Historicisms in the picture are an oral account. Lesson-excursion to the painting by N.P. Bogdanov-Belsky "Oral calculation". Memorial plaque on the school wall

05.03.2020

Lesson objectives:

development of observation abilities;
development of thinking abilities;
development of abilities to express thoughts;
instilling interest in mathematics;
touching the art of N.P. Bogdanov-Belsky.

DURING THE CLASSES

Learning is work that educates and shapes a person.

Four pages from the life of the painting

Page one

The painting “Oral Counting” was painted in 1895, that is, 110 years ago. This is a kind of anniversary of the painting, 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 standing in front) have turned away from the board and are remembering something, or maybe counting. One boy whispers something into the ear of a man, apparently a teacher, while the other appears to be eavesdropping.

- Why are they wearing bast shoes?

- Why are there no girls here, only boys?

– Why do they stand with their backs to the teacher?

-What are they doing?

You probably already understood that students and a teacher are depicted here. Of course, the students’ costumes are unusual: some of the guys are wearing bast shoes, and one of the characters in the picture (the one depicted in the foreground) also 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 poorly; 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, the guys are 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 into school. Studying was “not their business,” and not all of the boys studied.

Page two

This painting is called “Oral Counting”. Look how intently the boy depicted in the foreground of the picture thinks. Apparently the teacher gave me a difficult task. But this student will probably finish his work soon, and there shouldn’t be any mistakes: he takes mental arithmetic very seriously. But the student who whispers something in the teacher’s ear has apparently already solved the problem, but his answer is not entirely correct. Look: the teacher listens to the student’s answer carefully, but there is no approval on his face, which means the student did something wrong. Or maybe the teacher is patiently waiting 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 that stands in front: it’s immediately clear that he is the best student in the class.

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

- But try it.

I will write on the board the way you are used to writing:

(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, and the resulting amount divided by 365.

– That’s the problem (you can’t solve such an example quickly, especially in your head). Still, try to count verbally; I will help you in difficult places. Ten ten is 100, everyone knows that. Eleven multiplied by eleven is also not difficult to count: 11 10 = 110, and even 11 is 121 in total. 12 12 is also not difficult to count: 12 10 = 120, and 12 2 = 24, and the total will be 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, but these numbers still need to be added, and then the sum divided by 365. No, you won’t be able to calculate this yourself.

- We'll have to help a little.

– What numbers did you get?

– 100, 121, 144, 169 and 196 – many have counted this.

– 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 you divide by?

– Also at 365!

– How much do you get if the sum of the first three numbers is divided by 365?

- One! – everyone will already understand this.

– Now add up the remaining two numbers: 169 and 196. How much do you get?

– Also 365!

– Here’s an example, and a very simple one. It turns out there are only two!

- Only to solve it, you need to know well that the sum can not be divided 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 painting is called “Oral Counting”. It was written by the artist Nikolai Petrovich Bogdanov-Belsky, who lived from 1868 to 1945.

Bogdanov-Belsky knew his little heroes very well: he grew up among them and was once a shepherd. “...I am the illegitimate son of a poor little girl, that’s why Bogdanov, and Belsky became named after the district,” the artist said about himself.

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

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

Many portraits and landscapes were painted by Bogdanov-Belsky, but in people’s memory he remained, first of all, as an artist who was able to poetically and truly tell about smart rural children who greedily sought knowledge.

Who among us is not familiar with the paintings “At the School Door”, “Beginners”, “Essay”, “Village Friends”, “At the Sick Teacher”, “Voice Test” - these are the names of just a few of them. Most often the artist depicts children at school. Charming, trusting, focused, thoughtful, full of lively interest and always marked by natural intelligence - this is how Bogdanov-Belsky knew and loved peasant children, and who immortalized them in his works.

Page four

The artist depicted real-life students and a teacher in this picture. From 1833 to 1902 lived the famous Russian teacher Sergei Alexandrovich Rachinsky, a remarkable representative of Russian educated people of the century before last. 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 is passing the exam” for the title of teacher primary classes. Using his own funds, he opens a school for peasant children in the village of Tatyevo, Smolensk province, and becomes a teacher there. So, his students calculated so well orally that all visitors to the school were surprised. As you can see, the artist depicted S.A. Rachinsky together with his students at a lesson in oral problem solving. By the way, the artist himself N.P. Bogdanov-Belsky was a student of S.A. Rachinsky.

