Rachinsky's paintings. Nikolai Bogdanov-Belsky

Lesson Objectives:

• development of the ability to observe;
• development of the ability to think;
• development of the ability to express thought;
• instilling an interest in mathematics;
• touching the art of N.P. Bogdanov-Belsky.

DURING THE CLASSES

Teaching is the work that educates and shapes a person.

Four pages from the life of a painting

Page one

The painting “Mental Account” was painted in 1895, that is, 110 years ago. This is a kind of anniversary of the picture, which is the creation of human hands. What is shown in the picture? Some boys have gathered around the blackboard and are looking at something. Two boys (these are the ones in front) turned away from the blackboard and remember something, or maybe they count. One boy whispers something into the ear of a man, presumably the teacher, while the other appears to be eavesdropping.

- And why are they in bast shoes?

“Why are there no girls here, only boys?”

Why are they standing with their backs to the teacher?

– What are they doing?

You have probably already understood that students and a teacher are depicted here. Of course, the costumes of the students are unusual: some of the guys are wearing bast shoes, and one of the characters in the picture (the one in the foreground), in addition, has a torn shirt. It is clear that this picture is not from our school life. Here is the inscription on the picture 1895 - the time of the old pre-revolutionary school. The peasants then lived in poverty, they themselves and their children wore bast shoes. The artist depicted peasant children here. Only at that time, few of them could study even in elementary school. Look at the picture: after all, only three of the students are wearing bast shoes, and the rest are in boots. Obviously, guys from rich families. Well, why girls are not depicted in the picture is also not difficult to understand: after all, at that time, girls, as a rule, were not accepted to school. Teaching was “not their business”, and not all of the boys studied.

Page two

This picture is called "Mental Account". See how the boy in the foreground of the picture thinks intently. It is evident that the teacher gave a difficult task. But, probably, this student will soon finish his work, and there should be no mistake: he takes mental counting very seriously. But the student who whispers something in the teacher's ear, apparently, has already solved the problem, only his answer is not quite correct. Look: the teacher listens attentively to the student's answer, but there is no approval on his face, which means that the student did something wrong. Or maybe the teacher patiently waits for others to count correctly, just like the first one, and therefore is in no hurry to approve his answer?

- No, the first one will give the correct answer, the one in front: it is immediately clear that he is the best student in the class.

And what task did the teacher give them? Can't we solve it too?

- But try it.

I will write on the board as you used to write:

(10 10+11 11+12 12+13 13+14 14):365

As you can see, each of the numbers 10, 11, 12, 13 and 14 must be multiplied by itself, the results added up, and the resulting sum divided by 365.

– This is the task (you won’t solve such an example soon, and even in your mind). But still try to count verbally, in difficult places I will help you. Ten ten is 100, everyone knows that. Eleven times eleven is also easy to count: 11 10=110, and even 11 is 121 in total. 144. I also calculated that 13 13=169 and 14 14=196.

But while I was multiplying, I almost forgot what numbers I got. Then I remembered them, and after all, these numbers still need to be added, and then the sum should be divided by 365. No, you yourself will not be able to calculate this.

- I'll have to help a little.

- What numbers did you get?

- 100, 121, 144, 169 and 196 - this was counted by many.

- Now you probably want to add all five numbers at once, and then divide the results by 365?

We will do it differently.

- Well, let's add the first three numbers: 100, 121, 144. How much will it be?

How much should be divided?

– Also on 365!

- How much will it be if the sum of the first three numbers is divided by 365?

- One! - everyone will figure it out.

- Now add the other two numbers: 169 and 196. How much will it be?

– Also 365!

- Here is an example, and quite simple. It turns out that only two!

- Only to solve it, you need to know well that the sum can be divided not all at once, but in parts, each term separately, or in groups of two or three terms, and then add up the resulting results.

Page three

This picture is called "Mental Account". It was painted by the artist Nikolai Petrovich Bogdanov-Belsky, who lived from 1868 to 1945.

Bogdanov-Belsky knew his little heroes very well: he grew up in their environment, was once a shepherd boy. “... I am the illegitimate son of a poor woman, that’s why Bogdanov, and Belsky became the name of the county,” the artist said about himself.

He was lucky to get into the school of the famous Russian teacher Professor S.A. Rachinsky, who noticed the artistic talent of the boy and helped him get an art education.

N.P. Bogdanov-Belsky graduated from the Moscow School of Painting, Sculpture and Architecture, studied under such famous artists like V.D. Polenov, V.E. Makovsky.

Many portraits and landscapes were painted by Bogdanov-Belsky, but he remained in the memory of people, first of all, as an artist who managed to poetically and faithfully tell about the smart rural children eagerly reaching for knowledge.

Which of us is not familiar with the paintings “At the Doors of the School”, “Beginners”, “Composition”, “Village Friends”, “At the Sick Teacher”, “Voice Test”, - these are the names of just some of them. Most often, the artist depicts children at school. Charming, trusting, concentrated, thoughtful, full of lively interest and always marked by a natural mind - Bogdanov-Belsky knew and loved peasant children like that, immortalized in his works like that.

Page Four

The artist depicted non-fictional students and teachers in this picture. From 1833 to 1902, the famous Russian teacher Sergei Aleksandrovich Rachinsky, a remarkable representative of Russian educated people of the century before last, lived. He was a doctor of natural sciences and a professor of botany at Moscow University. In 1868 S.A. Rachinsky decides to go to the people. "He takes the exam" for the title of teacher primary school. At his own expense, he opens a school for peasant children in the village of Tatyevo, Smolensk province, and becomes a teacher there. So, his students counted so well orally that all the visitors to the school were surprised at this. As you can see, the artist depicted S.A. Rachinsky with his students at the lesson of oral problem solving. By the way, the artist N.P. Bogdanov-Belsky was a student of S.A. Rachinsky.

