Picture of oral arithmetic in a rural school. Bogdanov - Belsky Oral counting

Famous Russian artist NIKOLAI PETROVICH BOGDANOV-BELSKY

wrote a unique and incredible life story in 1895.

The work is called “ORAL ACCOUNT”,

and in the full version

"VERBAL COUNTING. AT S.A. RACHINSKY’S PEOPLE’S SCHOOL.”

The painting is done in oil on canvas and depicts a 19th century rural school during an arithmetic lesson.

A simple Russian class, children dressed in peasant clothes: bast shoes, trousers and shirts. All this fits very harmoniously and laconically into the plot, unobtrusively bringing to the world a thirst for knowledge on the part of the ordinary Russian people.

Schoolchildren solve interesting and complex example to solve fractions in your head. They are deep in thought and searching for the right solution. Someone thinks at the board, someone stands on the sidelines and tries to collate knowledge that will help in solving the problem. Children are completely absorbed in finding the answer to the question posed; they want to prove to themselves and the world that they can do it.

The canvas depicts 11 children and only one boy quietly whispers in the teacher’s ear, perhaps the correct answer.

The teacher is standing nearby a real man, Sergei Aleksandrovich Rachinsky is a famous 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 unique technique teaching mental arithmetic, instilling in village children its skills and the basics of mathematical thinking.

The warm color scheme brings the kindness and simplicity of the Russian people, there is no envy and falsehood, no evil and hatred, children from different families with different incomes came together to make the only right decision.

This is sorely lacking in our modern life, where people are used to living completely differently, regardless of the opinions of others.

Nikolai Petrovich Bogdanov-Belsky, himself a former student of Rachinsky, dedicated the painting to an episode from the life of the school with the creative atmosphere that reigned in the lessons, to his teacher, the great genius of mathematics, whom he knew and respected well.

Now the painting is in Moscow in the Tretyakov Gallery, if you are there, be sure to take a look at the pen of the great master.

The problem depicted in the picture could not be presented to students in a standard primary school: the curriculum of one-class and two-class primary public schools did not provide for the study of the concept of degree.

However, Rachinsky did not follow the standard training course; he was confident in the excellent mathematical abilities of most peasant children and considered it possible to significantly complicate the mathematics curriculum.

SOLUTION

First way

There are several ways to solve this expression. If you learned squares of numbers up to 20 or up to 25 at school, then most likely it will not cause you much difficulty.

This expression is equal to: (100+121+144+169+196) divided by 365, which ultimately becomes the quotient of 730 and 365, which equals: 2. To solve the example this way, you may need to use mindfulness skills and the ability to keep a few things in mind intermediate answers.

Second way

If you didn’t learn the meaning of squares of numbers up to 20 at school, then a simple method based on the use of a reference number may be useful to you. This method allows you to simply and quickly multiply any two numbers less than 20. The method is very simple, you need to add one to the first number of the second, multiply this amount by 10, and then add the product of the units. For example: 11*11=(11+1)*10+1*1=121. The remaining squares are also: 12*12=(12+2)*10+2*2=140+4=144

13*13=160+9=169

14*14=180+16=196

Then, having found all the squares, the task can be solved in the same way as shown in the first method.

Third way

Another method involves using a simplification of the numerator of a fraction, based on the use of the formulas for the square of the sum and the square of the difference.

If we try to express the squares in the numerator of a fraction through the number 12, we get the following expression. (12 - 2)2 + (12 - 1)2 + 122 + (12 + 1)2 + (12 + 2)2. If you know the formulas for the square of the sum and the square of the difference well, then you will understand how this expression can easily be reduced to the form: 5*122+2*22+2*12, which equals 5*144+10=730. To multiply 144 by 5, simply divide this number by 2 and multiply by 10, which equals 720. Then we divide this expression by 365 and get: 2.

Fourth solution

Also, this problem can be solved in 1 second if you know the Rachinsky sequences.

in the 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 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...

It is difficult to say which of the proposed methods of calculation is the simplest: everyone chooses their own based on the characteristics of their own mathematical thinking.

