How to compare different pedagogical systems with each other using the object-hierarchical method of structuring and dosing information

Sennitskaya Elena Vladimirovna Mater's Degree student of the Department of General Psychology and History of Psychology at Novosibirsk State Pedagogical University 630090, Russia, Nso oblast', g. Novosibirsk, ul. Tereshkovoi, 33, kv. 58 activist07@mail.ru Other publications by this author

Introduction

The American philosopher Thomas Kuhn (1922-1996) in his book "The Structure of Scientific Revolutions" ^[1] wrote that every science in one way or another faces such a problem as the lack of cumulativeness, that is, the gradual and steady accumulation of knowledge. In other words, the development in science most often occurs not due to the systematic accumulation of knowledge, but by replacing some theories with others, as a result of which much of what has been achieved is forgotten.

Pedagogy also demonstrates the truth of this statement. For example, until recently, it was enthusiastically talked about the prospects that programmed learning brings with it: the idea of dividing the educational material into clearly dosed portions, arranged in a certain sequence, so that any student could, without experiencing overload, master them independently and, if desired, return to the stage he needed, caused universal approval – but now this the direction does not enjoy the same popularity. In addition, the term "programmed learning", which originally meant the dosing and algorithmization of educational material, is increasingly being replaced by the concept of "computer-assisted learning". Another example is the method of V.F. Shatalov, the effectiveness of which was much discussed in the late 1980s. However, little attention is currently paid to this approach.

What explains the fact that sometimes there is not an enrichment of the old concept with new knowledge, but a complete displacement of one by another? According to the author of this work, this happens in cases when the old and the new seem to be something completely different from each other, it is difficult to compare, in other words, when there is no clear categorical apparatus to make the research results comparable. Note that the infinite displacement of some concepts by others is not observed only in one science – mathematics, since mathematics operates with homogeneous objects – numbers. From this we can conclude that the more mathematics there is in science, the more chances it has to keep its achievements. Consequently, the main problem of any science, including pedagogy and pedagogical psychology, is the need to clarify the concepts used in it by introducing quantitative certainty. At the same time, the questions about what is better – the method of V.F. Shatalov or programmed learning, the system of V.V. Zankov or the system of L.V. Davydov – seem unsolvable, since it would seem that we are talking about things too complex, complex, which are difficult to compare with each other.

Nevertheless, there is a way to present classes on any of these systems in the same formalized form, which will allow you to visually judge the similarities and differences between them. We are talking about object-hierarchical modeling ^[2]. In short, its essence boils down to the fact that the lesson (or the chapter of the textbook) is presented in the form of a hierarchical scheme, where the following parameters are visible:

1) how many directions (branches of the hierarchical scheme) does the lesson consist of;

2) how many levels of hierarchy does each branch have;

3) what is the value of linear sequences (i.e. how many objects are contained at each step of the hierarchy);

4) how many known objects reveal the essence of each unknown object (it has been experimentally established ^[3] that there should be 3-5 of them);

5) do the lower stages of the hierarchical scheme of the lesson contain such objects that are not disclosed due to the proper number of known ones; in other words, does the periphery of the object-hierarchical structure contain unknown objects;

6) at which stages of the lesson objects are represented in static, and at which – in motion.

An example of such a presentation of a training session is given in ^[2]. The article ^[3] also presents the results of experiments on the influence of structuring and dosing of educational material on the attention and discipline of students, and in the article ^[4] – on their emotional state. The works ^{[3, 4]} describe an object-hierarchical model of the lesson, which provides maximum attention and memorization while maintaining a favorable emotional state of students.  

Thus, in order to objectively compare any competing pedagogical systems, it is proposed to present those classes that their authors consider exemplary illustrations of these systems in the form of hierarchical models, and compare them according to the above six parameters. In a similar way, entire training courses can be compared by presenting them as a set of interrelated hierarchical schemes.