This picture is a hymn to the teacher and the student.

When I come to the Tretyakov Gallery with another group then, of course, I know that mandatory list pictures that you can't miss. I keep everything in my head. From start to finish, lined up in one line, these paintings should tell the story of the development of our painting. With all that is not a small part of our national heritage and spiritual culture. These are all pictures, so to speak, of the first order, which cannot be avoided without the history not being flawed. But there are some that are completely and not required to be shown. And my choice here depends only on me. From my location to the group, from the mood, but also the availability of free time.

Well, the painting "Oral Account" by the artist Bogdan-Belsky is exclusively for the soul. And I can't get past it. Yes, and how to get through, because I know in advance that the attention of our foreign friends in this particular picture will manifest itself to such an extent that it will be simply impossible not to stop. Well, do not drag them away by force.

Why? This artist is not one of the most famous Russian painters. His name is known for the most part by experts - art critics. But this picture will make, nevertheless, stop anyone. And it will attract the attention of a foreigner to no lesser extent.

Here we stand, and for a long time we examine with interest everything in it, even the most small parts. And I understand that I don’t need to explain much here. Moreover, I feel that with my words I can even interfere with the perception of what I see. Well, as if I started to give comments at a time when the ear wants to enjoy the melody that has captured us.

Nevertheless, some explanations still need to be made. Even necessary. What do we see? And we see eleven village boys immersed in the thought process in search of an answer to a mathematical equation written on the blackboard by their dodgy teacher.

Thought! So much in this sound! Thought in commonwealth with difficulty created man. Auguste Rodin gave us the best evidence of this in his Thinker. But when I look at this famous sculpture, and I saw its original in the Rodin Museum in Paris, then it gives rise to some strange feeling in me. And, oddly enough, it is a feeling of fear, and even horror. Some kind of bestial power emanates from the mental tension of this creature, placed in the courtyard of the museum. And I involuntarily see the wonderful discoveries that this creature sitting on a rock is preparing for us in its tormenting mental effort. For example, opening atomic bomb threatening to destroy humanity itself along with this Thinker. And we already know for certain that this bestial man will come to the invention of a terrible bomb that can wipe out all life on earth.

But the boys of the artist Bogdan-Belsky do not frighten me at all. Against. I look at them and feel how warm sympathy for them is born in my soul. I want to smile. And I feel the joy that surges to my heart from contemplating the touching scene. The mental search expressed in the faces of these boys delights and excites me. It also makes you think about something else.

The picture was painted in 1895. A few years earlier, in 1887, the infamous circular was adopted.

By this circular approved by the emperor Alexander III and received the ironic name “about the cook's children” in society, it was instructed the educational authorities to allow only well-to-do children in the gymnasium and progymnasium, that is, “only such children who are in the care of persons representing sufficient guarantee of proper home supervision over them and in providing them with the necessary for learning convenience. My God, what a wonderful clerical syllable.

And further in the circular it was explained that “with the steadfast observance of this rule, gymnasiums and pro-gymnasiums will be freed from the admission of children of coachmen, lackeys, cooks, laundresses, small shopkeepers and similar people to them.

Like this! Now look at these young quick-witted Newtons in bast shoes and tell me how many chances they have to become "reasonable and great."

Though some people might get lucky. Because they were all lucky with the teacher. He was famous. Moreover, he was a teacher from God. His name was Sergey Alexandrovich Rachinsky. Today, he is almost unknown. And he so deserved all his life to remain in our memory. Take a closer look at him. Here he sits surrounded by his bastard students.

He was a botanist, mathematician, and also a professor at Moscow University. But most importantly, he was a teacher not only by profession, but also by his entire mental make-up, by vocation. And he loved children.

Having gained learning, he returned to his native village of Tatevo. And he built this school that we see in the picture. Yes, and with a hostel for village children. Because, let's tell the truth, he did not accept everyone at school. He himself selected unlike Leo Tolstoy, whom he accepted into his school all the surrounding children.

Rachinsky created his own technique for oral account, which, of course, not everyone could learn. Only the chosen ones. He wanted to work with selected material. And he got the desired result. Therefore, do not be surprised that such a difficult task is solved by children in bast shoes and shirts for graduation.

And the artist Bogdanov-Belsky himself went through this school. And how could he forget his first teacher. No, he couldn't. And this picture is a tribute to the memory of a beloved teacher. And Rachinsky taught at this school not only mathematics, but also, along with other subjects, painting and drawing. And he was the first to notice the boy's attraction to painting. And he sent him to continue studying this subject not just anywhere, but to the Trinity-Sergius Lavra, to the icon-painting workshop. And then - more. The young man continued to comprehend the art of painting at the no less famous Moscow School of Painting, Sculpture and Architecture, on Myasnitskaya Street. And what teachers he had! Polenov, Makovsky, Pryanishnikov. And then Repin. One of the paintings of the young artist "The Future Monk" was bought by Empress Maria Feodorovna herself.

That is, Sergei Alexandrovich gave him a ticket to life. And after that, how could an already established artist thank his teacher? And that's just this picture. This is the biggest thing he could do. And he did the right thing. Thanks to him, today we also have a visible image of this wonderful person, teacher Rachinsky.

Lucky, of course, the boy. Just incredibly lucky. Well, who was he? Illegitimate son of a laborer! And what a future he could have if he did not get into the school of the famous teacher.

The teacher wrote a mathematical equation on the blackboard. You can easily see it. And rewrite. And try to decide. Once there was a math teacher in my group. He carefully rewrote the equation on a piece of paper in a notebook and began to solve. And I decided. And spent at least five minutes on it. Try it too. And I don't even bother. Because I didn't have such a teacher at school. Yes, I think that even if I had, I would not have succeeded. Well, I'm not a mathematician. And to this day.

