The famous Russian artist Nikolai Petrovich Bogdanov-Belsky painted a unique and incredible life story in 1895. The work is called "Oral Account", and in full version"Verbal counting. IN public school S. A. Rachinsky.
Nikolai Bogdanov-Belsky. Verbal counting. In the folk school of S. A. Rachinsky
The picture is painted in oil on canvas, it depicts a rural school of the 19th century during an arithmetic lesson. Students solve interesting and complex example. They are in deep thought and searching for the right solution. Someone thinks at the blackboard, someone stands on the sidelines and tries to compare 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.
Nearby stands a teacher whose prototype is Rachinsky himself, a famous botanist and mathematician. No wonder the picture was given such a name, it is in honor of a professor at Moscow University. The canvas depicts 11 children and only one boy quietly whispers in the teacher's ear, perhaps the correct answer.
The picture depicts a simple Russian class, the children are dressed in peasant clothes: bast shoes, pants and shirts. All this very harmoniously and succinctly fits into the plot, unobtrusively bringing to the world the craving for knowledge on the part of the simple Russian people.
Warm colors bring kindness and simplicity of the Russian people, there is no envy and falsehood, there is 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 in a completely different way, regardless of the opinions of others.
Nikolai Petrovich dedicated the painting to his teacher, the great genius of mathematics, whom he knew and respected well. Now the picture is in Moscow in Tretyakov Gallery, be there, be sure to take a look at the pen of the great master.
description-kartin.com
Nikolai Petrovich Bogdanov-Belsky (December 8, 1868, village of Shitiki, Belsky district, Smolensk province, Russia - February 19, 1945, Berlin, Germany) - Russian artist-itinerant, academician of painting, chairman of the Kuindzhi Society.
The picture shows a village school late XIX centuries during an arithmetic lesson while solving a fraction in your head. Teacher - a real man, Sergei Alexandrovich Rachinsky (1833-1902), botanist and mathematician, professor at Moscow University.
On the wave of populism in 1872, Rachinsky returned to his native village of Tatevo, where he created a school with a hostel for peasant children, developed unique technique learning 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 a school with a creative atmosphere that reigned in the classroom.
An example is written on the chalkboard for students to solve:
The task depicted in the picture could not be offered to the students of the standard elementary school: the program of one-class and two-class elementary public schools did not provide for the study of the concept of degree. However, Rachinsky did not follow the typical training course; he was confident in the excellent mathematical abilities of most peasant children and considered it possible to significantly complicate the mathematics program.
Solution of the Rachinsky problem
First way to solve
There are several ways to solve this expression. If you learned the 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: (100+121+144+169+196) divided by 365, which eventually becomes the quotient of 730 and 365, which is: 2. intermediate answers.
The second way to solve
If you didn’t learn the squares of numbers up to 20 in school, then a simple method based on the use of a reference number may come in handy. This method allows you to simply and quickly multiply any two numbers less than 20. The method is very simple, you need to add the unit of the second to the first number, multiply this amount by 10, and then add the product of units. For example: 11*11=(11+1)*10+1*1=121. The rest of the 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.
The third solution
Another way 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 the fraction through the number 12, we get the following expression. (12 - 2) 2 + (12 - 1) 2 + 12 2 + (12 + 1) 2 + (12 + 2) 2 . If you know well the formulas for the square of the sum and the square of the difference, then you will understand how this expression can be easily reduced to the form: 5*12 2 +2*2 2 +2*1 2, 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.
The fourth solution
Also, this problem can be solved in 1 second if you know the Rachinsky sequences.
Rachinsky sequences for mental counting
To solve the famous Rachinsky problem, you can also use additional knowledge about the regularities of the sum of squares. It's about about those sums that are called Rachinsky sequences. So mathematically, you can prove that the following sums of squares are equal:
3 2 +4 2 = 5 2 (both sums equal 25)
10 2 +11 2 +12 2 = 13 2 +14 2 (the sum is 365)
21 2 +22 2 +23 2 +24 2 = 25 2 +26 2 +27 2 (which is 2030)
36 2 +37 2 +38 2 +39 2 +40 2 = 41 2 +42 2 +43 2 +44 2 (which equals 7230)
To find any other Rachinsky sequence, it is enough to simply write the equation the following kind(note that always in such a sequence, the number of summed squares on the right is one less than on the left):
n 2 + (n+1) 2 = (n+2) 2
This equation reduces to quadratic equation and is easily solved. In this case, "n" is 3, which corresponds to the first Rachinsky sequence described above (3 2 +4 2 = 5 2).
