The story of one masterpiece. Bogdanov-Belsky

known to many. The picture shows a rustic school of the end of the XIX century during the lesson of arithmetic when solving the fraction in the mind.

Teacher - a real man, Sergey Alexandrovich Rachinsky (1833-1902), Botanist and Mathematics, Professor of Moscow University. In 1872, Rachinsky returned to his native village Tatevo, where he created a school with a hostel for peasant children, developed a unique learning technique oral accountBy putting the rustic kids his skills and the basics of mathematical thinking. The episode from the life of the school with a creative atmosphere that reigned in the lessons, and dedicated to his work Bogdanov-Belsky, in the past student Rachinsky.

However, with all the fame of the picture, few of the victims of her who sawed it in the content of that "difficult task", which is depicted on it. It is that an oral account is to quickly find the result of the calculation:

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

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

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

Really because

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

Wikipedia to count the value of the numerator offers the following way:

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

10 2 + (10 2 + 2 · 10 · 1 + 1 2) + (10 2 + 2 · 10 · 2 + 2 2) + (10 2 + 2 · 10 · 3 + 3 2) + (10 2 + 2 · 10 · 4 + 4 2) \u003d

5 · 100 + 2 · 10 · (1 + 2 + 3 + 4) + 1 2 + 2 2 + 3 2 + 4 2 \u003d

500 + 200 + 30 \u003d 730 \u003d 2 · 365.

As for me, is too wonderful. It is easier to do otherwise:

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

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

5 · 12 2 + 2 · 4 + 2 · 1 \u003d 5 · 144 + 10 \u003d 730,

The above arguments can be performed orally - 12 2 Of course, you need to remember, doubled the works of the squares of the bouncements on the left and right from 12 2 mutually destroyed and can not be considered, but5 · 144 \u003d 500 + 200 + 20 - not difficult.

We use this technique and orally we will find the amount:

48 2 + 49 2 + 50 2 + 51 2 + 52 2 \u003d 5 · 50 2 + 10 \u003d 5 · 2500 + 10 \u003d 12510.

Let's complicate

84 2 + 87 2 + 90 2 + 93 2 + 96 2 \u003d 5 · 8100 + 2 · 9 + 2 · 36 \u003d 40500 + 18 + 72 \u003d 40590.

Race Rachinsky

Algebra gives us a tool to raise the question about this interesting features Row of numbers

10, 11, 12, 13, 14

more widely: is this a number of five consecutive numbers, the sum of the squares of the first three of which is equal to the sum of the squares of the last two?

Describing the first of the desired numbers through X, we have an equation

x 2 + (x + 1) 2 + (x + 2) 2 \u003d (x + 3) 2 + (x + 4) 2.

It is more convenient, however, it is not first to designate it, but the second of the desired numbers. Then the equation will have a simpler type

(x - 1) 2 + x 2 + (x + 1) 2 \u003d (x + 2) 2 + (x + 3) 2.

Opening a bracket and making simplifications, we get:

x 2 - 10x - 11 \u003d 0,

from

x 1 \u003d 11, x 2 \u003d -1.

There are, therefore, two rows of numbers possessing the required property: Rapid

10, 11, 12, 13, 14

and ranks

2, -1, 0, 1, 2.

Indeed,

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

Two!!!

I would finish I would like the bright and touching memories of the author of the author's blog V. Sparkov in the article about the squares of two digits and not only about them ...

Once, in the year about 1962, our "mathematics", the love of Josephovna Drabkin, gave this task and us, 7-graders.

I was then very fond of the new KVN-Ohm who appeared. Painted for the team of the city of Fryazino near Moscow. "Fryazins" differed by a special ability to apply the logical "express analysis" to solve any task, "pulling" the very tricky question.

I could not count in mind to quickly. However, by applying the "Fryazin" method, I figured, the answer should be expressed in an integer. Otherwise, this is no longer an "oral account"! This number could not be a unit - even if there were equal 5 hundred in the numerator, the answer was clearly more. On the other hand, before the number "3" he obviously de reached.

- Two!!! - I blurted out, for a second, ahead of my friend, Lenya Strubova, best mathematics Our school.

- Yes, indeed two, - confirmed Lenya.

- How did you think? - asked the love of Josephovna.

- I did not think. Intuition - I replied under the laughter of the whole class.

- If I did not consider it - the answer is not considered - "Scalaburila" love Josephovna. Lenya, didn't you think too?

- No, why, Peredko answered Lenya. It was necessary to fold 121, 144, 169 and 196. I pairly folded the numbers the first and third, the second and fourth. This is more comfortable. It turned out 290 + 340. The total amount, including the first hundred - 730. We divide on 365 - we get 2.

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

* * *

... years have passed. Our city acquired his "miracle of the world" - mosaic paintings in underground transitions. There were many transitions, paintings - even more. The topics were the most different - the defense of Rostov, space ... In the central transition, under the crossroads of Engels (now - large garden) - Voroshilovsky made a whole panorama of the main stages life path soviet man - maternity hospital - kindergarten - School, graduation ball ...