And I realized this already in the fifth grade. Even though I was still very small, but even then I realized that all these brackets and squiggles in no way, in no way, would be useful to me in life. They won't come out sideways. And in no way these numbers did not excite my soul. On the contrary, they were only indignant. And I do not have a soul for them to this day.

At that time, I still unconsciously found my attempts to solve all these numbers with all sorts of icons useless and even harmful. And they evoked nothing but a quiet and unspoken hatred in me. And when all sorts of cosines with tangents came, complete darkness ensued. It pissed me off that all this algebraic bullshit only kept me away from more useful and exciting things in the world. For example, from geography, astronomy, drawing and literature.

Yes, since then I have not learned what cotangents and sines are. But I don’t feel any pain or regret about it either. The absence of this knowledge did not affect everything in my already and not small life. It is still a mystery to me today how electrons run at incredible speed inside an iron wire for terrible distances, creating an electric current. Yes, and that's not all. In some small fraction of a second, they can suddenly stop and run together back. Well, let them run, I think. Whoever is interested, let him do it.

But that's not the point. And the question was that even in those small years of my life I did not understand why it was necessary to torment me with something that my soul completely rejected. And I was right in my painful doubts.

Later, when I became a teacher myself, I found the answer to everything. And the explanation is that there is such a bar, such a level of knowledge that Public School so that the country does not lag behind others in its development, following the lead of losers like me.

To find a diamond or a grain of gold, you need to process tons of waste rock. It is called dump, unnecessary, empty. But without this unnecessary breed and a diamond with grains of gold, not to mention nuggets, is also not found. Well, so I and others like me were this very dump breed, which was only needed to nurture needed by the country mathematicians and even mathematical prodigies. But how could I then know about it with all my attempts to solve the equations that the good teacher wrote to us on the blackboard. That is, with my torments and inferiority complexes, I contributed to the birth of real mathematicians. And there is no escape from this obvious truth.

So it was, so it is, and so it will always be. And I know this for certain today. Because I am not only a translator, but also a French teacher. I teach and I know for sure that of my students, and in each group there are approximately 12 of them, two to three students will know the language. The rest are crap. Or dump rock, if you like. For various reasons.

It is you in the picture that you see eleven enthusiastic boys with burning eyes. But this is a picture. But life is not like that at all. And any teacher will tell you that.

There are different reasons why not. To be clear, let me give you the following example. A mother comes to me and asks how long it will take me to teach her boy French. I don't know what to answer her. I mean, I know, of course. But I don’t know how to answer without offending the assertive mother. And she should answer the following:

Language in 16 hours is only on TV. I do not know the degree of interest and motivation of your boy. There is no motivation - and plant at least three tutor professors with your dear child, nothing will come of it. And then there is another important thing like abilities. And some have these abilities, while others do not have them at all. So the genes, God or someone else unknown to me decided. For example, a girl wants to learn ballroom dancing, and God gave her neither a sense of rhythm, nor plasticity, nor, just oh horror, an appropriate figure (well, she became fat or lanky). And so you want. What are you going to do here if nature itself has risen across. And so it is in every case. And in language learning too.

But, really, in this place I want to put a big comma to myself. Not so simple. Motivation is a moving thing. Today it is not, but tomorrow it appeared. That is what happened to me myself. My first teacher of French, dear Rosa Naumovna, seemed to be very surprised when she learned that it was her subject that would become the work of my whole life.

*****
But back to the teacher Rachinsky. I confess that I am immeasurably more interested in his portrait than in the personality of the artist. He was a well-born nobleman and not at all a poor man. He had his own estate. And to all this he had a learned head. After all, it was he who first translated The Origin of Species by Charles Darwin into Russian. Although here is a strange fact that struck me. He was a deeply religious person. And at the same time, he translated the famous materialistic theory, which was absolutely disgusting to his soul.

He lived in Moscow on Malaya Dmitrovka, and was familiar with many famous people. For example, with Leo Tolstoy. And it was Tolstoy who inspired him to the cause of public education. Even in his youth, Tolstoy was fond of the ideas of Jean-Jacques Rousseau, the Great Enlightener was his idol. He, for example, wrote a wonderful pedagogical work"Emil or about education". I not only read it, but wrote on it coursework At the institute. To tell the truth, Rousseau, as it seemed to me, put forward ideas in this work, well, more than original ones. And Tolstoy himself was fascinated by the following thought of the great educator and philosopher:

“Everything comes out good from the hands of the Creator, everything degenerates in the hands of man. He forces one soil to nourish the plants grown on another, one tree to bear the fruit of another. He mixes and confuses climates, elements, seasons. He disfigures his dog, his horse, his slave. He turns everything upside down, distorts everything, loves the ugly, the monstrous. He does not want to see anything the way nature created it, not excluding man: and he needs to train a man, like a horse for an arena, he needs to remake in his own way, as he uprooted a tree in his garden.

And in his declining years, Tolstoy tried to put into practice the above wonderful idea. He wrote textbooks and manuals. Wrote the famous "ABC" He also wrote children's stories. Who does not know the famous Filippok or the story about the bone.
*****

As for Rachinsky, here, as they say, two kindred souls met. So much so that, inspired by the ideas of Tolstoy, Rachinsky left Moscow and returned to his ancestral village of Tatevo. And built by example famous writer with their own money, a school and a hostel for gifted village children. And then he completely became the ideologist of the parochial school in the countries.

This is his activity in the field of public education was noticed at the very top. Here, read what Pobedonostsev writes about him to Emperor Alexander III:

“If you please remember how a few years ago I reported to you about Sergei Rachinsky, a respectable man who, having left his professorship at Moscow University, went to live in his estate, in the most remote wilderness of the Belsky district of the Smolensk province, and lives there without a break here for more than 14 years, working from morning to night for the benefit of the people. He took a deep breath new life into a whole generation of peasants ... He became a true benefactor of the area, having founded and leads, with the help of 4 priests, 5 public schools, which now represent a model for the whole earth. This is a wonderful person. Everything that he has, and all the means of his estate, he gives to the penny for this business, limiting his needs to the last degree.

