The regularity of stimulating learning.
The regularity of learning management.
The regularity of teaching methods.
The regularity of the quality of education.
The effectiveness of each new stage of training depends on: the productivity of the previous stage and the results achieved on it; the nature and volume of the material being studied; organizational and pedagogical impact of trainers; learner learning; training time.
The effectiveness of didactic methods depends on: knowledge and skills in applying the methods; learning objectives; content of training; the age of the students; educational opportunities (learnability) of students; material and technical support; organization of the educational process.
The productivity of training depends on: the intensity of feedback in the training system; the validity of corrective actions.
The productivity of training depends on: internal stimuli (motives) of training; external stimuli.
As a result of the research, four general factors have been identified that determine in the complex the formation of the products of the didactic process: 1) educational material; 2) organizational and pedagogical influence; 3) learners' learning ability; 4) time.
Educational material contains general reasons for informational origin.
As part of this factor, two complex ones stand out: objective (pure) information - the content, the amount of educational material, its quality, the form of presentation; information acquired in the process of didactic processing - method, structure, and accessibility of presentation.
As part of factor of organizational and pedagogical influence there are two complex ones:
- a factor of organizational and pedagogical influence in the classroom - teaching and learning methods, organizational forms, educational situations, teacher's performance, students' performance, monitoring and checking work results, type and structure of a training session, practical application of adoptive knowledge, skills, use of teaching aids, equipment educational process, learning conditions;
- a factor of influence with educational goals outside of school hours - the amount and nature of help from parents, adults, friends; the regime of educational work; supervision by adults; using the media for purposes, reading literature; organization of independent educational work; participation in circles; communication with adults for cognitive purposes and many other factors.
Learning Factor - This is the ability of students to learn and the ability to achieve their projected results at a given time. In this factor, there are also two complex factors:
- the factor of learning in the classroom - the level of general training (erudition) of the trainees; the ability to master certain educational material, assimilation of knowledge, abilities, skills; general abilities for educational and cognitive activity; general characteristics of attention; peculiarities of students' thinking when studying a specific academic subject; general characteristics of thinking; psychological orientation towards the conscious and lasting assimilation of educational material; motivation for learning; the rate of assimilation of knowledge and skills; student health; the age of the trainees; their value orientations; discipline; orientation towards the future profession; lifestyle and many other reasons;
- the factor of learning in extracurricular activities - self-control; will and perseverance; purposefulness; working capacity; value orientations; stimulation; motivation; health status; features of the perception of cognitive activity in general; abilities; the speed of memorization and assimilation; level and features of thinking; age and individual characteristics, etc.
IN time factor can be distinguished:
- the factor of time spent directly in the lesson;
- the factor of time spent on self-preparation.
Among the above learning factors, the factor of organizational and pedagogical influence has the greatest effective effect. Therefore, in the practice of organizing the didactic process, it is necessary, first of all, to take care of the proper learning conditions, providing the educational process with the necessary means, the use of effective technologies, teaching methods, and the use of progressive organizational forms.
As a result of the research, four general factors have been identified that determine in the complex the formation of the products of the didactic process: 1) educational material; 2) organizational and pedagogical influence; 3) learners' learning ability; 4) time.
Educational material contains general reasons for informational origin.
As part of this factor, two complex ones stand out: objective (pure) information - the content, the amount of educational material, its quality, the form of presentation; information acquired in the process of didactic processing - method, structure, and accessibility of presentation.
As part of factor of organizational and pedagogical influence there are two complex ones:
- a factor of organizational and pedagogical influence in the classroom - teaching and learning methods, organizational forms, educational situations, teacher's performance, students' performance, monitoring and checking work results, type and structure of a training session, practical application of adoptive knowledge, skills, use of teaching aids, equipment educational process, learning conditions;
- a factor of influence with educational goals outside of school hours - the amount and nature of help from parents, adults, friends; the regime of educational work; supervision by adults; using the media for purposes, reading literature; organization of independent educational work; participation in circles; communication with adults for cognitive purposes and many other factors.
