions, which is now called the pedagogy of cooperation.

Obviously, it is the harmony between the elements of the Komensky’s system that ensures its high efficiency for several centuries, but, as it will be shown below, it was achieved on the basis of difficult compromises and therefore, in the process of civilization and culture development, it can be violated in many weak points. In the context of the current rapid changes in all spheres of life, with the unprecedented mobility of production technologies, means of production, types and methods of professional activity, the above mentioned threat of losing the systemic stability of known pedagogical technologies becomes real. For this reason, the issue on strengthening the sustainability of existing pedagogical systems comes to the fore in importance.

An important support for solving this research problem is provided by the principle of minimum sufficiency of A. Einstein, according to which "everything should be done as simply as possible, but not simpler." Based on this principle, it can be assumed that the sharp and sweeping criticism of Komensky and traditional education, reaching the idea of a complete rejection of them, is not entirely fair. It is wiser, first of all, to analyze those initial assumptions and self-restrictions that were made to simplify the theory, but ceased to correspond to the new realities of the modern world. Then, to fix the situation, it will be enough to limit ourselves to targeted correction of existing systems. The main purpose of this article is to carry out such an analysis.

In the field of education, the difficulties of combining various elements into an integral pedagogical system are closely related to the urgent problem of individualization of training and education. On this occasion P.F. Kapterev wrote: "Personal characteristics must be constantly kept in mind when upbringing, otherwise it will not correspond to the needs of the subject, it will be stereotyped, too abstract and unsuitable in this case" [2, p. 28]. At the same time, he noted that "it is impossible to scientifically create individual pedagogy, since science deals with the general, and not with the particulars." To resolve the contradiction between what is required and what is achievable, P.F. Kapterev proposed to entirely shift the burden of individualization to family education, believing that “the application of the general principles of education to the properties of a given personality is a matter of the skills of parents and educators, a matter of their creativity” [2, p. 28].

In the second, supplemented edition of the cited work, published in 1913, P.F. Kapterev significantly expanded the analysis of the problems of family education and stated that family education can, to a certain extent, be called a newly discovered area of scientific pedagogy. At the same time, he still maintained that individualization of education is impossible in ordinary school education. With 30 to 40 students per class, it is difficult for teachers and educators to reach individual students to study and deal with them according to their personal characteristics.

At first glance, this entire theoretical structure is well substantiated, but if “it is impossible to scientifically create individual pedagogy,” then the family, when performing such complex and responsible functions of education, is actually left without any support. In addition, with the lengthening of educational trajectories, the time of interaction of the student with the family decreases and the family's ability to influence his development decreases. Let's remember that in the Lyceum where A.S. Pushkin studied, lyceum students were not allowed to go home even on vacation. Further, due to the significant complication of the subjects being studied, the likelihood of serious failures in mastering the material increases, and they can negatively affect personal development. Within the framework of family education, apart from the generative source of such problems, the situation cannot be corrected, so the individualization of education should become the concern of school education. It can be assumed that an unspoken ban on the search for such opportunities was formed due to fears of violating the above-mentioned condition for the efficiency of education in this case, the inevitable complication of the models of the educational process.

As a result, we see the following chain of dependencies. The growing demands on the education system on the part of society and the state make the learning process more and more intense and thereby exacerbate the problem of individualization of education. At the same time, the found method of ensuring the economy of education narrows the scope for finding solutions to this problem within the framework of the simplest (linear) models of managing educational processes. They, in turn, leave little chance of stimulating personal development in the learning process. Attempts to shift the solution of the urgent and acute problem of individualization to the family run up against the parents' lack of special training and assistance from science.

If we consider the education system as a closed system, then due to the presence of such a large number of unresolved internal problems and contradictions, one would expect the fading of educational processes. But the history of education shows otherwise. The history of mathematics in the 19th century is especially illustrative in this respect. F. Klein in his monograph noted several distinctive features of this time. Firstly, during this period “mathematical physics” was completely created, new areas of mathematics appeared, “pure mathematics began to come to the fore imperiously as well” [3, p. 14], that is, the progress of mathematics itself did not slow down, but accelerated.