This picture is a hymn to the teacher and student.

known to many. The painting shows a village school late XIX century during an arithmetic lesson while solving fractions in your head.

Teacher - a real man, Sergei Aleksandrovich Rachinsky (1833-1902), botanist and mathematician, professor at Moscow University. In the wake of populism in 1872, Rachinsky returned to his native village of Tatevo, where he created a school with a dormitory for peasant children, developed a unique method of teaching mental arithmetic, instilling in the 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 the school with the creative atmosphere that reigned in the lessons.

However, for all the fame of the picture, few who saw it delved into the content of the “difficult task” that is depicted in it. It consists in verbal counting quickly find the calculation result:

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

365

The talented teacher cultivated mental counting in his school, based on the masterly use of the properties of numbers.

The numbers 10, 11, 12, 13 and 14 have an interesting feature:

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

Indeed, since

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

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

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.

In my opinion, it’s too tricky. It's easier to do it differently:

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,

730	= 2.
365

The above reasoning can be carried out orally - 12 2 , of course, you need to remember, double the products of the squares of binomials to the left and right of 12 2 are mutually destroyed and they can not be counted, but 5·144 = 500 + 200 + 20 - not difficult.

Let’s use this technique 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 it:

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

Rachinsky series

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

10, 11, 12, 13, 14

more generally: is this the only series of five consecutive numbers, the sum of the squares of the first three of which is equal to the sum of the squares of the last two?

Denoting the first of the required 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 required 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 Raczynski series

10, 11, 12, 13, 14

and a row

2, -1, 0, 1, 2.

Indeed,

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

Two!!!

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

Once upon a time, around 1962, our “mathematician”, Lyubov Iosifovna Drabkina, gave this task to us, 7th graders.

At that time I was very interested in the newly appeared KVN. I was rooting for the team city near Moscow Fryazino. The “Fryazinians” were distinguished by their special ability to use logical “express analysis” to solve any problem, to “pull out” the most tricky issue.

I couldn't do the math quickly in my head. However, using the “Fryazin” method, I figured that the answer should be expressed as an integer. Otherwise, this is no longer an “oral count”! This number could not be one - even if the numerator had the same 5 hundreds, the answer would be clearly greater. On the other hand, he clearly didn’t 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 count at all. Intuition - I answered to the laughter of the whole class.

“If you didn’t count it, the answer doesn’t count,” Lyubov Iosifovna made a pun. Lenya, didn’t you count either?

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

- Well done! But remember for the future - in a row double 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 is equal to 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 pictures. The topics were very different - the defense of Rostov, space... In the central passage, under the Engels intersection (now Bolshaya Sadovaya) - Voroshilovsky made a whole panorama about the main stages life path Soviet man- maternity hospital - kindergarten- school, prom...

In one of the “school” paintings one could see a familiar scene - the solution to a problem... Let’s call it like this: “Rachinsky’s problem”...

...Years passed, people passed... Cheerful and sad, young and not so young. Some remembered their school, while others “used 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. Still, let’s hope that in this common phrase the main word is “temporarily”...

Sources: Ya.I. Perelman. Entertaining algebra (Moscow, “Science”, 1967), Wikipedia,

Many have seen the picture “Mental arithmetic in a public school.” Late 19th century public school, blackboard, intelligent teacher, poorly dressed children, 9–10 years old, enthusiastically trying to solve a problem written on the board in their minds. The first person to decide tells the answer to the teacher in a whisper, so that others do not lose interest.

Now let's 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, but our children were taught so poorly?!

Don't rush to be indignant. Take a closer look at the picture. Don’t you think that the teacher looks too intelligent, somehow like a professor, and is dressed with obvious pretension? Why in school class such a high ceiling and an expensive stove with white tiles? Is this really what village schools and their teachers looked like?

Of course, they didn't look like that. The painting is called “Oral arithmetic in the public school of S.A. Rachinsky.” Sergei Rachinsky is a professor of botany at Moscow University, a man 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 a business there (of course, for own account) experimental public school.