Learning Factor - This is the ability of students to learn and the ability to achieve their projected results at a given time. In this factor, there are also two complex factors:
- the factor of learning in the classroom - the level of general training (erudition) of the trainees; the ability to master certain educational material, assimilation of knowledge, abilities, skills; general abilities for educational and cognitive activity; general characteristics of attention; peculiarities of students' thinking when studying a specific academic subject; general characteristics of thinking; psychological orientation towards the conscious and lasting assimilation of educational material; motivation for learning; the rate of assimilation of knowledge and skills; student health; the age of the trainees; their value orientations; discipline; orientation towards the future profession; lifestyle and many other reasons;
- the factor of learning in extracurricular activities - self-control; will and perseverance; purposefulness; working capacity; value orientations; stimulation; motivation; health status; features of the perception of cognitive activity in general; abilities; the speed of memorization and assimilation; level and features of thinking; age and individual characteristics, etc.
IN time factor can be distinguished:
- the factor of time spent directly in the lesson;
- the factor of time spent on self-preparation.
Among the above learning factors, the factor of organizational and pedagogical influence has the greatest effective effect. Therefore, in the practice of organizing the didactic process, it is necessary, first of all, to take care of the proper learning conditions, providing the educational process with the necessary means, the use of effective technologies, teaching methods, and the use of progressive organizational forms.
As a result of the research, four general factors have been identified that determine in the complex the formation of the products of the didactic process: 1) educational material; 2) organizational and pedagogical influence; 3) learners' learning ability; 4) time.
Educational material contains general reasons for informational origin.
As part of this factor, two complex ones stand out: objective (pure) information - the content, the amount of educational material, its quality, the form of presentation; information acquired in the process of didactic processing - method, structure, and accessibility of presentation.
As part of factor of organizational and pedagogical influence there are two complex ones:
- a factor of organizational and pedagogical influence in the classroom - teaching and learning methods, organizational forms, educational situations, teacher's performance, students' performance, monitoring and checking work results, type and structure of a training session, practical application of adoptive knowledge, skills, use of teaching aids, equipment educational process, learning conditions;
- a factor of influence with educational goals outside of school hours - the amount and nature of help from parents, adults, friends; the regime of educational work; supervision by adults; using the media for purposes, reading literature; organization of independent educational work; participation in circles; communication with adults for cognitive purposes and many other factors.
Learning Factor - This is the ability of students to learn and the ability to achieve their projected results at a given time. In this factor, there are also two complex factors:
- the factor of learning in the classroom - the level of general training (erudition) of the trainees; the ability to master certain educational material, assimilation of knowledge, abilities, skills; general abilities for educational and cognitive activity; general characteristics of attention; peculiarities of students' thinking when studying a specific academic subject; general characteristics of thinking; psychological orientation towards the conscious and lasting assimilation of educational material; motivation for learning; the rate of assimilation of knowledge and skills; student health; the age of the trainees; their value orientations; discipline; orientation towards the future profession; lifestyle and many other reasons;
- the factor of learning in extracurricular activities - self-control; will and perseverance; purposefulness; working capacity; value orientations; stimulation; motivation; health status; features of the perception of cognitive activity in general; abilities; the speed of memorization and assimilation; level and features of thinking; age and individual characteristics, etc.
IN time factor can be distinguished:
- the factor of time spent directly in the lesson;
- the factor of time spent on self-preparation.
Among the above learning factors, the factor of organizational and pedagogical influence has the greatest effective effect. Therefore, in the practice of organizing the didactic process, it is necessary, first of all, to take care of the proper learning conditions, providing the educational process with the necessary means, the use of effective technologies, teaching methods, and the use of progressive organizational forms.
The problem of learning factors in didactics is considered in the context of its productivity. It is to this concept that the causal relationships operating in the educational process should be tied, which in this case are called product-generating (product-forming, elementary) causes. How much and what quality of the educational product is produced in the educational process, what its productivity will be, entirely depends on which of these reasons and how they are intertwined in the interaction of teachers and students. That is why the productogenic cause in didactics is understood as an arbitrarily small, but necessarily integral, cause-and-effect relationship, the dismemberment of which into its component parts is impossible without losing its meaning.
A significant cause formed from at least two product-generating causes of one group is denoted by the term “single factor”. In turn, their combination forms the so-called "common factor", the further combination of which forms complex learning factors. At the top of the factorial hierarchy are the general factors that unite all, without exception, the productogenic causes of a certain group, previously summarized into single, general and complex factors.
