Picture of oral calculation at the Rachinsky school. Nikolai Bogdanov-Belsky. Verbal counting. At the public school of S. A. Rachinsky. At the Tatev school

In one of the halls of the Tretyakov Gallery you can see a famous painting by the 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 there are real people, painted by him from life - people whom he knew and loved, and the main character is 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 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 to the comprehensive education of 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, meets interesting people, studies philosophy, literature, music and much more. After some time, he writes several scientific papers and receives a doctorate and a professorship in botany at Moscow University. But his interests were not limited to scientific frameworks. The future rural teacher was engaged in literary creativity, wrote poetry and prose, played the piano to perfection, 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 will henceforth become his life’s work.

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 on the school board in the painting “Mal Calculus.” 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 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. 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. 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. 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 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 the former manager's house.

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 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 at Tatev secondary 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 the Civil War he 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 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 =???

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 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 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.

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.

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 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 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 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 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 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.

This picture is called “Oral arithmetic at Rachinsky’s school,” and it was painted by the same boy who is in the foreground in the picture.
He grew up, graduated from this parochial school of Rachinsky (by the way, a friend of K.P. Pobedonostsev, the ideologist of parochial schools) and became a famous artist.
Do you know who we are talking about?

P.S. By the way, did you solve the problem?))

"Verbal counting. At the public school of S. A. Rachinsky” is a painting written in 1985 by the artist N. P. Bogdanov-Belsky.

On the canvas we see a lesson in mental calculation in a village school of the 19th century. The teacher is a very real, historical person. This is a mathematician and botanist, professor at Moscow University Sergei Aleksandrovich Rachinsky. Fascinated by the ideas of populism, in 1872 Rachinsky came from Moscow to his native village of Tatevo and created a school there with a dormitory for village children. In addition, he developed his own method of teaching mental arithmetic. By the way, the artist Bogdanov-Belsky was himself a student of Rachinsky. Pay attention to the problem written on the board.

Can you solve it? Give it a try.

About Rachinsky rural school, who at the end of the 19th century instilled in village children the skills of mental calculation and the basics of mathematical thinking. The illustration for the note, a reproduction of a painting by Bogdanov-Belsky, depicts the process of solving the fraction 102+112+122+132+142365 in the mind. Readers were asked to find the simplest and most rational method of finding the answer.

As an example, a calculation option was given in which it was proposed to simplify the numerator of the expression by grouping its terms differently:

102+112+122+132+142=102+122+142+112+132=4(52+62+72)+112+(11+2)2=4(25+36+49)+121+121 +44+4=4×110+242+48=440+290=730.

It should be noted that this solution was found “honestly” - in the mind and blindly, while walking with the dog in a grove near Moscow.

More than twenty readers responded to the invitation to send their solutions. Of these, slightly less than half suggest representing the numerator in the form

102+(10+1)2+(10+2)2+(10+3)2+(10+4)2=5×102+20+40+60+80+1+4+9+16.

This is M. Graf-Lyubarsky (Pushkino); A. Glutsky (Krasnokamensk, Moscow region); A. Simonov (Berdsk); V. Orlov (Lipetsk); Kudrina (Rechitsa, Republic of Belarus); V. Zolotukhin (Serpukhov, Moscow region); Yu. Letfullova, 10th grade student (Ulyanovsk); O. Chizhova (Kronstadt).

The terms were even more rationally represented as (12−2)2+(12−1)2+122+(12+1)2+(12+2)2, when the products ±2 by 1, 2 and 12 cancel each other out, B Zlokazov; M. Likhomanova, Yekaterinburg; G. Schneider, Moscow; I. Gornostaev; I. Andreev-Egorov, Severobaykalsk; V. Zolotukhin, Serpukhov, Moscow region.

Reader V. Idiatullin offers his own way of converting amounts:

102+112+122=100+200+112−102+122−102=300+1×21+2×22=321+44=365;

132+142=200+132−102+142−102=200+3×23+4×24=269+94=365.