At one of the "school" paintings, a familiar scene could be seen - the solution of the problem ... Let's call it: "Rachinsky's task" ...

... We took years, people passed ... merry and sad, young and not very. Someone recalled his school, someone at the same time "moved the brains" ...

Wonderfully worked masters tiled and artists who were led by Yuri Nikitovich Labin residents!

Now the "Rostov miracle" is "temporarily unavailable." Trade was coming to the fore - in direct and figurative sense. Nevertheless, we hope that in this wearing a phrase - the main word "temporarily" ...

Sources: Ya.I. Pererelman. Entertaining algebra (Moscow, "Science", 1967), Wikipedia,

Objectives lesson:

• development of abilities to observe;
• development of ability to think;
• development of ability to express thought;
• increasing interest in mathematics;
• touching the art of N.P. Bogdanova-Belsky.

DURING THE CLASSES

Human learning is a work that brings up and forms a person.

Four pages from the life of the picture

First page

The painting "Oral Account" was written in 1895, that is, 110 years ago. This is a kind of anniversary of the painting, which is the creation of man's hands. What is shown in the picture? Some boys gathered near the class board, and consider something. Two boys (these are those that stand ahead) turned away from the board and recall something, and maybe believe. One boy whispers something in the ear man, apparently, teacher, and the other seems to be overheard.

- Why are they in the lapties?

- Why there are no girls, only one boys?

- Why are they standing back to the teacher?

- What do they do?

You already, right, realized that students and teachers were depicted here. Of course, students' costumes are unusual: some guys in the lapties, and at one of the heroes of the picture (the one that is depicted on foreground), In addition, and the shirt of the torn. It is clear that this picture is not from our school life. So the inscription in the picture is 1895 - the time of the old pre-revolutionary school. The peasants lived then poorly, they themselves and their children went to the noodles. The artist portrayed 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 in the noodles, and the rest - in boots. Obviously guys from families rich. Well, why the girls are not depicted in the picture, it is also not difficult to understand: after all, at that time, girls, as a rule, did not accept the school. The study was "not their business", and the boys did not go far away.

Page Two

This picture is called "oral account." See how the boy depicted in the foreground of the painting is concentrated. A teacher gave a difficult task. But, probably, this student will soon finish its work, but there should be no mistakes: he really belongs to an interpretation. But the student who whispers something in the ear teacher is visible, already decided the task, only the answer is not quite correct. See: The teacher listens the student's answer carefully, but on his face it is no approval, it means that the student did something wrong. Or maybe the teacher patiently expects when otherwise they count rightly, as the first and therefore in no hurry to approve his answer?

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

And what task gave them a teacher? Will you be able to solve it and we?

- But try.

On the board, I will write as you used to write:

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

As can be seen, each of the numbers 10, 11, 12, 13 and 14 must be multiplied by itself, the results are folded, and the resulting amount is divided by 365.

- That's the task (such an example will not soon decide, and even in the mind). Still, try to count orally, in difficult places I will help you. Ten ten - 100, it knows everyone. Eleven multiplied by eleven - it is also not difficult to count: 11 · 10 \u003d 110, and even 11 - only 121. 12 · 12 - this is also not slyly to count: 12 · 10 \u003d 120, and even 12 · 2 \u003d 24, and everything will be 144. I also counted that 13 · 13 \u003d 169 and 14 · 14 \u003d 196.

But while I have multiplied, then almost forgot what numbers I got. Then I remembered them, and after all, these numbers need to be further folded, but then the amount is divided by 365. No, it's already you can not calculate.

- We'll have to help a little.

- What numbers did you get?

- 100, 121, 144, 169 and 196 - they counted many.

"Now you probably want to add all five numbers at once, and then share the results for 365?"

- We will do it differently.

- Well, lay down the first three numbers: 100, 121, 144. How much will it turn out?

- And to share how much you need?

- Also on 365!

- How much will it work out if the sum of the first three numbers is divided into 365?

- One! - It's already every will convert.

- Now fold the remaining two numbers: 169 and 196. How much will it work out?

- also 365!

- This is the example, and quite simple. It turns out only two!

- Only for his decision, it is necessary to know well that the amount can not be divided immediately all, and in parts each term separately, or by groups in two or three terms, and then fold the resulting results.

Third page

This picture is called "oral account." Posted by her artist Nikolai Petrovich Bogdanov-Belsky, who lived from 1868 to 1945.

Bogdanov-Belsky knew his little heroes very well: grew in their medium, was once a shepherd. "... I am an illegitimate son of a poor bobillot, because of Bogdanov, and Belsky became the name of the county," the artist told about himself.

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

N.P. Bogdanov-Belsky graduated from the Moscow School of Painting, Scary and Architecture, studied in such famous artistslike V.D. Polenov, V.E. Makovsky.

A lot of portraits and landscapes are written by Bogdanov-Belsky, but in the memory of people he remained, above all, as an artist, who managed to poetically and correctly, to tell about the intended rural defector, greedily stretching for knowledge.