In the scientific pedagogical literature, sometimes specific factors are also distinguished, which, for some reason, cannot be reduced to any product-generating cause and included in the factors considered earlier.
Undoubtedly, the allocation of the named factors of the educational process is very important for the implementation of the so-called "factor analysis", which is the object of scientific activity of educational researchers. In pedagogical practice, only general factors are mainly taken into account. By now, four of them are the most taken into account.
1. Educational material. Contains general reasons for informational origin. This takes into account that educational information is subdivided into cognitive (carrying knowledge) and control - signals about how to assimilate cognitive information.
At the same time, as part of this general factor, two complex ones are logically distinguished: objective information (content, quantity of educational material, its quality) and didactic processing (method of presentation, structure, availability of educational material).
2. Organizational and pedagogical influence. It unites a large group of product-related causes that characterize the activities of the teacher and the quality levels of the organization of the educational process. In this factor, two complex ones also stand out: the organizational and pedagogical influence in the classroom (teaching and learning methods, organizational forms, the performance of the teacher and students, control and verification of results) and the educational influence outside the classroom (the volume, control and nature of assistance from parents, other adults and friends, the mode of educational work, the study of additional literature).
3. Learning ability of students. This factor represents the ability to learn and the ability of students to achieve their stated learning goals at a given time. It also highlights two complex factors: learning ability in classrooms (the general level of preliminary training of students, their ability to master educational material, thinking peculiarities, etc.) and learning ability after school hours (self-control, will, perseverance, purposefulness of learning, etc.). ).
4. The time required to study the material. In this general factor, the time spent in the lesson is highlighted (the time of perception of educational information, the initial comprehension of knowledge and their consolidation, the required number of repetitions, etc.), as well as the time spent on independent work (time for doing homework, visiting optional and additional classes).
The considered and a number of other factors have both objective and subjective bases, but, manifested in interconnection, with the same intensity affect the productivity and quality of the educational process of an educational institution. Along with the goals, functions and motives, they not only characterize the learning process in a certain way, but also influence the formation of its methodological foundations.
The fourth general factor is "Time". It is possible to distinguish the time spent in it: 1) directly in the lesson; 2) for self-study (self-study).
The time spent in the lesson includes: the time of perception and primary assimilation of knowledge; consolidation and consolidation of the studied; the frequency of monitoring, repetition and consolidation; time elapsed after completion of training; the time of storing information in memory in accordance with the target setting; to perform training exercises and apply knowledge and skills; to review what has been learned; for systematization; preparation and issuance of an answer and many other specific costs.
Time spent on self-study: time spent on homework; to read additional literature; visiting electives and additional classes; participation in the work of circles; hobby classes and other expenses.
In this factor, there are more than 20 common factors associated with different costs of time for training and preparation for it. In total, as confirmed by factor analysis, at least 150 general factors affect the course and results of learning in a lesson, and the number of product-related causes reaches 400–450, and this is probably not a complete register of them.
So, the productivity of the didactic process is determined by the complex influence of four general factors. What are the proportions of their influence if the productivity of training fluctuates between 0-100%? Long-term experiments carried out using a complex technique have shown that the factors have different weight of influence, that is, their contribution to the formation of the final product turns out to be different (Fig. 8). In conditions of normal education, organizational and pedagogical influence (OPV) is more significant than others - 32%, followed by the importance of learners' learning ability - 28, educational material - 24 and time - 16%. In conditions of deviation of learning from the general norm, this ratio changes.
The greatest influence of OPV is easily explained by the fact that this factor contains the greatest number of product-generating causes. Therefore, in the practice of organizing the didactic process, it is necessary, first of all, to take care of creating appropriate learning conditions, providing the educational process with the necessary means, using effective technologies, teaching methods, and using progressive organizational forms.
Fig. 8. Influence of factors on the productivity of the didactic process
BS
Vi. Are the requirements for the use of factor analysis in didactics indicated correctly (yes - no)?