So the solution famous example Rachinsky, can be produced in the mind even faster than described in this article, simply by knowing the second Rachinsky sequence, namely:
10 2 +11 2 +12 2 +13 2 +14 2 = 365 + 365
As a result, the equation from the picture of Bogdan-Belsky takes the form (365 + 365)/365, which undoubtedly equals two.
Also, the Rachinsky sequence can be useful for solving other problems from the collection "1001 tasks for mental counting" by Sergei Rachinsky.
Evgeny Buyanov
photo clickable
Many have seen the painting "Mental Counting in a Public School". The end of the 19th century, a folk school, a board, an intelligent teacher, poorly dressed children, 9-10 years old, are enthusiastically trying to solve the problem written on the board in their minds. The first to decide communicates the answer in the teacher's ear, in a whisper, so that others do not lose interest.
Now look at the problem: (10 squared + 11 squared + 12 squared + 13 squared + 14 squared) / 365 =???
Crap! Crap! Crap! Our children at the age of 9 will not solve such a problem, at least in their minds! Why were grimy and barefoot village children taught so well in a one-room wooden school, while our children are taught so badly?!
Don't be quick to get angry. Take a look at the picture. Don't you think that the teacher looks too intelligent, somehow like a professor, and is dressed with obvious pretense? Why in school class such a high ceiling and an expensive stove with white tiles? Did they look like this village schools and teachers in them?
Of course they didn't look like that. The picture is called "Mental Counting in a Folk School S.A. Rachinsky". Sergey Rachinsky is a professor of botany at Moscow University, a person with certain government connections(for example, a friend of the chief prosecutor of the Synod Pobedonostsev), a landowner - in the middle of his life he abandoned all his affairs, went to his estate (Tatevo in the Smolensk province) and started there (of course, at his own expense) an experimental folk school.
The school was one-class, which did not mean that it taught for one year. In such a school they taught then 3-4 years (and in two-class schools - 4-5 years, in three-class schools - 6 years). Word one-class meant that children of three years of study make up a single class, and one teacher deals with them all within the same lesson. It was quite a tricky thing: while the children of one year of study were doing some writing 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 converged poorly with each other. Firstly, Rachinsky considered the teaching of the Church Slavonic language and the Law of God to be the basis of education for the people, and not so much explanatory as consisting in memorizing prayers. Rachinsky firmly believed that knowing by heart a certain amount of prayers, the child will certainly grow up as a highly moral person, and the very sounds of the Church Slavonic language will already have an effect that improves morality. For practice in the language, Rachinsky recommended that children be hired to read the Psalter over the dead (sic!).
Secondly, Rachinsky believed that it was useful for the peasants and they needed to quickly count in their minds. teaching mathematical theory Rachinsky was not very interested, but he did a very good job of mental counting in his school. The students firmly and quickly answered how much change per ruble should be given to someone who buys 6 3/4 pounds of carrots at 8 1/2 kopecks per pound. The squaring shown in the painting was the most complex mathematical operation studied at his school.
And finally, Rachinsky was a supporter of a very practical teaching of the Russian language - the students were not required to have any special spelling skills or good handwriting, they were not taught theoretical grammar at all. The main thing was to learn how to read and write fluently, albeit in a clumsy handwriting and not very competently, but it’s clear what a peasant could use in everyday life: simple letters, petitions, etc. Some manual labor was taught at Rachinsky’s school, the children sang in chorus, And that's where education ends.
Rachinsky was a real enthusiast. School became his whole life. Rachinsky's children lived in a hostel and were organized into a commune: they performed all the housekeeping work for themselves and the school. Rachinsky, who had no family, spent all the time with the children from early morning until late at night, and since he was a very kind, noble and sincerely attached person to children, his influence on the students was enormous. By the way, Rachinsky gave the first child who solved the problem a gingerbread (in the literal sense of the word, he did not have a whip).
themselves school lessons took 5-6 months a year, and the rest of the time Rachinsky worked individually with older children, preparing them for admission to various educational institutions of the next level; elementary folk school was not directly related to other educational institutions and after it it was impossible to continue training without additional training. Rachinsky wanted to see the most advanced of his students as elementary school teachers and priests, so he prepared children mainly for theological and teacher's seminaries. There were significant exceptions - first of all, it was the author of the painting himself, Nikolai Bogdanov-Belsky, whom Rachinsky helped to get into the Moscow School of Painting, Sculpture and Architecture. But, oddly enough, to lead peasant children along the main road educated person– gymnasium / university / public service- Rachinsky did not want to.