D. Kopylov (St. Petersburg) recalls one of the most famous mathematical discoveries of S. A. Rachinsky: there are five consecutive natural numbers, the sum of the squares of the first three of which is equal to the sum of the squares of the last two. These numbers are shown on the chalkboard. And if Rachinsky’s students knew the squares of the first fifteen to twenty numbers by heart, the task was reduced to adding three-digit numbers. For example: 132+142=169+196=169+(200−4). Hundreds, tens and units are added separately, and all that remains is to count: 69−4=65.

In a similar way, Y. Novikov, Z. Grigoryan (Kuznetsk, Penza region), V. Maslov (Znamensk, Astrakhan region), N. Lakhova (St. Petersburg), S. Cherkasov (Tetkino, Kursk region) solved the problem .) and L. Zhevakin (Moscow), who also proposed a fraction calculated in a similar way:

102+112+122+132+142+152+192+22365=3.

A. Shamshurin (Borovichi, Novgorod region) used a recurrent formula of the type A2i=(Ai−1+1)2 to calculate the squares of numbers, which greatly simplifies the calculations, for example: 132=(12+1)2=144+24+1 .

Reader V. Parshin (Moscow) tried to apply the rule of rapid raising to the second power from E. Ignatiev’s book “In the Kingdom of Ingenuity,” discovered an error in it, derived his own equation and applied it to solve the problem. In general, a2=(a−n)(a+n)+n2, where n is any number less than a. Then
112=10×12+12,
122=10×14+22,
132=10×16+32
etc., then the terms are grouped rationally so that the numerator ends up being 700 + 30.

Engineer A. Trofimov (p. Ibresi, Chuvashia) made a very interesting analysis of the numerical sequence in the numerator and converted it into an arithmetic progression of the form

X1+x2+...+xn,where xi=ai+1−ai.

For this progression the statement is true

Xn=2n+1, that is, a2n+1=a2n+2n+1,

Where does equality come from?

A2n+k=a2n+2nk+n2

It allows you to mentally count the squares of two to three-digit numbers and can be used to solve the Rachinsky problem.

Finally, it turned out that the correct answer could be obtained through estimates rather than exact calculations. A. Polushkin (Lipetsk) notes that although the sequence of squares of numbers is not linear, you can take the square of the average number - 12 - five times, rounding it: 144 × 5 ≈ 150 × 5 = 750. A 750:365≈2. Since it is clear that mental arithmetic must operate with integers, this answer is certainly correct. It was received in 15 seconds! But it can still be checked additionally by estimating “from below” and “from above”:

102×5=500,500:365>1
142×5=196×5<200×5=1000,1000:365<3.

More than 1, but less than 3, therefore - 2. Exactly the same assessment was carried out by V. Yudas (Moscow).

The author of the note “Fulfilled Prediction” G. Poloznev (Berdsk, Novosibirsk region) rightly noted that the numerator must certainly be a multiple of the denominator, that is, equal to 365, 730, 1095, etc. Estimation of the magnitude of partial sums clearly indicates the second number.

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.

For more details, see: http://www.nkj.ru/archive/articles/6347/ (Science and life, Mental arithmetic)

This painting also depicts Rachinsky and the author.

While working in a rural school, Sergei Aleksandrovich Rachinsky brought into the world: Bogdanov 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 of the 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. Ch. tank building designer, 1948-61 - beginning. OKB at Kirovsky plant. In 1961-91 - deputy. prev state Institute of the USSR 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 (there is an initiative to canonize him as a saint of the Russian Orthodox Church), a tireless worker, a rural teacher we have forgotten and an amazing thinker, for whom L.N. Tolstoy learned to build a rural school, P.I. Tchaikovsky received recordings of 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 is a pseudonym prefix, since the painter was born in the village of Shitiki, Belsky district, Smolensk province) came from the poor and was just a student of Sergei Alexandrovich, who in thirty years 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 forty people!) or professional artists (three students, including Bogdanov), but also, say, a law teacher for the royal children, as a graduate of the St. Petersburg Theological Academy Archpriest Alexander Vasiliev, or a monk of the Trinity-Sergius Lavra, like Titus (Nikonov).