Secondly, the ideal of eighteenth-century universality was abandoned. Due to the growing volume of mathematical knowledge, even the most universal mind, according to F. Klein, “is no longer able to synthesize the whole in itself and use it fruitfully outside of itself” [3, p. 15]. Mathematicians began to master only a small part of mathematics and published their works in the form of scattered articles that did not contain connections with general issues and therefore were not available to a wide range of readers. Thirdly, in the 19th century, “scientific life began to be influenced by major social shifts caused by the French Revolution and the historical events that followed it” [3, p. 14]. Because of them and in spite of the named circumstances, which burden the development of education, there was an unimaginable influx of people who wanted to acquire the now prestigious teaching profession.

Here we have a vivid example of the collision of two powerful and oppositely directed processes – the rapidly growing inaccessibility of mathematics for those who begin to study it, and at the same time, an equally rapid increase in the number of those who decided to engage in its active development. This means that even if the influence of external factors on the state of education and science is not very noticeable, in fact it is very strong.

This conclusion is important and deserves to be consolidated in terms of the philosophy of openness. “To accept our concept of non-closedness,” S.I. Yakovlenko writes, “we only need to admit a rather obvious fact: if we consider sufficiently long times, then many important properties of any system accessible to our observation will be determined by its openness, and attempts to explain the behavior of an open system based only on its internal properties will inevitably lead to a dead end” [4, p. 45]. Indeed, without taking into account the socio-cultural processes from the assessments we obtained based on the analysis of the works of P.F. Kapterev, it would be impossible to predict the rise of science, and hence education. Therefore, we need to continue our research in an extended formulation of the problem.

A good scientific foundation for the implementation of this approach was created in the works of N.V. Gusseva. In the monograph [5] she carried out a socio-philosophical analysis of the foundations of human development in the context of civilization and culture. The central link in the work is a versatile analysis of the understanding, interpretation and implementation of the individual's activities. From the numerous consequences obtained in the monograph, we single out two interpretations of activity, which set an important guideline for further research. According to the first of them, activity as a system of actions determines the so-called civilizational approach, and the understanding of activity as a holistic and practical connection with the world determines the position of considering the world and man, science and education as cultural phenomena, where culture manifests itself as a process, not as a result. Thanks to this distinction between types of activity, it is possible to clearly see not only the fact of alienation of a person, about which the supporters of the theory of the Social Contract, including T. Hobbes, began to write, but also the dynamics of alienation.

The essence of the matter here is that even a holistic activity as a way and form of manifestation of human subjectivity, his creative essence leads to a certain result, and he, in turn, begins to exist independently of a person and thereby is included in the civilization process. Thus, the subject body of civilization, its inert layer is constantly increasing and the scope for the manifestation of human creative activity and, accordingly, for culture as a process, generally speaking, is narrowing.

The universal property of living matter protects from the complete damping of these processes, according to L. Pasteur and V.I. Vernadsky [6]. This property lies in the fact that living matter exists in a series of births and deaths. It is the change of human generations that opens up to each new generation of people a huge field for manifestations of creative activity – the entire space of civilization, in order to adapt to life in which it is required to de-objectify the gigantic experience of previous generations. Without effective help from the education system, an individual cannot travel a path of several millennia in his short life, therefore the state of educational processes, including their smallest episodes, can and do have global – civilizational significance.

To substantiate this thesis, let us turn to the history of mathematics in ancient Greece, rich in unique events. First of all, it should be noted the rapid rise of mathematics in the period from the 6th to the 4th century BC, which, according to I.G. Bashmakova, “seemed to border on a miracle” [7, p. 225]. It was in Greece that “logical proof was systematically introduced into mathematics, and its separate sections began to be built as deductive systems” [7, p. 226]. It is significant that logic itself received its initial development not in mathematics, but in connection with the establishment of democracy in Athens and other cities of Greece and the unfolding ideological struggle of political parties. Note that science also originated in Ancient Greece. According to A.E. Levin, “science arose once, and subsequently this "act of creation" has never been repeated. The importance of this fact and the need for its comprehensive understanding do not diminish in the least from the fact that it happened twenty-five centuries ago” [8, p. 101].