This approach is of particular interest for evaluating tasks proposed for independent solution, because each task also represents a hierarchical structure in which an object or a number of objects is missing and is subject to reconstruction using those objects that are known. It also allows for a more in-depth analysis of age-related features of thinking (for example, those described by Zh. Piaget ^[5]) by presenting typical ways of reasoning in graphical form.

The proposed method can also serve as a basis for the development of the approaches of L.N. Landa ^[6] and G.S. Altshuller ^[7], aimed at teaching adults and children to reflect on tasks in accordance with certain algorithms, since the method of hierarchical modeling allows you to present the problem and ways to solve it visually, graphically.

Nevertheless, the main purpose of this work is to demonstrate how the method can serve as a new tool for analyzing those concepts that have entered the history of pedagogy as certain achievements.

Ideas of teachers-thinkers of the past from the point of view of the object-hierarchical method

The founder of pedagogical science, the Czech teacher Jan Amos Komensky (1592-1670), did not formulate such a task as a clear dosage of educational material, but, nevertheless, his first ever illustrated textbook "The World of Sensual Things in Pictures" (1658) ^[8] reveals a clear desire for this.

This is a collection of dialogues between a teacher and a student in Latin, where each of the dialogues is devoted to one topic – one global object, which is viewed from all sides, and the author's desire to make sure that each generalized concept (usually representing the name of the topic of the lesson) is revealed by a certain number of specific examples of a subject nature (as a rule, from 4 up to 7). Each dialogue takes one turn and is accompanied by a picture that accumulates everything that is said in the dialogue. We emphasize that this is fundamentally at odds with the structure of modern textbooks, where there are many disparate pictures, and a paragraph often combines several non-equilibrium semantic blocks that are loosely interconnected.

According to Komensky, one should study four hours a day, and the rest of the time should be devoted to independent work (principle 6). Why exactly so many? The great didacticist does not explain this, however, given such a feature of the "World of Sensible Things" as the strict subordination of each lesson to a single topic, it can be concluded that Komensky did not consider it reasonable to study more than four topics in a row, and these topics should relate to the same subject. In particular, in the foundation 4 Komensky writes: "For the sake of all that is holy, I implore you to take measures to ensure that when studying grammar you do not interfere with dialectics, and at a time when the mind is busy with dialectics, do not involve rhetoric, and when we study Latin, Greek should be postponed. Otherwise, the objects will interfere with each other... So, let there be an order in schools in which students would study only one subject at the same time."

These arguments are consistent with the experimentally established conclusion stated in articles ^{[3, 4]} that the object-hierarchical structure of the lesson in the form of four branches revealing one global topic is optimal.

From the point of view of the object-hierarchical method, the approach practiced in the Waldorf schools ^[10], the ideological basis of which was laid by the Austrian philosopher Rudolf Steiner (1861-1925), is of great interest. These educational institutions, established in 1919, operate according to the immersion method.

From the standpoint of object-hierarchical modeling, the immersion method is the ordering of information into structures that have a very large hierarchy depth. Meanwhile, it has been experimentally established ^[3] that the depth of the hierarchy within one lesson has limitations due to the influence of the number of hierarchy steps on attention and memorization. In addition, it is undesirable that the classes following in a row contain similar material, since memory interference and forgetting of what has been passed occurs. Thus, the experience of Waldorf schools demonstrating high efficiency should be quantified using the object-hierarchical method, since the attempts of some schools working according to traditional methods to introduce immersion teaching leads both to a sharp increase in academic performance and to failures, depending on the intuitive feeling of the optimal amount of information by specific teachers.   

Let's consider from the point of view of the object-hierarchical method the ideas of the school of the French teacher and psychologist Celestin Frenet (1896-1966), who replaced the work with the textbook with tasks with cards ^[11]. The reason for the innovation was just a desire to individualize learning so that each student progressed at a pace convenient for him, but the transition to flashcards led to other interesting results that S. Frenet had not originally planned.