Working in a rural school

Sergei Alexandrovich Rachinsky brought out to people:

Bogdanova I. L. - infectious disease specialist, doctor of medical sciences, corresponding member of the USSR Academy of Medical Sciences;

Vasiliev Alexander Petrovich (September 6, 1868 - September 5, 1918) - archpriest, confessor royal family, a teetotaler pastor, a patriot-monarchist;

Sinev Nikolai Mikhailovich (December 10, 1906 - September 4, 1991) - Doctor of Technical Sciences (1956), Professor (1966), Honored Worker of Science and Technology of the RSFSR. In 1941 - deputy chief designer for tank building, 1948-61 - head of the design bureau at the Kirov plant. In 1961-91 - Deputy Chairman of the USSR State Committee on the Use of Atomic Energy, laureate of Stalin and State awards(1943, 1951, 1953, 1967) and many others.

S.A. Rachinsky (1833-1902), a representative of an ancient noble family, was born and died in the village of Tatevo, Belsky district, and meanwhile was a corresponding member of the Imperial St. Petersburg Academy of Sciences, who devoted his life to the creation of a Russian rural school. Last May marked the 180th anniversary of the birth of this outstanding Russian man, a true ascetic, a tireless worker, a forgotten rural teacher and an amazing thinker.

Whose L.N. Tolstoy learned to build a rural school,

P.I. Tchaikovsky received recordings folk songs,

and V.V. Rozanov was spiritually mentored in matters of writing.

By the way, the author of the above-mentioned painting, Nikolai Bogdanov-Belsky, came from poverty and was a student of Sergei Alexandrovich, who over thirty years, at his own expense, created about three dozen rural schools and, at his own expense, helped the brightest of his students to realize themselves professionally, who became not only rural teachers (about 40 people!) or professional artists (3 students, including Bogdanov), but also a teacher of the law for the royal children, a graduate of the St. Petersburg Theological Academy, Archpriest Alexander Vasiliev, and a monk of the Trinity-Sergius Lavra, like Titus (Nikonova).

Rachinsky built not only schools, but also hospitals in Russian villages; the peasants of Belsky district called him nothing less than “dear father.” Through the efforts of Rachinsky, temperance societies were recreated in Russia, uniting tens of thousands of people throughout the empire by the early 1900s.

Now this problem has become even more urgent, drug addiction has now grown into it. It is gratifying that the teetotaling path of the enlightener has again been picked up, that temperance societies named after Rachinsky are appearing in Russia again

Russian pedagogues and ascetics looked upon teaching as a holy mission, a great service to the noble goals of raising spirituality among the people.”

“The May Man” Sergei Rachinsky passed away on May 2, 1902. Dozens of priests and teachers, rectors of theological seminaries, writers, and scientists came to his funeral. In the decade before the revolution, more than a dozen books were written about Rachinsky’s life and work, and the experience of his school was used in England and Japan.

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

The teacher is a real person, 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 of quickly finding the result of a calculation by mental calculation:

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 sought 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 from the Moscow region town of 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, 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 series of 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 has come to the fore - directly 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 "Oral calculation in 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 solve it reports the answer to the teacher in the ear, 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 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 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. Teaching mathematical theory Rachinsky had little interest, but he performed very well in oral 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 supporter 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 understandably, 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).

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 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 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, leading peasant children along the main road educated person- 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 spiritual 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 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 question of passing subsidies through the Duma church schools, almost all the funds went to the Zemstvo people.

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 a parish priest who was underpaid and ignored, 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 the teaching of 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 counting techniques, omitting all arithmetic and algebraic transformations that required 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 Aleksandrovich Rachinsky was born in the Tatevo estate, 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 of Tatevo for this. 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 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, and 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. A combination of theoretical and practical classes 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 Aleksandrovich gave the children interesting problems to solve, and they definitely had to be solved orally, in their heads. 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 saw the talent of a painter and helped him develop, completely taking over his future art education. In the future, the entire work of the Itinerant artist Nikolai Petrovich Bogdanov-Belsky (1868-1945) will be dedicated to peasant life, school and favorite 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. A picturesque lake whose clear waters reflect the park. 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. From built at the end of the 18th century majestic building now only the skeleton 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 shortly after his death in 1902. This is a building built according to the project German architect 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” are 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 boy depicted in foreground In the painting, the artist depicted himself - 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 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 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 open faces 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.

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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?

Of course, they didn't look like that. The painting is called "Oral arithmetic in a public school" 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 , at his own expense) 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). Word classmate meant that children of three years of study form a single class, and one teacher teaches them all within one 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 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.

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 supporter 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 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 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.

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 the certain influence of Rachinsky’s ideas, the ecclesiastical department decided that the zemstvo school would be of no use - the liberals would not teach children anything good - and in the mid-1890s they began to develop their own independent network of parochial schools.

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 zemstvo school tried to turn the teaching of 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.