The consequences of these changes in mathematics are very significant. The transfer of systematized knowledge is more stable due to the appearance of additional protection against the accidental loss of individual elements. The initial provisions and rules of inference, constituting a small part of the theory, potentially carry all of its content. Thanks to this, the deductive structure of the theory becomes an instrument of compression, reduction of material. Moreover, the proof plays a leading role in this construction, since it allows the entire system to be recovered from a small kernel. Therefore, the deductive structure of theories turned out to be an important support in scientific and pedagogical communication. However, these revolutionary changes did not lead to finding the "royal road to mathematics," the difficulties of mastering it only shifted to the initial concepts of a deductive system. V.I. Arnold described them as follows: “The usual deductive-axiomatic scholastic style is that the presentation of a mathematical theory begins with an unmotivated definition. The psychological difficulties to which this leads the reader, are almost insurmountable for a normal person” [9, p. 118]. Such concepts become powerful barriers to the assimilation of the whole theory, points of a sharp separation of the theory from the actual life experience of the individual, points of clear alienation from him of this theory.

Here we come to a key point in our historical excursion. While the energy of overcoming was fed from the outside, and learning in one way or another contributed to the personal development of the individual, the interconnected development of culture, civilization and education was progressive, but this movement is unstable and may stop due to seemingly insignificant reasons. G. Freudenthal's statement about Euclid's “Principles” is characteristic: “This geometrized algebra, divorced from life, a useless invention by fanatics of method and precision, became one of the reasons for the degeneration of Greek mathematics. Of course, as long as, along with the official Euclidean-Archimedean mathematics, heuristic methods of algebra and the infinitesimal were also taught, young people could master the straitjacket of official science. But as soon as these traditions were broken, everything perished” [10, p. 13]. Note that it died for more than a thousand years, in fact, before the famous tournament between Fiore and Tartaglia, during which Tartaglia received a mathematical result of fundamental importance, which neither ancient nor Eastern mathematicians knew.

O. Spengler also noted indirectly the growing role of point factors in the processes of alienation. In his book "The Decline of Europe", published in 1918, he called the first chapter "On the Meaning of Number". Combining such diverse problems, Spengler insisted on the need to "distinguish between becoming and what has become" and emphasized that "becoming is always at the heart of what has become, and not vice versa". In violation of this principle in relation to the preparation of new generations, Spengler saw a threat to Europe and a prerequisite for its decline. In a more general form, problems of this kind were developed by Hegel, and then by K. Marx, relying on the concepts of "objectification" and "de-objectification".

The particular difficulty of introducing the concept of number in elementary school was also pointed out by E.V. Ilyenkov. On the basis of a logical-philosophical analysis of the old method of teaching counting, he came to the conclusion that it was not nature that was to blame for the decrease in the number of children capable of mathematics, but didactics. “Those ideas about the relation of the abstract to the concrete, the general to the singular, quality to quantity, thinking to the sensuously perceived world, which were the basis of many didactic developments, are to blame” [11, p. 199].

What are the real achievements of the modern education system with such an aggravation of its internal and external problems and contradictions? At the macro level, they can be assessed using a specific type of culture identified by researchers - global culture. It differs from other types of cultures in that it does not have any centers of localization and “territorial binding”. Yu.A. Sukharev showed that “the bearer of global culture is a transnational group of individuals engaged in highly intellectual creative professional activities in the field of information technology, science, education, with a specific system of non-material motivation and a complex of value-semantic regulations. (...) The main system-forming element of the new culture is creativity, creative production activity” [12, p. 9]. Thus, a powerful rise of culture as a process is taking place at the present time, but only a small group of people are directly involved in this. This circumstance gives rise to the rapid growth of social differentiation and cultural polarization both between countries and within developed countries.

The given characteristics of global culture demonstrate a strong interdependence between the development of culture, society and an individual. At the same time, in the presence of the aforementioned transnational group of people, there is still no organizationally unified and equally distinguishable transnational education system. This comparison allows us to believe that the rapid growth of technology, science and education in the world is based not so much on the use of new reserves in the organization of education, but on the multistage selection of students and specialists. The emerging innovative education should play a special role in accelerating this growth, but, as shown in our article [13], its methodological problems remain acute and unresolved. At the same time, elements of traditional education are clearly present in its organizational forms. It follows from this that a special emphasis on only innovative moments – for all their relevance for modern education and for modern society – does not provide adequate models of educational processes. To overcome these methodological difficulties, the study of innovative education should be included in the broader context of education development, taking into account its internal and external factors. As a result, we once again come to the conclusion about the relevance of building an effective mass developmental education.