It is obvious that a small card in which the essence of the studied material is briefly outlined is nothing more than a way of dosing information. Considering that the cards were made of standard size (13.5 * 21 and 21 * 27 cm), it is clear that too much information could not fit on them. At the same time, some of the cards contained algorithms for completing tasks, in other words, S. Frenet engaged in programmed learning long before the appearance of this term. Nevertheless, as can be seen further, the teacher himself did not fully understand the reasons for the success of his school.

From the point of view of the object-hierarchical method, small portions of information contained in the cards and isolated from the rest of the course material are separate units of information, manipulating which the student can more easily build a wide variety of hierarchical communication systems. Unlike the material located in the textbook, flashcards are blocks of information that can be transferred from topic to topic and applied to completely different tasks, as opposed to the material that, in the view of schoolchildren, is "attached" to a specific topic of the textbook.

As you know, S. Frenet demonstrated the tremendous effectiveness of teaching his native language by reading, writing and editing texts (grammatical rules were studied from him directly from edited or readable texts). According to Frenet, the whole secret was that children do not perform exercises, but produce something real.

Note that nothing real is done in the process of reading the text, however, the study of grammar from the text being read is as effective as from the one being compiled or edited. Frenet does not notice that the generally accepted exercises in the native language are mostly linear structures (i.e. located at the same level of hierarchy, an overabundance of which does not contribute to the involuntary attention of the student, as described in detail in work 3), or structures with a chaotic hierarchy that cause overwork.

The text is an ordered hierarchical structure with interconnected sublevels. It can be considered both from the point of view of meaning, and as an alternation of fragments of a certain type (descriptions, narratives and reasoning), and as a set of means of artistic expression (epithets, metaphors, comparisons, etc.), and as syntactic structures with a certain punctuation, and as a number of phrases with different types of connection, and as individual words with their morphology, spelling and morphemics. Meanwhile, studying the material inside one hierarchical structure always causes a minimum of tension.

Of great interest, of course, is the modern pedagogical system of V.F. Shatalov (born in 1927), and not only the reasons for its success, but also the explanation that it has not been widely introduced into practice. Apparently, the latter happened for the reason that some teachers who tried to use Shatalov's methodology in their work, relying on his books, failed: the transition from the traditional study of theory to a simplified presentation of material based on drawings on a poster in some cases led to the destruction of discipline. This happened, for example, at first and during the experiment described by the author of this work ^[3]. The fact is that the mass replacement of generalized concepts with objective, visually representable ones leads to an increase in linear sequences of objects at each of the hierarchy levels, which, as the experiment described in ^[3] shows, contributes to distraction and violation of discipline. If the teacher has a rich experience and a developed sense of proportion in relation to the quantity and structure of the information taught, the grouping of the educational material is done correctly: generalized concepts are preserved, and each of them is revealed in a linear sequence of no more than 5 visually representable examples. If experience and intuition are insufficient, this can lead to a hasty conclusion that the method "does not work", and the excellent results of V.F. Shatalov himself are due only to the charismatic personality of the teacher. In fact, the problem lies in the insufficient specification of the method regarding the rules of structuring and dosing of information, which does not guarantee the correctness of its reproduction.

Indeed, Shatalov's methodology does not contain detailed rules for organizing educational information in the classroom. Nevertheless, it contains the principles of structuring it on a reference signal (a poster with a schematic image of what is being discussed in the lesson) ^[12]. So, according to V.F. Shatalov, the elements depicted on the poster should preferably be combined into 4-5 blocks, and these blocks should be autonomous. They should be separated from each other graphically, and each of the blocks should be understood separately from the others. Note that this consideration is fully consistent with what was established as a result of the experiment about the influence of the structure of the lesson on the attention of students ^[3].