1) Instructions to the investigated;
2) the methods used;
3) rating scales, methods of calculating results;
4) the time for completing tasks, if it was limited;
5) test reliability coefficient;
6) statistical indicators - the nature of the distribution of results, the arithmetic mean or standard deviation;
7) characteristics of the sample and methods of its formation;
8) method for calculating correlation coefficients;
9) arguments for using this particular method, and not any other method;
10) interpretation of factors;
11) references to identical or related studies;
12) an explanation of how the research carried out advances the learning theory.
RB
Hierarchy of learning factors
Isolation and registration of reasons influencing learning is only the beginning of a systematic study of product-related causes. For diagnosing, forecasting, designing didactic processes, developing effective technologies for managing the productivity of learning, the question of the hierarchy (subordination, correlation) of factors is extremely important. Answering it, it is necessary to establish which factors to the greatest extent determine the productivity of the educational process, which teachers-practitioners should pay attention to first of all. It will be possible to take into account the influence of all product-generating factors, without exception, only in the distant future. Table 5 shows the hierarchy of learning factors established by your professor on the basis of long-term research using ranking, factor and correlation analysis, expert assessments, electronic modeling, computer verification, and other methods. The first 52 most significant factors are ranked in descending order of the weight of their influence, which is defined as the coefficient of mutual conjugation (correlation), established according to the Pearson criterion and expressing the degree of influence of each factor on the productivity of learning.
In addition to the already listed advantages arising from factor analysis (the possibility of performing high-quality professional analysis, diagnosing, predicting and designing didactic processes), knowledge of the hierarchy of factors, the quantitative values \u200b\u200bof the influence of each of them on the productivity of learning opens up fundamentally new approaches to solving many problems of the theory and practice of teaching , in particular - the use of computers for calculating productivity according to the given parameters, optimization of the strategy for achieving the given results.
Table 5
Influence of learning factors on the productivity of the didactic process
Thanks to this knowledge, the development of didactic systems from art, accessible only to masters with pedagogical flair and developed pedagogical intuition, turns into an everyday operation of creating and testing various training options and choosing the optimal one according to the established criteria.
Practitioners are already using applied computer programs, in particular the packages "Electronic School", "School Methodical Service", "Virtual Schoolboy", which help to calculate everything that can be practically considered in the educational process based on the selected factors and knowledge about their influence on the productivity of this process. Their application gradually turns didactics into a precisely calculated technological process of achieving a given learning productivity.
RB
"Dwarfs" become monsters
Recently, there have been intensive movements of factors within the hierarchy. "Dwarfs" become giants, and vice versa.
At the first ranking, they were not even included in the first 50, and today they are already in full swing in the pedagogical processes. It is primarily about health factors - environmental, geophysical, sanitary and hygienic.
Since the time of J. Korczak, the words “pain”, “suffering”, “blood” have not appeared on the pages of pedagogical literature. And today we cannot escape the facts - an increasing number of schools find themselves in the zones of man-made and ecological disasters. It is not up to schoolchildren who are suffocating from lack of oxygen: ringing in the ears or suddenly gushing blood from the nose directs his thoughts in a completely different direction. If the situation does not change, then, perhaps, arguments about the influence of other factors on the productivity of learning will very soon lose all meaning.
It is known: not only magnetic storms and sudden changes in atmospheric pressure, but a whole range of geophysical factors affect our well-being, activity and performance. The concept of "hard days" has already entered the pedagogical lexicon. According to the available data, their exclusion from the general monthly budget of working time not only does not lead to a decrease in labor productivity, but, on the contrary, increases the quantity and, most importantly, the quality of the work performed; the percentage of marriage is decreasing, the curves of accidents and injuries are decreasing, relations between people are improving, the invariable attributes of "hard days" disappear - irritability, anxiety, nervousness.
Is there a connection between geophysical factors and the productivity of teaching and upbringing of schoolchildren, the performance of teachers, the nature of relations in school collectives? Everything suggests that there is such a connection and, possibly, the influence of these factors is stronger than we assume. Little is known about the magnitude, nature, and intensity of communication, because it is only now that they begin to study it closely under the pressure of the growing number of school ailments and refusals to work. In our country and abroad, observations have been accumulated that irrefutably prove that among students and especially teachers a large percentage of meteorological dependences. There is no doubt that the effect of geophysical factors is aggravated by unfavorable and, in some regions, by hazardous environmental factors. Pupils and their mentors going through "hard days" would probably look better in the interior of a hospital room than in a temple of mental labor.