Is it possible to achieve this in the existing socio-cultural conditions? The fundamental possibility of giving an optimistic answer to this question is confirmed by the works of N.N. Nechaev, in which the psychological aspects of higher architectural education are studied [14]. This research was updated by the change in the social conditions of architectural education and the transformation of the profession of an architect into a mass profession. It was no longer possible to count on spontaneous pre-university training and the giftedness of students, students began “special training for obtaining higher architectural education from a professional zero” [14, p. 243]. For an active response to the changed conditions, a transition was made to the management of the educational process based on a changing target function.

Among the three stages of preparation identified, the first takes a special place. “The first stages – the beginning – are the most dependent (from the point of view of a professional architect) and in this sense the most distant from the actual way of professional action. But it is on it that professional actions are maximally highlighted, clearly described, extremely detailed and objectified. This is the most controlled process of a student's activity on the part of a teacher – and in this regard, outwardly, the most uncreative stage ”[14, p. 279]. The selection of this stage was forced; a lot of efforts now had to be spent on the formation of the required initial conditions directly in the learning process – already within the framework of higher education. This helped to solve the main problem at the second and third stages of training – the task of forming the professional creativity of the architect.

The first stage of training was mainly aimed at strengthening the personal component of the educational process, but this time delay had a positive effect on the final result, since it led to an increase in the quality, and then to an acceleration of the educational process. Note that more complex (nonlinear) management models were required for active accounting and correction of the personal aspects of learning, which, in turn, opened up the possibility of applying new achievements of psychological science.

The article [15] provides a similar example of solving the problem of adaptation of freshmen to university studies within the framework of the course of mathematical analysis. This problem is becoming more acute due to the growing gap between the level of training of schoolchildren and the needs of the university, as well as due to the presence of complex concepts and a developed formal apparatus in this course. Therefore, from the very beginning of training, it was necessary to fill in the gaps in previous training, to strengthen the propaedeutics of a number of concepts and, at the same time, to restore the students' initiative. In addition to the previous example, a significant upgrade of current control was required here. The result of its application has surpassed all initial expectations.

In modern conditions, the problems of the control system in the field of education should be treated with increased attention. First of all, because, as it is shown in [16], at the present time this system is in the state of systemic and structural crisis and thus inhibits the development of education. In particular, in the transition to more complex management models, it will be necessary to carefully control the moments of switching between the personal and meaningful direction of management. If in the first of the two examples cited three stages of training covered the entire period of study at the university, then in the second example active corrective measures were concentrated at the beginning of the first semester of training and therefore the required switching was carried out not according to a predetermined plan, but based on feedback.

The limiting localization of corrective intervention in the educational process in place and time arises when assisting a student in understanding the initial concepts of axiomatic theory in mathematics. Most students are helpless in front of such concepts, and according to the meaning of the axiomatic method, their propaedeutics is not provided for in curricula. In case of urgent need, the teacher has to carry out this work outside the plan, at the expense of internal reserves of management and control and as intensively as possible. Such a difficult pedagogical problem can be solved only on the basis of active assistance in the development of the student's thinking. The article [17] shows how exactly this problem can be solved with the help of a special organization of current control.

Conclusions. Many problems of modern pedagogy and education are generated by the rapidity of social and cultural changes, but there are also internal reasons for the intensification of crisis phenomena. They are connected with the fact that paradigmatic ideas, formed under the influence of the works of great predecessors, can no longer lead to the required solutions. Since, due to objective reasons, the student is becoming an ever weaker link in the system of educational relations, in the new paradigm of education, the personal component of the educational process should be significantly strengthened, and learning itself should become developmental. For this it is necessary to switch to more complex models of educational process management. This will allow resolving a number of systemic contradictions that have accumulated in pedagogical theory. With the complication of management models, the overall efficiency of education can increase many times over – both by liberating the creative energy of students and teachers, and by improving the quality of the educational process.

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