And here is what Nicholas II himself writes in the name of Sergei Rachinsky:

“The schools you founded and run, being among the parochial ones, have become a nursery of educated figures in the same spirit, a school of labor, sobriety and good morals, and a living model for all such institutions. close to heart My concern for public education, which you worthily serve, prompts Me to express my sincere gratitude to you. I stay with you, benevolent Nikolay"

In conclusion, having plucked up courage, I want to add a few words of my own to the statements of the two persons mentioned above. These words will be about the teacher.

In the world there are a lot of professions. All living things on Earth are busy trying to prolong their existence. And above all, in order to find something to eat. Both herbivores and carnivores. Both the big ones and the smallest ones. All! And the man too. But a person has a lot of such opportunities. The choice of activities is overwhelming. That is, the occupations that a person indulges in in order to earn his bread, his living.

But of all these occupations, there is an insignificant percentage of those professions that can give complete satisfaction to the soul. The vast majority of all other things come down to a routine, daily repetition of the same thing. The same actions of mental and physical order. Even in the so-called creative professions. I won't even name them. Without the slightest chance For spiritual growth. Stamp the same nut all your life. Or drive on the same rails in a straight line and figuratively until the end of your pensionable length of service. And there's nothing you can do about it. Such is our human universe. It is arranged in a life who as can.

But, I repeat, there are few professions in which the whole life and the whole work of life is based solely on spiritual need. One of them is the teacher. WITH capital letter. I know what I'm talking about. Since I myself have been in this topic for many years. A teacher is both an earthly cross, and a calling, and torment, and joy all together. Without all this, there is no teacher. And there are enough of them, even among those who have work book in the profession column it is written - a teacher.

And you need to prove your right to be a teacher every day, from the very second when you crossed the threshold of the class. And sometimes it's not so easy. Do not think that beyond this threshold only happy moments of your life are waiting for you. And you should also not count on the fact that the small people will meet you all in anticipation of the knowledge that you are ready to put into their heads and souls. That the entire class space is inhabited entirely by angelic, incorporeal cherubs. These cherubs know how to bite like that sometimes. And how much it hurts too. This nonsense needs to be put out of your head. On the contrary, you must remember that in this bright room with huge windows, ruthless animals are waiting for you, who still have a difficult path to becoming human. And it is the teacher who must lead them along this path.

I distinctly remember one such "cherub" when I first came to class during my internship. I was warned. There is one boy there. Not very simple. And God help you deal with it.

How much time has passed, but I still remember it. If only because he had some strange last name. Noak. That is, I knew that the PLA is the People's liberation army China. But here ... I went in and instantly figured out this asshole. This sixth grader, who was sitting at the last desk, put one of his feet on the table when I appeared. Everyone got up. Except him. I realized that this Noak wanted to immediately declare to me and everyone else in this manner who is their boss here.

Sit down, children, I said. Everyone sat down and waited with interest to continue. Noack's leg remained in the same position. I approached him, still not knowing what to do or what to say.

Are you going to sit like this the whole lesson? Very uncomfortable posture! - I said, feeling a wave of hatred rise in me for this insolent, intent on disrupting my first lesson in my life.

He did not answer, turned away and made a forward movement with his lower lip as a sign of complete contempt for me. And he even spat in the direction of the window. And then, not realizing what I was doing, I grabbed him by the collar and kicked him out of the classroom into the corridor with a kick in the ass. Well, he was still young and hot. There was an unusual silence in the classroom. As if it were completely empty. Everyone looked at me dumbfounded. "Vo gives" - someone whispered loudly. A desperate thought flashed through my head: “That's it, I have nothing else to do at school! End!" And I was very wrong. This was only the beginning of the long journey of my teaching.

Ways of happy peak joyful moments and cruel disappointments. At the same time, I remember another teacher. Teacher Melnikov from the film "We'll Live Until Monday." There was a day and an hour when a deep depression befell him. And it was from what! “You sow here a reasonable, good eternal, and henbane grows - a thistle,” he once said in his hearts. And he wanted to leave school. At all! And he didn't leave. Because if you are a real teacher, then this is for you forever. Because you understand that you will not find yourself in any other business. Do not express yourself to the fullest. Got it - be patient. It is a great duty and a great honor to be a teacher. And this is exactly how Sergei Alexandrovich Rachinsky understood this, who, of his own free will, placed himself at the black blackboard for his entire life term.

P.S. If you still tried to solve this equation on the board, then the correct answer will be 2.

Many have seen the picture "Mental account in public school"The end of the 19th century, a folk school, a blackboard, an intelligent teacher, poorly dressed children, 9–10 years old, enthusiastically try to solve the problem written on the blackboard in their minds. The first one who decides tells the answer to the teacher in the ear, in a whisper, so that others do not lose interest.

Now look at the problem: (10 squared + 11 squared + 12 squared + 13 squared + 14 squared) / 365 =???

Crap! Crap! Crap! Our children at the age of 9 will not solve such a problem, at least in their minds! Why were grimy and barefoot village children taught so well in a one-room wooden school, while our children are taught so badly?!

Don't be quick to get angry. Take a look at the picture. Don't you think that the teacher looks too intelligent, somehow like a professor, and is dressed with obvious pretense? Why in school class such a high ceiling and an expensive stove with white tiles? Did the village schools and the teachers in them really look like this?