According to some reports, the number of "twos" and "threes" on "difficult days" is 40-50% higher than their number on ordinary days. Teacher P. Mazur from Lebedinskaya secondary school in Donetsk region conducted his own research on this issue: “I carefully looked through class journals for several months of this and last year, analyzed my current academic performance on geophysically unfavorable days and compared it with my academic performance on ordinary days. And what? There was a constant pattern - the number of unsatisfactory assessments increased significantly ”. Of course, this is a hard-to-prove connection, because a “two” is usually a consequence of a complex of reasons. Only large-scale studies carried out according to a special technique will clarify the share of geophysical factors proper.
German teachers also conducted observations aimed at finding out how the weather affects the attentiveness of students. 200 schoolchildren, pupils of grades 2 and 3, selected thematic pictures according to certain criteria. The studies were carried out in 17 different weather conditions, grouped into two types: cyclonic - with low atmospheric pressure, and anticyclonic - with high. It turned out that at low pressure the exercises were performed 17% better, in anticyclonic conditions the number of errors increased by 20% compared to the average results.
In this regard, let us pay attention to biorhythms - cyclical fluctuations of intellectual, physical and emotional activity. Is education influenced by biorhythms? On this score, there is conflicting evidence, but, apparently, in those days when all the curves are in the negative phase, it is futile to expect high results.
According to our observations, such a connection exists. The computer program "Biorhythm" was used to detect it. Pupils of grades 9-10 worked with her for 2 minutes after each informatics lesson. Attention was drawn to the phases of biorhythms of those schoolchildren who received unsatisfactory and excellent marks in the lesson. The statistics of coincidences of high academic performance with a positive phase and low performance with a negative one is 10–12%. However, the question remains open with biorhythms. Here is a methodological difficulty: until it is reliably established from what moment to count them - from the moment a person is born or from the moment the embryo is formed - we will not get reliable data.
Recognition of the influence of environmental and geophysical factors prompts us to identify general and regional conditions that should be taken into account in the design and implementation of the educational process. The latter, which is confirmed by practice, are increasingly becoming decisive in solving issues of the duration of training sessions, the transition to a 5-day working week, structuring the academic year, and many others. School laws today make it possible to design and organize the process based on local conditions.
Sat
Let's discuss a professional secret
Could you supplement what has been said with your observations? Have you ever seen adverse manifestations of climatic and geophysical influences on school processes? How did you act in the event of an unfavorable set of circumstances?
RB
Know to prevent
The factor by itself means little. It's all about how it is used, how it works for the end goal. Control, for example, is an important and universally recognized factor in productivity, but again, it can be turned into a powerful incentive, or it can be made a brake on the way to achieving high results. The same is the case with all other reasons subject to the will of teachers.
The achievements of cooperation pedagogy are the best proof of this. It is enough just to shift the emphasis in the relationship between teachers and students, so that many habitually acting factors play with new facets, and some of the traditionally inhibiting the process of teaching and upbringing become catalysts. For example, the eternal scourge of the school is a large amount of material being studied. For thinking teachers, he is not a hindrance, but even a help in the formation of general methods of thinking, the identification and understanding of large-scale connections.
By the way in which the same factors are used, what preference is given, one can distinguish not only pedagogical systems, technologies, but also the approaches of individual teachers. This proves that the scale of the value of factors is not constant, it is mobile and dynamic. In the pedagogy of cooperation - let's continue the comparison - the factors generated by the new relationships between teachers and students have come to the fore. Did you know about them before? Of course, but they did not pay due attention. Here's an example. In the 50s and 60s, a wave of research appeared, proving a well-known truth - the knowledge by students of the goals and objectives of the work ahead increases the productivity of learning. And what? Have authoritarian-minded teachers started to take care of such a "trifle"? It took the selfless devotion of innovative teachers to destroy the stereotype - the student is not an "attachment" to the school and the subject, but the subject of the active assimilation of scientific knowledge, and who, if not him, should first of all know what and for what purpose will be studied, to what extent it important and meaningful for him personally.