The school was one-class, which did not mean that they taught there for one year. In such a school they taught for 3-4 years (and in two-year schools - 4-5 years, in three-year schools - 6 years). The word one-class meant that children of three years of study form a single class, and one teacher teaches them all within one lesson. It was a rather tricky business: while the children of one year of study were doing some kind of written exercise, the children of the second year were answering at the blackboard, the children of the third year were reading a textbook, etc., and the teacher alternately paid attention to each group.

Rachinsky's pedagogical theory was very original, and its different parts somehow did not fit together well. Firstly, Rachinsky considered the basis of education for the people to be teaching the Church Slavonic language and the Law of God, and not so much explanatory as consisting in memorizing prayers. Rachinsky firmly believed that a child who knew a certain number of prayers by heart would certainly grow up to be a highly moral person, and the very sounds of the Church Slavonic language would already have a moral-improving effect. To practice the language, Rachinsky recommended that children hire themselves out to read the Psalter over the dead (sic!).

Secondly, Rachinsky believed that it was useful and necessary for peasants to quickly count in their heads. Rachinsky had little interest in teaching mathematical theory, but he did very well in mental arithmetic at 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. Squaring, as depicted in the painting, was the most difficult mathematical operation studied in his school.

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

Rachinsky was a real enthusiast. School became his whole life. Rachinsky’s children lived in a dormitory and were organized into a commune: they performed all the maintenance work for themselves and the school. Rachinsky, who had no family, spent all his time with children from early morning until late evening, and since he was a very kind, noble person and sincerely attached to children, his influence on his students was enormous. By the way, Rachinsky gave the first child who solved the problem a carrot (in the literal sense of the word, he didn’t have a stick).

Sami school lessons occupied 5–6 months of the 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; the primary public school was not directly connected with others educational institutions and after it it was impossible to continue training without additional preparation. Rachinsky wanted to see the most advanced of his students as teachers primary school and priests, so he prepared children mainly for theological and teacher seminaries. There were also significant exceptions - first of all, this was the author of the picture himself, Nikolai Bogdanov-Belsky, whom Rachinsky helped to get into Moscow school painting, sculpture and architecture. But, oddly enough, leading peasant children along the main path of an educated person is a gymnasium / university / civil 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 Rachinsky's ideas, the religious department decided that the zemstvo school would be of no use - liberals would not teach children anything good - and in the mid-1890s they began to develop their own independent network of parochial schools.

In some ways, parochial schools were similar to Rachinsky's school - they had a lot of Church Slavonic language and prayers, and other subjects were correspondingly reduced. But, alas, the advantages of the Tatev school were not passed on to them. The priests had little interest in school affairs, ran the schools under pressure, 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 did not like the parochial school, because they realized that they hardly taught anything useful there, and they were of little interest in prayers. 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 original pedagogy, designed for the deep involvement and enthusiasm of the teacher, immediately dies during mass reproduction, falling into the hands of uninterested and lethargic people. But for that time it was a big bummer. Parochial schools, which by 1900 made up 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 talk of passing subsidies to church schools through the Duma; almost all the funds went to the zemstvo residents.

The more widespread zemstvo school was quite different from Rachinsky’s school. To begin with, the Zemstvo people 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 in the zemstvo school was taught worse than in Rachinsky, and in a smaller volume. The course ended with operations with simple fractions and non-metric system of measures. The teaching did not go as far as exponentiation, so ordinary elementary school students simply would not understand the problem depicted in the picture.

The zemstvo school tried to turn teaching the Russian language into world studies, through the so-called explanatory reading. The technique was that by dictating educational text in Russian, the teacher also further explained to the students what was said in the text itself. In this palliative way, Russian language lessons also turned into geography, natural history, history - that is, into all those developmental subjects that had no place in the short course of a one-grade school.

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

By the way, what method do schoolchildren use to solve a problem on the board? Only straight forward: 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, requiring calculations on paper.

For some reason, the picture shows only boys, while all the materials show that Rachinsky taught children of both sexes. What this means is unclear.