Rachinsky wrote popular pedagogical articles and continued to enjoy a certain influence in the capital's intellectual circles. The most important was the acquaintance with the ultra-influential Pobedonostsev. Under a certain influence of the ideas of Rachinsky, the spiritual department decided that there would be no sense in the Zemstvo school - the liberals would not teach children good - and in the mid-1890s began to develop their own independent network of parochial schools.
In some ways, the parish schools were similar to the Rachinsky school - they had a lot of Church Slavonic and prayers, and the rest of the subjects were accordingly reduced. But, alas, the dignity of the Tatev school was not transferred to them. Priests showed little interest in school affairs, ran 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 disliked the parochial school, because they realized that they hardly taught anything useful there, and prayers were of little interest to them. By the way, it was the teachers of the church school, recruited from pariahs of the clergy, who turned out to be one of the most revolutionized professional groups of that time, and it was through them that socialist propaganda actively penetrated into the village.
Now we see that this is a common thing - any author's pedagogy, designed for the deep involvement and enthusiasm of the teacher, immediately dies with mass reproduction, falling into the hands of uninterested and sluggish people. But for that time it was big bummer. Parish schools, which by 1900 accounted for about a third of primary public schools, turned out to be disliked by everyone. When, starting in 1907, the state began to send elementary education a lot of money, there was no question of passing subsidies to church schools through the Duma, almost all the funds went to the Zemstvo.
The more common zemstvo school was quite different from the Rachinsky school. For starters, the Zemstvo considered the Law of God completely useless. It was impossible to refuse his teaching, according to political reasons, so the Zemstvos pushed him into a corner as best they could. The law of God was taught by an underpaid and neglected parish priest, with corresponding results.
Mathematics at the Zemstvo school was taught worse than at Rachinsky, and to a lesser extent. The course ended with operations with simple fractions and non-metric system of measures. Up to raising to a degree, training did not reach, so the students of an ordinary elementary school simply would not understand the task depicted in the picture.
The zemstvo school tried to turn the teaching of the Russian language into world science, through the so-called explanatory reading. The technique consisted in dictating educational text in Russian, the teacher also additionally explained to the students what was said in the text itself. In such a palliative way, the lessons of the Russian language also turned into geography, natural history, history - that is, into all those developmental subjects that could not find a place in the short course of a one-class school.
So, our picture depicts not a typical, but a unique school. This is a monument to Sergei Rachinsky, unique personality and teacher, the last representative of that cohort of conservatives and patriots, to which one could not yet attribute famous expression"Patriotism is the last refuge of a scoundrel." The mass public school was economically equipped much poorer, the mathematics course in it was shorter and simpler, and teaching was weaker. And, of course, the students of an ordinary elementary school could not only solve, but also understand the problem reproduced in the picture.
By the way, how do students solve the problem on the board? Only direct, head-on: multiply 10 by 10, remember the result, multiply 11 by 11, add both results, and so on. Rachinsky believed that the peasant did not have writing materials at hand, so he taught only oral methods of counting, omitting all arithmetic and algebraic transformations that required calculations on paper.
famous Russian artist NIKOLAI PETROVICH BOGDANOV-BELSKY
wrote a unique and incredibly life story in 1895.
The work is called "ORAL ACCOUNT",
and in the full version
"VERBAL COUNTING. AT THE PEOPLE'S SCHOOL S.A. RACHINSKY.
The picture is painted in oil on canvas, it depicts a rural school of the 19th century during an arithmetic lesson.
A simple Russian class, the children are dressed in peasant clothes: bast shoes, trousers and shirts. All this very harmoniously and succinctly fits into the plot, unobtrusively bringing to the world the craving for knowledge on the part of the simple Russian people.
Students solve an interesting and complex example of solving a fraction in their mind. They are in deep thought and searching for the right solution. Someone thinks at the blackboard, someone stands on the sidelines and tries to compare 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.
Nearby is a teacher, a real person, Sergei Aleksandrovich Rachinsky, a famous botanist and mathematician, professor at Moscow University. rural children his skills and basics of mathematical thinking.