Of course they didn't look like that. The picture is called "Mental counting in the folk school of S.A. Rachinsky." Sergey Rachinsky - professor of botany at Moscow University, a person with certain government connections(for example, a friend of the chief prosecutor of the Synod Pobedonostsev), a landowner - in the middle of his life he abandoned all his affairs, went to his estate (Tatevo in the Smolensk province) and started there (of course, at his own expense) an experimental public school.

The school was one-class, which did not mean that it taught for one year. In such a school they taught then 3-4 years (and in two-class schools - 4-5 years, in three-class schools - 6 years). The word one-class meant that children of three years of study make up a single class, and one teacher deals with them all within the same lesson. It was quite a tricky thing: while the children of one year of study were doing some kind of written exercise, the children of the second year answered at the blackboard, the children of the third year read the textbook, etc., and the teacher alternately paid attention to each group.

Rachinsky's pedagogical theory was very original, and its different parts somehow poorly converged with each other. Firstly, Rachinsky considered the teaching of the Church Slavonic language and the Law of God to be the basis of education for the people, and not so much explanatory as consisting in memorizing prayers. Rachinsky firmly believed that knowing by heart a certain amount of prayers, the child will certainly grow up as a highly moral person, and the very sounds of the Church Slavonic language will already have an effect that improves morality.

Secondly, Rachinsky believed that it was useful for the peasants and they needed to quickly count in their minds. teaching mathematical theory Rachinsky was not very interested, but he did a very good job of mental counting in his school. The students firmly and quickly answered how much change per ruble should be given to someone who buys 6 3/4 pounds of carrots at 8 1/2 kopecks per pound. The squaring shown in the painting was the most complex mathematical operation studied at his school.

And finally, Rachinsky was a supporter of a very practical teaching of the Russian language - the students were not required to have any special spelling skills or good handwriting, they were not taught theoretical grammar at all. The main thing was to learn to read and write fluently, albeit in a clumsy handwriting and not very competently, but it’s clear that a peasant could come in handy in everyday life: simple letters, petitions, etc. Even at Rachinsky’s school some manual labor was taught, the children sang in chorus, And that's where education ends.

Rachinsky was a real enthusiast. School became his whole life. Rachinsky's children lived in a hostel and were organized into a commune: they performed all the housekeeping work for themselves and the school. Rachinsky, who had no family, spent all the time with the children from early morning until late at night, and since he was a very kind, noble and sincerely attached to children, his influence on the students was enormous. By the way, Rachinsky gave the first child who solved the problem a gingerbread (in the literal sense of the word, he did not have a whip).

School classes themselves took 5–6 months a year, and the rest of the time Rachinsky worked individually with older children, preparing them for admission to various educational institutions of the next level; elementary folk school was not directly related to other educational institutions and after it it was impossible to continue training without additional training. Rachinsky wanted to see the most advanced of his students as teachers. elementary school and priests, so that he prepared children mainly for theological and teacher's seminaries. There were also significant exceptions - first of all, this is the author of the painting himself, Nikolai Bogdanov-Belsky, whom Rachinsky helped to get into the Moscow School of Painting, Sculpture and Architecture. But, oddly enough, to lead peasant children along the main path of an educated person - a gymnasium / university / public service- Rachinsky did not want to.

Rachinsky wrote popular pedagogical articles and continued to enjoy a certain influence in the capital's intellectual circles. The most important was the acquaintance with the ultra-influential Pobedonostsev. Under a certain influence of the ideas of Rachinsky, the spiritual department decided that there would be no sense in the zemstvo school - the liberals would not teach children good - and in the mid-1890s began to develop their own independent network of parochial schools.

In some ways, the parochial schools were similar to the Rachinsky school - they had a lot of Church Slavonic and prayers, and the rest of the subjects were reduced accordingly. But, alas, the dignity of the Tatev school was not transferred to them. The priests showed little interest in school work, ran the schools under duress, did not teach in these schools themselves, and hired the most third-rate teachers, and paid them noticeably less than in zemstvo schools. The peasants took a dislike to the parochial school, because they realized that they almost didn’t teach anything useful there, and prayers were of little interest to them. By the way, it was the teachers of the church school, recruited from pariahs of the clergy, who turned out to be one of the most revolutionized professional groups of that time, and it was through them that socialist propaganda actively penetrated into the village.

Now we see that this is a common thing - any author's pedagogy, designed for the deep involvement and enthusiasm of the teacher, immediately dies with mass reproduction, falling into the hands of uninterested and sluggish people. But for that time it was big bummer. Church-parish schools, which by 1900 accounted for about a third of primary public schools, turned out to be disliked by everyone. When, starting in 1907, the state began to send elementary education a lot of money, there was no question of passing subsidies to church schools through the Duma, almost all the funds went to the Zemstvo.

The more common zemstvo school was quite different from the Rachinsky school. For starters, the Zemstvo considered the Law of God completely useless. It was impossible to refuse his teaching, according to political reasons, so the Zemstvos pushed him into a corner as best they could. The law of God was taught by an underpaid and neglected parish priest, with corresponding results.

Mathematics at the Zemstvo school was taught worse than at Rachinsky, and to a lesser extent. The course ended with operations with simple fractions and non-metric units. Up to raising to a degree, training did not reach, so the students of an ordinary elementary school simply would not understand the task depicted in the picture.

The zemstvo school tried to turn the teaching of the Russian language into world science, through the so-called explanatory reading. The technique consisted in dictating educational text in Russian, the teacher also additionally explained to the students what was said in the text itself. In such a palliative way, the lessons of the Russian language also turned into geography, natural history, history - that is, into all those developing subjects that could not find a place in the short course of a one-class school.

So, our picture depicts not a typical, but a unique school. This is a monument to Sergei Rachinsky, unique personality and teacher, the last representative of that cohort of conservatives and patriots, to which one could not yet attribute famous expression"Patriotism is the last refuge of a scoundrel." The mass public school was economically equipped much poorer, the mathematics course in it was shorter and simpler, and teaching was weaker. And, of course, the students of an ordinary elementary school could not only solve, but also understand the problem reproduced in the picture.