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 educator has again been picked up, that temperance societies named after Rachinsky are again appearing in Russia, and this is not some “AlAnon” (the American Society of Alcoholics Anonymous, reminiscent of a sect and, unfortunately, leaked to us in the early 1990s ). Let us recall that before the October Revolution of 1917, Russia was one of the most non-drinking countries in Europe, second only to Norway in the “palm of sobriety”.

Professor S.A. Rachinsky

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The writer V. Rozanov drew attention to the fact that the Tatev school of Rachinsky became the mother school, from which “more and more new bees fly away and in a new place do the work and faith of the old. And this faith and deed consisted in the fact that Russian ascetic teachers looked at teaching as a holy mission, a great service to the noble goals of raising spirituality among the people.”

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“Have you been able to meet the heirs of Rachinsky’s ideas in modern life?” - I ask Irina Ushakova, and she talks about a man who shared the fate of the people's teacher Rachinsky: both his lifetime veneration and post-revolutionary desecration. In the 1990s, when she was just beginning to study Rachinsky’s activities, I. Ushakova often met with Tatev school teacher Alexandra Arkadyevna Ivanova and wrote down her memories. Father A.A. Ivanova, Arkady Averyanovich Seryakov (1870-1929), was Rachinsky’s favorite student. He is depicted in Bogdanov-Belsky’s painting “At a Sick Teacher” (1897) and it seems we see him at the table in the painting “Sunday Readings in a Country School”; on the right, under the portrait of the sovereign, Rachinsky is depicted and, I think, Fr. Alexander Vasiliev.

N.P. Bogdanov-Belsky. Sunday readings at a rural school, 1895

In the 1920s, when the darkened people, together with the tempters, destroyed, along with the lordly estates, all the good structures of the nobles, the Rachinsky family crypts were desecrated, the temple in Tatev was turned into a repair shop, and the estate was plundered. All teachers, students of Rachinsky, were expelled from the school.

Remains of a house in the Rachinsky estate (photo 2011)

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In the book “S.A. Rachinsky and his school,” published in Jordanville in 1956 (our emigrants kept this memory, unlike us), tells about the attitude of the Chief Prosecutor of the Holy Synod, K.P., towards the rural educator Rachinsky. Pobedonostsev, who on March 10, 1880 wrote to the heir to the Tsarevich, Grand Duke Alexander Alexandrovich (we read, as if about our days): “The impressions of St. Petersburg are extremely difficult and desolate. To live in such a time and to see at every step people without direct activity, without clear thought and a firm decision, occupied with the small interests of their own self, immersed in the intrigues of their ambition, hungry for money and pleasure and chatting idly, is simply heartbreaking... Kind impressions come only from inside Russia, from somewhere in the countryside, from the wilderness. There is still a intact spring, from which it still breathes freshness: from there, and not from here, is our salvation.

There are people there with a Russian soul, doing good deeds with faith and hope... Still, it’s gratifying to see at least one like that... My friend Sergei Rachinsky, a truly kind and honest person. He was a professor of botany at Moscow University, but when he got tired of the strife and intrigue that arose there between the professors, he left his service and settled in his village, far from all railways... He truly became a benefactor of the whole area, and God sent him people - from the priests and landowners who work with him... This is not talk, but action and true feeling.”

On the same day, the heir to the Tsarevich answered Pobedonostsev: “...how you envy people who can live in the wilderness and bring true benefit and be far from all the abominations of city life, and especially St. Petersburg. I am sure that there are many similar people in Rus', but we don’t hear about them, and they work in the wilderness quietly, without phrases or boasting...”

N.P. Bogdanov-Belsky. At the school door, 1897

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N.P. Bogdanov-Belsky. Verbal counting. At the public school S.A. Rachinsky, 1895

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“The May Man” Sergei Rachinsky passed away on May 2, 1902 (Old Style). 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.

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 =???

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 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.

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 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.

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 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.

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 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 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 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.

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 primary 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 calculate: 11 10 = 110, and even 11 is 121 in total. 12 12 is also not difficult to calculate: 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 an art education.

N.P. Bogdanov-Belsky graduated from the Moscow School of Painting, Sculpture and Architecture, studied with such famous artists as 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 primary school teacher. 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.