Warm colors bring kindness and simplicity of the Russian people, there is no envy and falsehood, there is no evil and hatred, children from different families with different incomes came together to make the only right decision.
This is very lacking in our modern life, where people are used to living in a completely different way, regardless of the opinions of others.
Nikolai Petrovich Bogdanov-Belsky, himself a former student of Rachinsky, dedicated the picture to an episode from the life of the school with a creative atmosphere that reigned in the classroom, to his teacher, the great genius of mathematics, whom he knew and respected well.
Now the picture 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 task depicted in the picture could not be offered to students of a standard elementary school: the program of one-class and two-class elementary public schools did not provide for the study of the concept of a degree.
However, Rachinsky did not follow a typical curriculum; he was confident in the excellent mathematical abilities of most peasant children and considered it possible to significantly complicate the mathematics program.
SOLUTION
First way
There are several ways to solve this expression. If you learned the 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: (100+121+144+169+196) divided by 365, which eventually becomes the quotient of 730 and 365, which is: 2. intermediate answers.
Second way
If you didn’t learn the squares of numbers up to 20 in school, then a simple method based on the use of a reference number may come in handy. This method allows you to simply and quickly multiply any two numbers less than 20. The method is very simple, you need to add the unit of the second to the first number, multiply this amount by 10, and then add the product of units. For example: 11*11=(11+1)*10+1*1=121. The remaining squares are also found: 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 way 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 the 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 well the formulas for the square of the sum and the square of the difference, then you will understand how this expression can be easily 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.
The fourth solution
Also, this problem can be solved in 1 second if you know the Rachinsky sequences.
in a series of two-digit numbers - the first five of its representatives - have an amazing property. The sum of the squares of the first three numbers in the series (10, 11 and 12) is equal to the sum of the squares of the next two (13 and 14). And this sum equals 365. Easy to remember! So many days in a year. If the year is not a leap year. Knowing this property, the answer can be obtained in a second. Without any intuition...
It is difficult to say which of the proposed methods of calculation is the simplest: everyone chooses his own based on the characteristics of his own mathematical thinking.
Working in a rural school
Sergei Alexandrovich Rachinsky brought to the 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, pastor-teetotaler, 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 Design Bureau at the Kirov Plant. In 1961-91 - Deputy Chairman of the USSR State Committee for the Use of Atomic Energy, laureate of the Stalin and State Prizes(1943, 1951, 1953, 1967) and many others.
S.A. Rachinsky (1833-1902), representative of the 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 creating 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.
Who has L.N. Tolstoy learned to build a village school,
P.I. Tchaikovsky received recordings of folk songs,
and V.V. Rozanov was spiritually instructed in matters of writing.
By the way, the author of the above-mentioned picture, Nikolai Bogdanov - Belsky, came from the poor and was a student of Sergei Alexandrovich, who created about three dozen rural schools and at his own expense helped his brightest students to realize themselves professionally, who became not only rural teachers (about 40 people!) Or professional artists (3 pupils, including Bogdanov), but also the teacher of the king’s children, a graduate of the St. Petersburg Theological Academy, Archpriest Alexander Vasiliev , and a monk of the Trinity-Sergius Lavra, like Titus (Nikonov).
Rachinsky built not only schools, but also hospitals in Russian villages, the peasants of the Belsky district called him nothing more than "father of their own." Through the efforts of Rachinsky, sobriety societies were recreated in Russia, uniting tens of thousands of people throughout the empire by the beginning of the 1900s.
Now this problem has become even more urgent, drug addiction has now grown to it. It is gratifying that the sobriety path of the educator is again picked up, that sobriety societies named after Rachinsky are reappearing in Russia
Russian ascetic teachers looked at teaching as a holy mission, a great service to the noble goals of raising spirituality among the people.
"May Man" Sergei Rachinsky passed away on May 2, 1902. Dozens of priests and teachers, rectors of theological seminaries, writers, and scientists gathered for his burial. In the decade before the revolution, more than a dozen books were written about the life and work of Rachinsky, the experience of his school was used in England and Japan.
Many have seen the painting "Mental Counting in a Public School". The end of the 19th century, a folk school, a blackboard, an intelligent teacher, poorly dressed children, 9-10 years old, enthusiastically try to solve the problem written on the blackboard in their minds. The first to decide communicates the answer in the teacher's ear, in a whisper, so that others do not lose interest.