The pedagogy of cooperation has more fully taken into account other product-related causes that were previously considered secondary and insignificant. On the whole, she tried to release and mobilize internal reserves, the inexhaustible possibilities of the students themselves, to liberate the cognitive process, to introduce new personally significant stimuli. But we are still far from profound transformations in this area. Many factors, primarily of personal origin, still seem insignificant to us. We continue to roll on a well-worn track, relying on shared responsibility, healthy criticism and self-criticism.
However, everything is subject to rethinking. Even the fact that learning and development is an individual process, today we are forced to teach children in large groups by poverty. Of course, in these conditions, new factors come into play, which, in the absence of any other way out, we must put to service. In this case, we are talking about mutual learning, the power of which all teachers know, but they do not use enough.
While we are looking around trying to break the umbilical cord that connects us with the past, the world pedagogical practice is taking big steps along the path of the present, and not of imaginary cooperation.
... The working day of an American public school teacher begins at 7:30 am, although lessons will begin only at 8:30 am. Teachers use this hour not only for a general breakfast, discussion of news, but also for the current adjustment of the general strategy, achievement of unity and mutual understanding in the implementation of the educational process. Let's remember: A. Makarenko dreamed not about “stars”, but about teams of like-minded teachers, understanding how much this factor means in a properly organized educational process.
At 8.30, all teachers go out into the courtyard to meet the students arriving at the school, ask them about their health and news, and escort them to classes. Maybe this is being done in vain? Anyone who would have dared to single out such a factor yesterday would most likely be ridiculed.
Among the factors closing the hierarchy table, unexpectedly, there were reasons related to pedagogical technique - speech, facial expressions, physiognomic mask, gait, gesture, clothing, etc. in it the product is not significantly affected. They are greeted by clothes, escorted by the mind. Ask the children if the jacket of their favorite teacher was buttoned to all the buttons during the lesson - who paid attention to this? Children feel falsity, indifference, hypocrisy more acutely than adults, no one manages to fool them for a long time. Will smooth phrases hide the inability to predict and calculate the course of the process, to manage it with maximum benefit for the students?
Guess is good, but knowledge is better, said V. Hugo. Only knowledge reduces the risk of chance. Never before has pedagogy been so close to objective actions based on knowledge of product-related causes, there was no way to immediately check, confirm or refute the correctness of scientific recommendations. Not without reason we rely on new thinking, technology, and computerization. If the theory is correct and we apply it correctly in practice, the results will be true.
BS
Vii. What general factors combine the following product-related causes?
1. The level of general training.
Learning motivation.
Thinking of trainees.
The rate of assimilation of knowledge.
2. Time for the perception of knowledge.
Time elapsed after completion of training.
Time to review knowledge.
Time to organize.
4. Teaching methods.
Organizational forms.
Control and verification.
Conditions of education.
5. There is no correct answer.
VIII. Are the factors included in the top ten product-related causes listed correctly (yes - no)?
Motivation for learning.
Interest in educational work, cognitive activity.
Interest in the subject.
Attitude towards learning.
The need to learn.
Ability to learn.
The efficiency of students.
The scope of educational activities.
Training fitness.
Regularity of training, systematic implementation of educational tasks.
IB
Minimum law
Science goes in different ways towards the formulation of its laws and regularities. One of them is the method of internal analogies, which has not yet been studied much, but has already proven its effectiveness in various branches of knowledge.
Long-term studies of the complex influence of factors led to the creation of a visual spatial model of the productivity of the pedagogical process, the study of which made it possible to arrive at a theoretical formulation of the law of influence of the least factor.
What determines the quantity and quality of a pedagogical product? Let us recall the essence of the factors. They are understood as good reasons on which the course and results of the educational process depend. There are many reasons: as a first approximation, we identified over 200 of them. For the most important of them, the magnitudes and forms of influence on the final result were established, which made it possible to come up with computer diagnostics of the pedagogical process. Now you can quickly get detailed diagnostic cards. Open the book on page 406 for such a map; factors on it are shown in the form of bars of different heights, corresponding to the degree of their influence.