By the way, how do students solve the problem on the board? Only direct, head-on: multiply 10 by 10, remember the result, multiply 11 by 11, add both results, and so on. Rachinsky believed that the peasant did not have writing materials at hand, so he taught only oral methods of counting, omitting all arithmetic and algebraic transformations that required calculations on paper.

P.S. For some reason, only boys are depicted in the picture, while all the materials show that children of both sexes studied with Rachinsky. What that means, I couldn't figure it out.

In one of the halls Tretyakov Gallery you can see the famous painting by the artist N.P. Bogdanov-Belsky "Oral Account". It depicts a lesson in rural school. Classes are conducted by an old teacher. Village boys in poor peasant shirts and bast shoes crowded around. They solve the task proposed by the teacher with concentration and enthusiasm... A story familiar to many from childhood, but not many people know that this is not the artist's fiction and behind all the characters in the picture there are real people painted by him from nature - people whom he knew and loved, and most importantly actor- an elderly teacher, a man who played a key role in the artist's biography. His fate is amazing and unusual - after all, this man is a wonderful Russian teacher and educator, teacher of peasant children Sergey Alexandrovich Rachinsky (1833-1902)

N.P. Bogdanov-Belsky "Oral counting in the Rachinsky public school" 1895.

Future teacher S.A. Rachinsky.

Sergey Alexandrovich Rachinsky was born on the estate of Tatevo, Belsky district, Smolensk province in noble family. His father Alexander Antonovich Rachinsky, a former participant in the December movement, was exiled to his family estate Tatevo. Here, on May 2, 1833, the future teacher was born. His mother was the sister of the poet E.A. Baratynsky and the Rachinsky family closely communicated with many representatives of Russian culture. In the family, parents gave great attention comprehensive education for their children. All this was very useful to Rachinsky in the future. Having received excellent education at the natural faculty of Moscow University, he travels a lot, meets interesting people, studies philosophy, literature, music and much more. After a while he writes a few scientific works and receives a doctorate degree and the chair of a professor of botany at Moscow University. But his interests were not limited to scientific frameworks. The future rural teacher studied literary creativity, wrote poetry and prose, played the piano perfectly, was a collector of folklore - folk songs and handicrafts. Khomyakov, Tyutchev, Aksakov, Turgenev, Rubinstein, Tchaikovsky and Tolstoy often visited his apartment in Moscow. Sergei Alexandrovich was the author of the libretto for two operas by P.I. Tchaikovsky, who listened to his advice and recommendations and dedicated his first string Quartet. With L.N. Tolstoy Rachinsky had friendly and family relations, since the niece of Sergei Alexandrovich, the daughter of his brother, the rector of the Petrovsky (now Timiryazev) Academy Konstantin Alexandrovich Rachinsky - Maria was the wife of Sergei Lvovich, son of Tolstoy. The correspondence between Tolstoy and Rachinsky is interesting, full of discussions and disputes about public education.

In 1867, due to circumstances, Rachinsky left the professorship at Moscow University, and with it all the fuss metropolitan life, returns to his native Tatevo, opens a school there and devotes himself to teaching and educating peasant children. A few years later, the Smolensk village of Tatevo became known throughout Russia. Education and service common people from now on it will be his life's work.

Professor of Botany at Moscow University Sergei Alexandrovich Rachinsky.

Rachinsky is developing an innovative, unusual for that time, system of teaching children. The combination of theoretical and practical studies becomes the basis of this system. At the lessons, children were taught various crafts necessary for the peasants. The boys learned carpentry and bookbinding. They worked in the school garden and in the apiary. Natural history lessons were held in the garden, in the field and in the meadow. The pride of the school church choir and an icon painting workshop. At his own expense, Rachinsky built a boarding school for children who come from far away and do not have housing.

N.P. Bogdanov-Belsky "Sunday reading of the Gospel in the folk school of Rachinsky" 1895. In the picture, second from the right, S.A. Rachinsky.

The children received a varied education. At the lessons of arithmetic, they not only learned to add and subtract, but also mastered the elements of algebra and geometry, and in an accessible and exciting form for children, often in the form of a game, making amazing discoveries along the way. It is this discovery of his theory of numbers that is depicted on school board in the painting "Oral Account". Sergei Alexandrovich gave children interesting problems to solve, and they had to be solved verbally, in the mind. He said: "You can't run for a pencil and paper in the field, you have to be able to count in your mind."

S. A. Rachinsky. Figure N.P. Bogdanov-Belsky.

One of the first to enter the Rachinsky school was a poor peasant shepherd boy, Kolya Bogdanov, from the village of Shitiki, Belsk district. In this boy, Rachinsky saw the talent of a painter and helped him develop, completely taking over his future art education. In the future, all the work of the Wanderer artist Nikolai Petrovich Bogdanov-Belsky (1868-1945) will be devoted to peasant life, school and beloved teacher.

In the painting "On the Threshold of the School", the artist captured the moment of his first acquaintance with the Rachinsky school.

N.P. Bogdanov-Belsky "On the threshold of the school" 1897.

But what is the fate of the Rachinsky folk school in our time? Has the memory of Rachinsky been preserved in Tatev, once famous all over Russia? These questions worried me in June 2000 when I went there for the first time.

And finally, it is in front of me, spread among the green forests and fields, the village of Tatevo in the Belsky district, the former Smolensk province, and today attributed to the Tver region. It was here that the famous Rachinsky school was created, which so influenced the development of public education in pre-revolutionary Russia.

At the entrance to the estate, I saw the remains of a regular park with linden alleys and centuries-old oaks. A picturesque lake in the clear waters of which the park is reflected. A lake of artificial origin, fed by springs, was dug even under the grandfather of S.A. Rachinsky, the St. Petersburg Chief of Police Anton Mikhailovich Rachinsky.