Now look at the problem: (10 squared + 11 squared + 12 squared + 13 squared + 14 squared) / 365 =???
Crap! Crap! Crap! Our children at the age of 9 will not solve such a problem, at least in their minds! Why were grimy and barefoot village children taught so well in a one-room wooden school, while our children are taught so badly?!
Don't be quick to get angry. Take a look at the picture. Don't you think that the teacher looks too intelligent, somehow like a professor, and is dressed with obvious pretense? Why does the classroom have such a high ceiling and an expensive stove with white tiles? Did the village schools and the teachers in them really look like this?
Of course they didn't look like that. The picture is called "Mental counting in the folk school of S.A. Rachinsky." Sergei Rachinsky, 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, abandoned all his affairs in the middle of his life, went to his estate (Tatevo in the Smolensk province) and started there (of course, for own account) experimental folk school.
The school was one-class, which did not mean that it taught for one year. In such a school they taught then 3-4 years (and in two-class schools - 4-5 years, in three-class schools - 6 years). The word one-class meant that children of three years of study make up a single class, and one teacher deals with them all within the same lesson. It was quite a tricky thing: while the children of one year of study were doing some kind of written exercise, the children of the second year answered at the blackboard, the children of the third year read the textbook, etc., and the teacher alternately paid attention to each group.
Rachinsky's pedagogical theory was very original, and its different parts somehow poorly converged with each other. Firstly, Rachinsky considered the teaching of the Church Slavonic language and the Law of God to be the basis of education for the people, and not so much explanatory as consisting in memorizing prayers. Rachinsky firmly believed that a child who knew by heart a certain number of prayers would certainly grow up as 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 for the peasants and they needed to quickly count in their minds. Rachinsky was not very interested 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. The squaring shown in the painting was the most complex mathematical operation studied at his school.
And finally, Rachinsky was a supporter of a very practical teaching of the Russian language - the students were not required to have any special spelling skills or good handwriting, they were not taught theoretical grammar at all. The main thing was to learn to read and write fluently, albeit in a clumsy handwriting and not very competently, but it’s clear that a peasant could come in handy in everyday life: simple letters, petitions, etc. Even at Rachinsky’s school some manual labor was taught, the children sang in chorus, And that's where education ends.
Rachinsky was a real enthusiast. School became his whole life. Rachinsky's children lived in a hostel and were organized into a commune: they performed all the housekeeping work for themselves and the school. Rachinsky, who had no family, spent all the time with the children from early morning until late at night, and since he was a very kind, noble and sincerely attached person to children, his influence on the students was enormous. By the way, Rachinsky gave the first child who solved the problem a gingerbread (in the literal sense of the word, he did not have a whip).
School classes themselves took 5–6 months a year, and the rest of the time Rachinsky worked individually with older children, preparing them for admission to various educational institutions of the next level; the primary folk school was not directly connected with other educational institutions, and after it it was impossible to continue education without additional training. Rachinsky wanted to see the most advanced of his students as elementary school teachers and priests, so he prepared children mainly for theological and teacher's seminaries. There were also significant exceptions - first of all, this is the author of the painting himself, Nikolai Bogdanov-Belsky, whom Rachinsky helped to get into the Moscow School of Painting, Sculpture and Architecture. But, oddly enough, 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 the ideas of Rachinsky, the spiritual department decided that there would be no sense in the zemstvo school - the liberals would not teach children good - and in the mid-1890s began to develop their own independent network of parochial schools.
In some ways, the parochial schools were similar to the Rachinsky school - they had a lot of Church Slavonic and prayers, and the rest of the subjects were reduced accordingly. But, alas, the dignity of the Tatev school was not transferred to them. The priests showed little interest in school work, ran the schools under duress, did not teach in these schools themselves, and hired the most third-rate teachers, and paid them noticeably less than in zemstvo schools. The peasants took a dislike to the parochial school, because they realized that they almost didn’t teach anything useful there, and prayers were of little interest to them. By the way, it was the teachers of the church school, recruited from pariahs of the clergy, who turned out to be one of the most revolutionized professional groups of that time, and it was through them that socialist propaganda actively penetrated into the village.