In one of the halls Tretyakov Gallery can see famous painting artist N.P. Bogdanov-Belsky “Oral calculation”. It depicts a lesson in a rural school. The classes are taught by an old teacher. Village boys in poor peasant shirts and bast shoes crowded around. They are focused and enthusiastically solving the problem proposed by the teacher... The plot is familiar to many from childhood, but not many know that this is not the artist’s imagination and behind all the characters in the picture are real people, painted by him from life - 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 surprising and extraordinary - after all, this man is a wonderful Russian educator, teacher of peasant children, Sergei Alexandrovich Rachinsky (1833-1902)

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

Future teacher S.A. Rachinsky.

Sergei Alexandrovich Rachinsky was born on the Tatevo estate, Belsky district, Smolensk province, into a noble family. His father Alexander Antonovich Rachinsky, a former participant in the December movement, was exiled to his family estate of Tatevo for this. Here, on May 2, 1833, the future teacher was born. His mother was sister poet E.A. Baratynsky and the Rachinsky family closely communicated with many representatives of Russian culture. In the family, parents paid great attention comprehensive education for their children. All this was very useful to Rachinsky in the future. Having received an excellent education at the Faculty of Natural Sciences of Moscow University, he travels a lot, gets acquainted with interesting people, studies philosophy, literature, music and much more. After a while he writes several scientific works and received a doctorate and a professorship in botany at Moscow University. But his interests were not limited to scientific frameworks. The future rural teacher was studying 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 to Rachinsky. 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 Timiryazevsky) Academy Konstantin Aleksandrovich Rachinsky, Maria was the wife of Sergei Lvovich, Tolstoy’s son. The correspondence between Tolstoy and Rachinsky is interesting, full of discussions and disputes about public education.

In 1867, due to prevailing circumstances, Rachinsky left his professorship at Moscow University, and with it all the bustle of metropolitan life, returned to his native Tatevo, opened a school there and devoted himself to teaching and raising peasant children. A few years later, the Smolensk village of Tatevo becomes famous throughout Russia. Education and service to the common people from now on will become the work of his whole life.

Professor of botany at Moscow University Sergei Aleksandrovich 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. During the lessons, children were taught various crafts needed by peasants. The boys learned carpentry and bookbinding. We worked in the school garden and apiary. Natural history lessons were held in the garden, field and meadow. The pride of the school is the church choir and icon-painting workshop. At his own expense, Rachinsky built a boarding school for children coming from far away and without housing.

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

The children received a varied education. In arithmetic lessons, we not only learned how to add and subtract, but also mastered the elements of algebra and geometry, in an accessible and exciting form for children, often in the form of a game, making amazing discoveries along the way. It is precisely this discovery of number theory that is depicted in school board in the painting "Oral Account". Sergei Alexandrovich let the children decide interesting tasks and they definitely had to be solved orally, in the mind. He said: “You can’t run to the field for a pencil and paper, you have to be able to count in your head.”

S. A. Rachinsky. Drawing by N.P. Bogdanov-Belsky.

One of the first to go to Rachinsky's school was the poor peasant shepherd Kolya Bogdanov from the village of Shitiki, Belsky district. In this boy, Rachinsky recognized the talent of a painter and helped him develop, taking full charge of his future artistic education. In the future, all the work of the Itinerant artist Nikolai Petrovich Bogdanov-Belsky (1868-1945) will be dedicated to peasant life, school and his beloved teacher.

In the painting “On the Threshold of School,” the artist captured the moment of his first acquaintance with Rachinsky’s school.

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

But what is the fate of the Rachinsky public school in our time? Is the memory of Rachinsky preserved in Tatev, once famous throughout Russia? These questions worried me in June 2000, when I first went there.

And finally, it is in front of me, spread out among green forests and fields, the village of Tatevo in Belsky district, the former Smolensk province, and nowadays classified as part of 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 oak trees. Picturesque lake V clear waters which the park is reflected. The lake of artificial origin, fed by springs, was dug under S.A. Rachinsky’s grandfather, St. Petersburg Chief of Police Anton Mikhailovich Rachinsky.

Lake on the estate.

And so I approach a dilapidated manor house with columns. Only the skeleton of the majestic building, built at the end of the 18th century, now remains. Restoration of the Trinity Church has begun. Near the church, the grave of Sergei Aleksandrovich Rachinsky is 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 rest.

A manor's house in Tatev today.

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

Landlord's house in Tatev during Rachinsky's time.

Church in Tatev.