Lake on the estate.

And here I come to a dilapidated landowner's house with columns. From the majestic building built at the end of the 18th century, only the skeleton remains now. The restoration of the Trinity Church has begun. Near the church is the grave of Sergei Alexandrovich Rachinsky - a modest stone slab with the Gospel words inscribed on it at his request: "Man will not live on bread alone, but on every word that comes from the mouth of God." There, among the family tombstones, his parents, brothers and sisters are buried.

The manor house in Tatev today.

In the fifties, the landlord's house began to gradually collapse. In the future, the destruction continued, reaching its full apogee in the seventies of the last century.

The manor house in Tatev during the time of Rachinsky.

Church in Tatev.

The building of the wooden school has not been preserved. But the school was preserved in another two-story, brick house, the construction of which was conceived by Rachinsky, but carried out shortly after his death in 1902. This building, designed by a German architect, is considered unique. Due to a design error, it turned out to be asymmetrical - it lacks one wing. Only two more buildings were built according to the same project.

Rachinsky school building today.

It was nice to know that the school is alive, active and in many ways superior to the capital's schools. At this school, when I arrived there, there were no computers and other modern innovations, but there was a festive, creative atmosphere, teachers and children showed a lot of imagination, freshness, invention and originality. I was pleasantly surprised by the openness, heart, and cordiality with which I was greeted by students and teachers, led by the director of the school. Here, the memory of its founder is cherished. The school museum preserves relics related to the history of the creation of this school. Even the external design of the school and classrooms was bright and unusual, so unlike the standard official design that I had seen in our schools. These are windows and walls originally decorated and painted by the students themselves, and a code of honor hanging on the wall invented by them, and their own school anthem and much more.

Memorial plaque on the wall of the school.

Within the walls of the Tatev school. These stained-glass windows were made by the students of the school.

At the Tatev school.

At the Tatev school.

At the Tatev school today.

N.P. Museum Bogdanov-Belsky in former home manager.

N.P. Bogdanov-Belsky. Self-portrait.

All the characters in the painting “Mental Counting” are painted from life and in them the inhabitants of the village of Tatevo recognize their grandfathers and great-grandfathers. I want to tell you a little about how the life of some of the boys depicted in the picture developed. I was told about this by local old-timers who knew some of them personally.

S.A. Rachinsky with his students on the threshold of a school in Tatev. June 1891.

N.P. Bogdanov-Belsky "Oral counting in the folk school of Rachinsky" 1895.

Many people think that in the boy depicted in the foreground of the picture, the artist depicted himself - in fact, this is not so, this boy Vanya Rostunov. Ivan Evstafievich Rostunov was born in 1882 in the village of Demidovo in a family of illiterate peasants. Only in the thirteenth year did he enter the Rachinsky public school. Later he worked on the collective farm as an accountant, saddler, postman. For lack of a mail bag, before the war he carried letters in a cap. Rostunov had seven children. All of them studied at Tatev high school. Of these, one is a veterinarian, another is an agronomist, the third is a military man, one daughter is a livestock specialist, another daughter was a teacher and director of the Tatev school. One son died during the Great Patriotic War, and another, upon returning from the war, soon died from the consequences of injuries received there. Until recently, Rostunov's granddaughter worked as a teacher at the Tatev school.

The boy standing on the far left in boots and a purple shirt is Dmitry Danilovich Volkov (1879-1966), who became a doctor. During civil war worked as a surgeon in a military hospital. During the Great Patriotic War he was a surgeon in a partisan formation. In peacetime, he treated the residents of Tatev. Dmitry Danilovich had four children. One of his daughters was a partisan in the same detachment as her father and died heroically at the hands of the Germans. Another son was a participant in the war. The other two children are a pilot and a teacher. The grandson of Dmitry Danilovich was the director of the state farm.

The fourth from the left, the boy depicted in the picture is Andrey Petrovich Zhukov, he became a teacher, worked as a teacher in one of the schools created by Rachinsky and located a few kilometers from Tatev.

Andrey Olkhovnikov (second from right in the picture) also became a prominent teacher.

The boy on the far right is Vasily Ovchinnikov, a participant in the first Russian revolution.

The boy, dreaming and throwing his hand behind his head, is Grigory Molodenkov from Tatev.

Sergey Kupriyanov from the village of Gorelki whispers into the teacher's ear. He was the most gifted in mathematics.

The tall boy, thinking at the blackboard, is Ivan Zeltin from the village of Pripeche.

The permanent exhibition of the Tatev Museum tells about these and other residents of Tatev. There is a section dedicated to the genealogy of each Tatev family. Merits and achievements of grandfathers, great-grandfathers, fathers and mothers. The achievements of a new generation of students of the Tatev school are presented.

peering into open faces current Tatev schoolchildren, so similar to the faces of their great-grandfathers from the painting by N.P. Bogdanov-Belsky, I thought that maybe the source of spirituality, which the Russian teacher, the ascetic, my ancestor Sergey Aleksandrovich Rachinsky, relied on so much, had not yet completely died out.

known to many. The picture shows village school the end of the 19th century during an arithmetic lesson while solving a fraction in the mind.

Teacher - a real man, Sergei Alexandrovich Rachinsky (1833-1902), botanist and mathematician, professor at Moscow University. On the wave of populism in 1872, Rachinsky returned to his native village of Tatevo, where he created a school with a hostel for peasant children, developed unique technique teaching oral counting, instilling in village children his skills and the basics of mathematical thinking. Bogdanov-Belsky, himself a former student of Rachinsky, dedicated his work to an episode from the life of a school with a creative atmosphere that reigned in the classroom.