Now we see that this is a common thing - any author's pedagogy, designed for the deep involvement and enthusiasm of the teacher, immediately dies with mass reproduction, falling into the hands of uninterested and sluggish people. But for the time it was a big bummer. Church-parish schools, which by 1900 accounted for about a third of primary public schools, turned out to be disliked by everyone. When, beginning in 1907, the state began to allocate large amounts of money to primary education, there was no question of subsidizing church schools through the Duma; almost all the funds went to the Zemstvo.
The more common zemstvo school was quite different from the Rachinsky school. For starters, the Zemstvo considered the Law of God completely useless. It was impossible to refuse his teaching, for political reasons, so the zemstvos pushed him into a corner as best they could. The law of God was taught by an underpaid and neglected parish priest, with corresponding results.
Mathematics at the Zemstvo school was taught worse than at Rachinsky, and to a lesser extent. The course ended with operations with simple fractions and non-metric units. Up to raising to a degree, training did not reach, so the students of an ordinary elementary school simply would not understand the task depicted in the picture.
The zemstvo school tried to turn the teaching of the Russian language into world science, through the so-called explanatory reading. The method consisted in the fact that while dictating the educational text in the Russian language, the teacher also additionally explained to the students what the text itself says. In such a palliative way, the lessons of the Russian language also turned into geography, natural history, history - that is, into all those developing subjects that could not find a place in the short course of a one-class school.
So, our picture depicts not a typical, but a unique school. This is a monument to Sergei Rachinsky, 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 equipped much poorer, the mathematics course in it was shorter and simpler, and teaching was weaker. And, of course, the students of an ordinary elementary school could not only solve, but also understand the problem reproduced in the picture.
By the way, how do students solve the problem on the board? Only direct, head-on: multiply 10 by 10, remember the result, multiply 11 by 11, add both results, and so on. Rachinsky believed that the peasant did not have writing materials at hand, so he taught only oral methods of counting, omitting all arithmetic and algebraic transformations that required calculations on paper.
P.S. For some reason, only boys are depicted in the picture, while all the materials show that children of both sexes studied with Rachinsky. What that means, I couldn't figure it out.
Many have seen the painting "Mental Counting in a Public School". The end of the 19th century, a folk school, a blackboard, an intelligent teacher, poorly dressed children, 9-10 years old, enthusiastically try to solve the problem written on the blackboard in their minds. The first to decide communicates the answer in the teacher's ear, in a whisper, so that others do not lose interest.
Now look at the problem: (10 squared + 11 squared + 12 squared + 13 squared + 14 squared) / 365 =???
Crap! Crap! Crap! Our children at the age of 9 will not solve such a problem, at least in their minds! Why were grimy and barefoot village children taught so well in a one-room wooden school, while our children are taught so badly?!
Don't be quick to get angry. Take a look at the picture. Don't you think that the teacher looks too intelligent, somehow like a professor, and is dressed with obvious pretense? Why does the classroom have such a high ceiling and an expensive stove with white tiles? Did the village schools and the teachers in them really look like this?
Of course they didn't look like that. The picture is called "Mental counting in the folk school of S.A. Rachinsky." Sergei Rachinsky, 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, abandoned all his affairs in the middle of his life, went to his estate (Tatevo in the Smolensk province) and started there (of course, for own account) experimental folk school.
The school was one-class, which did not mean that it taught for one year. In such a school they taught then 3-4 years (and in two-class schools - 4-5 years, in three-class schools - 6 years). The word one-class meant that children of three years of study make up a single class, and one teacher deals with them all within the same lesson. It was quite a tricky thing: while the children of one year of study were doing some kind of written exercise, the children of the second year answered at the blackboard, the children of the third year read the textbook, etc., and the teacher alternately paid attention to each group.
Rachinsky's pedagogical theory was very original, and its different parts somehow poorly converged with each other. Firstly, Rachinsky considered the teaching of the Church Slavonic language and the Law of God to be the basis of education for the people, and not so much explanatory as consisting in memorizing prayers. Rachinsky firmly believed that a child who knew by heart a certain number of prayers would certainly grow up as a highly moral person, and the very sounds of the Church Slavonic language would already have a moral-improving effect. For practice in the language, Rachinsky recommended that children be hired to read the Psalter over the dead (sic!).
Secondly, Rachinsky believed that it was useful for the peasants and they needed to quickly count in their minds. Rachinsky was not very interested 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. The squaring shown in the painting was the most complex mathematical operation studied at his school.