We put on a mental experience, or, if you like, do it in nature. We take the diagnostic card shown in Fig. 31, fold it into a tube, glue the ends, glue the bottom. The result is a cylinder - something like a bucket or a barrel. Only its upper edge turned out to be uneven, composed of columns of different heights.
It is difficult to assume that the barrel was made with uneven upper edges (recall: a barrel is an old Russian measure of the volume of liquids, equal to 40 buckets, this is 491.96 liters). The barrel is made up of rivets - narrow planks. We have got a "pedagogical barrel" that simulates the educational process, ie, made up of narrow boards-factors of different heights.
Education, upbringing, human development is the filling of the hereditary program with information that is missing for life. From birth, the program contains only the primary set of instincts necessary for survival, and throughout life it is filled with the necessary knowledge, skills, ways of thinking and acting. Once people learned in a natural way, filling in the free areas of the hereditary program took a long time, now, to facilitate and speed up this process, schools have been invented where programs are filled in an organized way - quickly and efficiently, although not always in accordance with the requests of students.
Ancient allegories explained the education of a growing person as filling an “empty vessel”, putting written knowledge on a “blank board”. These simple, clear and understandable concepts find modern scientific confirmation: yes, “filling” of the hereditary program really takes place, and the more knowledge and skills remain “in the vessel”, the better the process goes, the more productivity it has. “Barrel” is a visual model of the formed product, where the total height of the vessel determines its size, and the height of each “rivet” corresponds to the influence of a separate cause.
What is the productivity of a process based on diverse and multi-level factors? In our model, the maximum possible result will be limited by the cut of the highest riveting, and actually obtained - by the cut of the lowest rivet. The difference between them will show the amount of the shortfall. It is clear that if you diligently increase the height of not the lowest "riveting", but all others, the result will not increase. Productivity depends on the height (intensity of influence) of the smallest (minimum) factor. To raise it, this factor should be increased.
Of course, in practice, everything is a hundred times more complicated. Nevertheless, the considered analogy, and most importantly, the ideas about the mechanisms of the formation of a pedagogical product, push us to the following conclusions:
1) the size and nature of the learning product are set by the target setting for the formation of an educated person: in the ideal case, this is a comprehensive and harmonious development, in real - a practically expedient and really achievable level;
2) the product, no matter how complex, is formed element by element, and not individual parts are of paramount importance, but their organic unity, which represents a new quality;
3) the product of training is created by the complex effect of product-generating factors, and here the decisive role is played not by the factors themselves and not even their combinations, but by the intensity of the action of various causes during the formation of the product;
4) the quantity and quality of the product depend on the magnitude of the acting factors and can be determined by measuring them and integrating their joint influence;
5) the greatest influence on the formation of the product is exerted by the constantly acting and most significant learning factors.
The productivity of the pedagogical process depends primarily on the factor with the lowest value. So we come to the concept of "minimum factor". It is he who plays a decisive role. In vain we would increase the importance of other factors - we will not get a better result, all our efforts will “flow out” through a hole punched by an insufficiently formed quality. The minimum factor fundamentally limits the level of training. Of course, every student has his own: someone - inattention, someone - thinking, someone - perseverance or efficiency. The minimum factor is the student's personal problem. Without increasing its value, it is futile to hope for a better result. Establishing what factor it is is the most important task of practical diagnostics. Taking into account the effect of the minimum factor, it is possible to confidently predict the development of the process and its results.
The principle of the minimum factor exists and operates in many aspects of human existence. For example, no matter how healthy all the internal organs of a person are, a disease of one is enough to make him feel sick and even die. The level of health is the state of the diseased organ itself, the same minimum factor. Likewise, in a TV or car: one low-quality part is enough for the overall reliability of the device to be low. The ancients were right - the strongest chain is never stronger than its weakest link.
Based on the law of the minimum factor, it is easy to explain the reasons for pedagogical errors. Wherever they took place, the teacher did not build up those factors that were in the minimum value. For example, a student lacks attentiveness, and the teacher stubbornly increases the number of repetitions or tries to mobilize thinking where it would be necessary to form the ability to learn. The conclusion is obvious: you need to carefully diagnose the qualities necessary for successful training, establish which of them are formed worse than others, and then bring them to the appropriate level.