However, with all the fame of the picture, few of those who saw it delved into the content of the "difficult task" that it depicts. It consists in quickly finding the result of the calculation by mental counting:

A talented teacher cultivated in his school an oral calculation based on the virtuoso use of the properties of numbers.

The numbers 10, 11, 12, 13 and 14 have a curious feature:

10 2 + 11 2 + 12 2 = 13 2 + 14 2 .

Indeed, since

100 + 121 + 144 = 169 + 196 = 365,

Wikipedia for calculating the value of the numerator suggests the following way:

10 2 + (10 + 1) 2 + (10 + 2) 2 + (10 + 3) 2 + (10 + 4) 2 =

10 2 + (10 2 + 2 10 1 + 1 2) + (10 2 + 2 10 2 + 2 2) + (10 2 + 2 10 3 + 3 2) + (10 2 + 2 10 4 + 4 2) =

5 100 + 2 10 (1 + 2 + 3 + 4) + 1 2 + 2 2 + 3 2 + 4 2 =

500 + 200 + 30 = 730 = 2 365.

For me, it's too smart. It's easier to do otherwise:

10 2 + 11 2 + 12 2 + 13 2 + 14 2 =

= (12 - 2) 2 + (12 - 1) 2 + 12 2 + (12 + 1) 2 + (12 + 2) 2 =

5 12 2 + 2 4 + 2 1 = 5 144 + 10 = 730,

The above reasoning is quite possible to carry out orally - 12 2 , of course, you need to remember that the double products of the squares of the binomials to the left and right of 12 2 cancel each other out and can be ignored, but 5 144 \u003d 500 + 200 + 20, - not difficult.

Let's use this trick and verbally find the sum:

48 2 + 49 2 + 50 2 + 51 2 + 52 2 = 5 50 2 + 10 = 5 2500 + 10 = 12510.

Let's complicate:

84 2 + 87 2 + 90 2 + 93 2 + 96 2 = 5 8100 + 2 9 + 2 36 = 40500 + 18 + 72 = 40590.

Rachinsky row

Algebra gives us the means to raise the question of this interesting feature series of numbers

10, 11, 12, 13, 14

more broadly: is it the only row of five consecutive numbers whose sum of the squares of the first three is equal to the sum of the squares of the last two?

Denoting the first of the desired numbers by x, we have the equation

x 2 + (x + 1) 2 + (x + 2) 2 = (x + 3) 2 + (x + 4) 2.

It is more convenient, however, to denote by x not the first, but the second of the desired numbers. Then the equation will have a simpler form

(x - 1) 2 + x 2 + (x + 1) 2 = (x + 2) 2 + (x + 3) 2 .

Opening the brackets and making simplifications, we get:

x 2 - 10x - 11 = 0,

where

x 1 = 11, x 2 = -1.

There are, therefore, two series of numbers that have the required property: the Rachinsky series

10, 11, 12, 13, 14

and row

2, -1, 0, 1, 2.

Indeed,

(-2) 2 +(-1) 2 + 0 2 = 1 2 + 2 2 .

Two!!!

I would like to finish with bright and touching memories of the author's blog V. Iskra in the article On the squares of two-digit numbers and not only about them ...

Once, in the year around 1962, our "mathematician", Lyubov Iosifovna Drabkina, gave this task to us, 7th graders.

I was then very fond of the newly appeared KVN-ohm. He supported the team of the city of Fryazino near Moscow. The “Fryazinians” were distinguished by their special ability to apply logical “express analysis” to solve any problem, “pulling out” the most tricky question.

I couldn't figure it out quickly. However, using the "Fryazin" method, I figured out that the answer should be expressed as an integer. Otherwise, this is no longer an “oral account”! This number could not be one - even if the numerator had the same 5 hundreds, the answer would be clearly more. On the other hand, he clearly did not reach the number "3".

- Two!!! - I blurted out, a second ahead of my friend, Lenya Strukov, the best mathematician in our school.

- Yes, indeed two, - Lenya confirmed.

- What did you think? - asked Lyubov Iosifovna.

- I didn't think so. Intuition - I answered to the laughter of the whole class.

- If you didn’t count, the answer doesn’t count - Lyubov Iosifovna “punned”. Lenya, didn't you count too?

- No, why not, Lenya answered sedately. It was necessary to add 121, 144, 169 and 196. I added the numbers one and three, two and four in pairs. It is more comfortable. It turned out 290 + 340. total amount, including the first hundred - 730. Divide by 365 - we get 2.

- Well done! But for the future, remember - in a series of two-digit numbers - the first five of its representatives - have an amazing property. The sum of the squares of the first three numbers in the series (10, 11 and 12) is equal to the sum of the squares of the next two (13 and 14). And this sum equals 365. Easy to remember! So many days in a year. If the year is not a leap year. Knowing this property, the answer can be obtained in a second. Without any intuition...

* * *

… Years have passed. Our city has acquired its own "Wonder of the World" - mosaic paintings in underground passages. There were many transitions, even more paintings. The topics were very different - the defense of Rostov, space ... In the central passage, under the intersection of Engels (now - Bolshaya Sadovaya) - Voroshilovsky made a whole panorama about the main stages of the life path of a Soviet person - a maternity hospital - kindergarten school, prom...

On one of the "school" pictures one could see a familiar scene - the solution of the problem ... Let's call it like this: "The Rachinsky Problem" ...

... Years passed, people passed ... Cheerful and sad, young and not very young. Someone recalled their school, someone at the same time "moved their brains" ...

The master tilers and artists, led by Yuri Nikitovich Labintsev, did a wonderful job!

Now the "Rostov miracle" is "temporarily unavailable." Trade came to the fore - literally and figuratively. Nevertheless, let's hope that in this common phrase - the main thing is the word "temporarily" ...

Sources: Ya.I. Perelman. Entertaining Algebra (Moscow, Nauka, 1967), Wikipedia,