And finally, Rachinsky was a supporter of a very practical teaching of the Russian language - the students were not required to have any special spelling skills or good handwriting, they were not taught theoretical grammar at all. The main thing was to learn to read and write fluently, albeit in a clumsy handwriting and not very competently, but it’s clear that a peasant could come in handy in everyday life: simple letters, petitions, etc. Even at Rachinsky’s school some manual labor was taught, the children sang in chorus, And that's where education ends.
Rachinsky was a real enthusiast. School became his whole life. Rachinsky's children lived in a hostel and were organized into a commune: they performed all the housekeeping work for themselves and the school. Rachinsky, who had no family, spent all the time with the children from early morning until late at night, and since he was a very kind, noble and sincerely attached person to children, his influence on the students was enormous. By the way, Rachinsky gave the first child who solved the problem a gingerbread (in the literal sense of the word, he did not have a whip).
School classes themselves took 5–6 months a year, and the rest of the time Rachinsky worked individually with older children, preparing them for admission to various educational institutions of the next level; the primary folk school was not directly connected with other educational institutions, and after it it was impossible to continue education without additional training. Rachinsky wanted to see the most advanced of his students as elementary school teachers and priests, so he prepared children mainly for theological and teacher's seminaries. There were also significant exceptions - first of all, this is the author of the painting himself, Nikolai Bogdanov-Belsky, whom Rachinsky helped to get into the Moscow School of Painting, Sculpture and Architecture. But, oddly enough, 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 the ideas of Rachinsky, the spiritual department decided that there would be no sense in the zemstvo school - the liberals would not teach children good - and in the mid-1890s began to develop their own independent network of parochial schools.
In some ways, the parochial schools were similar to the Rachinsky school - they had a lot of Church Slavonic and prayers, and the rest of the subjects were reduced accordingly. But, alas, the dignity of the Tatev school was not transferred to them. The priests showed little interest in school work, ran the schools under duress, did not teach in these schools themselves, and hired the most third-rate teachers, and paid them noticeably less than in zemstvo schools. The peasants took a dislike to the parochial school, because they realized that they almost didn’t teach anything useful there, and prayers were of little interest to them. By the way, it was the teachers of the church school, recruited from pariahs of the clergy, who turned out to be one of the most revolutionized professional groups of that time, and it was through them that socialist propaganda actively penetrated into the village.
Now we see that this is a common thing - any author's pedagogy, designed for the deep involvement and enthusiasm of the teacher, immediately dies with mass reproduction, falling into the hands of uninterested and sluggish people. But for the time it was a big bummer. Church-parish schools, which by 1900 accounted for about a third of primary public schools, turned out to be disliked by everyone. When, beginning in 1907, the state began to allocate large amounts of money to primary education, there was no question of subsidizing church schools through the Duma; almost all the funds went to the Zemstvo.
The more common zemstvo school was quite different from the Rachinsky school. For starters, the Zemstvo considered the Law of God completely useless. It was impossible to refuse his teaching, for political reasons, so the zemstvos pushed him into a corner as best they could. The law of God was taught by an underpaid and neglected parish priest, with corresponding results.
Mathematics at the Zemstvo school was taught worse than at Rachinsky, and to a lesser extent. The course ended with operations with simple fractions and non-metric units. Up to raising to a degree, training did not reach, so the students of an ordinary elementary school simply would not understand the task depicted in the picture.
The zemstvo school tried to turn the teaching of the Russian language into world science, through the so-called explanatory reading. The method consisted in the fact that while dictating the educational text in the Russian language, the teacher also additionally explained to the students what the text itself says. In such a palliative way, the lessons of the Russian language also turned into geography, natural history, history - that is, into all those developing subjects that could not find a place in the short course of a one-class school.
So, our picture depicts not a typical, but a unique school. This is a monument to Sergei Rachinsky, 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 equipped much poorer, the mathematics course in it was shorter and simpler, and teaching was weaker. And, of course, the students of an ordinary elementary school could not only solve, but also understand the problem reproduced in the picture.
By the way, how do students solve the problem on the board? Only direct, head-on: multiply 10 by 10, remember the result, multiply 11 by 11, add both results, and so on. Rachinsky believed that the peasant did not have writing materials at hand, so he taught only oral methods of counting, omitting all arithmetic and algebraic transformations that required calculations on paper.
For some reason, only boys are depicted in the picture, while all the materials show that children of both sexes studied with Rachinsky. What this means is not clear.