The wooden school building has not survived. But the school was preserved in another two-story brick house, the construction of which was planned by Rachinsky, but carried out soon 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 - one wing is missing. Only two more buildings were built according to the same design.

The 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. In this school, when I arrived there, there were no computers or 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, warmth, and cordiality with which the students and teachers, led by the school director, greeted me. The memory of its founder is cherished here. IN school museum they take care of relics associated with the history of the creation of this school. Even the external design of the school and classrooms was bright and unusual, so different from 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 invented by them hanging on the wall, 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 school students themselves.

At the Tatev school.

At the Tatev school.

At the Tatev school today.

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

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

All the characters in the painting “Oral Account” were painted from life and in them the residents of the village of Tatevo recognize their grandfathers and great-grandfathers. I want to talk a little about how the lives of some of the boys depicted in the picture turned out. Local old-timers who knew some of them personally told me about this.

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

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

Many people think that the artist depicted himself in the boy depicted in the foreground of the picture - in fact, this is not so, this boy is Vanya Rostunov. Ivan Evstafievich Rostunov was born in 1882 in the village of Demidovo into a family of illiterate peasants. Only at the age of thirteen I entered the Rachinsky public school. Subsequently, he worked on a collective farm as an accountant, saddler, and postman. Lacking a mail bag, before the war he carried letters in a cap. Rostunov had seven children. They all studied in Tatev high school. Of these, one was a veterinarian, another was an agronomist, another was a military man, one was a livestock specialist’s daughter, and 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 unit. IN Peaceful time treated 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 Andrei 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.

Andrei Olkhovnikov (second from the 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, daydreaming and with his hand behind his head, is Grigory Molodenkov from Tatev.

Sergei Kupriyanov from the village of Gorelki whispers in the teacher’s ear. He was the most talented in mathematics.

The tall boy, lost in thought 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 the new generation of students of the Tatev school are presented.

Peering into the open faces of today's 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 on which the Russian pedagogue ascetic, my ancestor Sergei Alexandrovich Rachinsky so strongly relied, may not have completely died out.

Many have seen the picture “Mental arithmetic in a public school.” The end of the 19th century, a public school, a blackboard, an intelligent teacher, poorly dressed children, 9–10 years old, enthusiastically trying to solve a problem written on the blackboard in their minds. The first person to decide tells the answer to the teacher in a whisper, so that others do not lose interest.

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

Don't rush to be indignant. Take a closer look at the picture. Don’t you think that the teacher looks too intelligent, somehow like a professor, and is dressed with obvious pretension? Why is there such a high ceiling and an expensive stove with white tiles in the school classroom? Is this really what village schools and their teachers looked like?

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

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

Now we see that this is a common thing - any original pedagogy, designed for the deep involvement and enthusiasm of the teacher, immediately dies during mass reproduction, falling into the hands of uninterested and lethargic people. But for that time it was a big bummer. Parochial schools, which by 1900 made up about a third of primary public schools, turned out to be disliked by everyone. When, starting in 1907, the state began to allocate a lot of money to primary education, there was no question of passing subsidies to church schools through the Duma; almost all the funds went to the zemstvo residents.

The more widespread zemstvo school was quite different from Rachinsky’s school. To begin with, the Zemstvo people considered the Law of God completely useless. It was impossible to refuse to teach him for 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 in the zemstvo school was taught worse than in Rachinsky, and in a smaller volume. The course ended with operations with simple fractions and the non-metric system of measures. The teaching did not go as far as exponentiation, so ordinary elementary school students simply would not understand the problem depicted in the picture.

The zemstvo school tried to turn teaching the Russian language into world studies, through the so-called explanatory reading. The technique consisted in the fact that while dictating an educational text in the Russian language, the teacher also additionally explained to the students what was said in the text itself. In this palliative way, Russian language lessons also turned into geography, natural history, history - that is, into all those developmental subjects that had no place in the short course of a one-grade school.

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

By the way, what method do schoolchildren use to solve a problem on the board? Only straight forward: 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 counting techniques, omitting all arithmetic and algebraic transformations that required calculations on paper.

P.S. For some reason, the picture shows only boys, while all the materials show that Rachinsky taught children of both sexes. I couldn't figure out what this means.