The principle of conciseness, put forward by V.F. Shatalov, provides only that the reference signal should not contain more than 300-600 printed characters, however, the instructions for drawing up reference signals do not contain any concepts about the hierarchical structure of the objects in question in the lesson, nor about observing a certain number of generalized and subject, visually representable concepts that they they do not disclose the observance of a certain depth of hierarchy (that is, the number of hierarchy steps at each stage of the lesson). Apparently, the absence of these concretizing explanations is the reason that not every teacher can repeat Shatalov's impressive results.

As for the reasons why programmed learning was undeservedly forgotten, the main one, apparently, is that its creators got carried away with the computer implementation of their training programs, and did not solve the problem of analyzing the complexity of texts and tasks. No units of measurement of information and corresponding methods have been developed. Instead, proponents of programmed learning have mechanically transferred the way information is measured from programming.

In computer science, a unit of information is 1 byte (= 8 bits) – a combination of eight zeros or ones, with which one character is encoded (any letter, digit, punctuation mark, mathematical sign, or even a space entered from the keyboard).

For a machine, the amount of information contained in a text is simply the number of letters, numbers, punctuation marks and spaces that it consists of. The computer does not take into account the amount of meaning in the text. He doesn't care if every sentence is filled with real meaning or if it's a meaningless set of words. Thus, the approach available in programming is completely unsuitable for analyzing the complexity of educational information.

How did the specialists in programmed learning themselves feel about this? Let us turn to the work of academician V.P. Bespalko, who is a recognized expert in this field.

"By means of cybernetics (more precisely, by means of information theory), it is possible to calculate only the formal information capacity, the volume of the message, and not their semantic value for the recipient... This fact has not yet found a proper assessment in didactics, and so far all didactic constructions are devoid of any measuring instruments and measurements [Highlighted by me, – E.S.]" ^{[13, p. 29]}.

Further, V.P. Bespalko admits that, even realizing this problem, supporters of this direction rely on the formal approach adopted in programming, as well as on the "Miller number", which, as was shown in ^[3], is actually redundant ^{[3, p. 32]}, and the conceptual apparatus, used in other psychological and pedagogical systems indicates that these methods are also absent there.

For the first time, a hierarchical approach to the representation of information is found in Tony Buzen under the name mind map (intelligence map). It is implemented in the form of a tree-like radial scheme, on which ideas related to branches departing from the central concept or idea are recorded in the form of words or drawings ^[14]. However, the Buzen method is not a way of constructing texts, but a way of converting texts into a graphic form illustrating their hierarchical structure. In addition, it does not contain any definition of the unit of information, nor any dosing rules. In particular, T. Buzen's software (iMindMap) for creating intelligence maps ^[15] does not limit either the number of branches emanating from the topic name or the depth of the hierarchy.

Conclusion

To date, the pedagogical recommendations are characterized by vagueness. Almost every methodological manual says that the material should not be too complex, but, on the other hand, should not be primitive. How should the teacher design the lesson? How can he calculate the time for individual tasks? There is no answer.

Programmed learning had a great chance of creating a method for measuring information, but this did not happen. Why? Because the scientific picture of the world at that time did not contain the idea of information as a hierarchical structure. In turn, the idea of presenting information in a hierarchical form could hardly have arisen before the advent of structured programming languages.

Writing a program in the form of a hierarchical structure was first used in the Algol language, developed in 1958, and the hierarchical representation of not a program, but various data began to be used only in the C language, the first book about which was published in 1978, however, the first programming language that represented data in a hierarchical form and became known to a wide range of people, including the humanities, the HTML language developed by the British scientist Tim Berners-Lee (born in 1955) by 1991 became. The language gained true fame already at the beginning of the XXI century. after HTML 2.0 was adopted as a standard for the design of web pages on the Internet. Meanwhile, the interest of teachers in programmed learning, which began its development in 1954, had already been largely lost due to the misconception that supposedly complex tasks like learning to understand a literary text or writing an exposition (essay) could not be algorithmized.

Thus, the present work suggests returning to the solution of psychological and pedagogical problems with a new tool of cognition - object-hierarchical modeling.