Who among us are not familiar with the paintings "at the school door", "newcomers", "writing", "rustic friends", "in a sick teacher", "voice testing", is the name of only some of them. Most often, the artist depicts children at school. Adorable, trusting, focused, thoughtful, full of living interest and always marked by a natural mind, knew such and loved the peasant kids Bogdanov-Belsky, such perpetuated in their works.

Fourth page

The artist depicted in this picture of unseen-minded students and teachers. From 1833 to 1902, the well-known Russian teacher Sergei Aleksandrovich Rachinsky lived, a wonderful representative of Russian educated people in a last century. He was a doctor of natural sciences and professor at Botany Moscow University. In 1868, S.A. Rachinsky decides to go to the people. "He holds the exam" on the title of teacher primary classes. Its funds opens up a school for peasant children in the village of Tatyevo Smolensk province and becomes a teacher in it. So, his disciples thought 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 in the lesson of the oral solution to the tasks. By the way, the artist N.P. Bogdanov-Belsky was a student S.A. Rakinsky.

This picture is the anthem to the teacher and the student.

Surely, everyone who has studied at school (especially in soviet time), remember a picture from the textbook "Mathematics", in which schoolchildren try to solve an example written on the board. Remembered? I am sure that yes.

Not so often pinched us at the time In order to activate our attention and instill love for the subject. Most approved manifestation: "You must learn!" , "This is your job,", etc.

But anyone (and in an adult, with a more conscious, so to speak, an approach) will involuntarily arise: "Why should I learn? Why do I need it? ".

And here you can go at least two ways. The first is to explain to the annoying young creation of his benefit from the exercise. And immediately it becomes clear that it is a dead end. Modern schoolchildren have no guidance and values \u200b\u200bin order to try and "tear claws", strain and deny themselves in something. I do not say that there are no such children at all. Their enough, and among my students such "conscious elements" a lot. But mostly, now learn either from under the stick, or, after the sleeves. And it grieves.

But at all times, and now especially, before the question of the motivation of students for learning was. And this article has the goal to awaken interest in mathematics with such techniques as an oral account.

"How can this be done?", - You ask.

"Very simple," I say in response.

Just look at the picture of the Russian artist N. P. Bogdanova-Belsky « Verbal counting. IN folk school S. A. Rakinsky. "

See what is depicted on it. This is a village school of the XIX century. And the real, unreasonable artist. And in the picture - as a real man, Rachinsky Sergey Alexandrovich (1833 - 1902), noble origin. The name may not be familiar for the majority. Nevertheless, the famous personality in teacher circles at the time. He was a professor at Moscow University, Dr. Botany, a good writer, a corresponding member of the Imperial St. Petersburg Academy of Sciences and others.

Merit of S.A. Rachinsky is enough: Starting with the fact that in 1872 he created a school with a hostel for peasant children, he himself taught there painting and drawing and raised a lot famous personalitiesCreated the first textbook on a "mental account" in Russia. But the most valuable for teachers of mathematics is that he developed a unique teaching methodology to the interpretation.

His famous phrase: "We will not beat the field behind the pencil and paper. It is necessary to decide mentally "herself speaks for itself. And here you will not argue.

Rachinsky reported to Emperor Alexander III so:

"You will remember remember how a few years ago I reported to you about Sergei Rachinsky, a spillible person who, leaving the professorship at Moscow University, went to live in his estate, in the most distant forest wilderness of the Belsky County of Smolensk province, and lives there is no one For more than 14 years, working in the morning to night for the benefit of the people. He breathed at all new life To the whole generation of peasants ... became truly benefactor, founding and leading, with the help of 4 priests, 5 folk schools, which are now a sample for the whole earth. This is a wonderful person. Everything that he has, and all the means of their estate, he gives to a penny on this matter, limiting his needs to the last degree "

And in response from Nicholas II, imperial words were sounded in the glory of the Great Metzenate-Pedagogue:

"Schools that are based on and led ... have become ... School of Labor, sobriety and good morals and a lively model for all such institutions. My close to my heart is a concern for folk education, which you are worthy of serving, encourages me to identify you sincere my appreciation. Staying for you a favorable nikolay "

So, as shown in the picture, causing your attention, at least the fact that children are depicted on it. Yes, not just frolic or chasing the dog, playing with hide and hide and caring apples in the neighbor garden (how many similar plots we know from painting)?

Picture "Oral account. In the folk school S.A. Rachinsky "

On the artist's canvas N. P. Bogdanova-Belsky An episode was discharged from the life of a school with the creative atmosphere, which reigned in the lessons of mathematics, asked by teachers of the Tatev School Rachinsky.

On the board was written non-pieces at first glance computational example:

But how he was interested in the guys who gathered at the board!

Someone thoughted alone, someone with a group of classmates discusses his ideas, someone pulled to the teacher, allegedly asking for support and whispering his answer to His response ("What if the guys would think then?")

And it would seem, it will not work ... and okay. This is just an example. "Think ...", - as he says the hero from the cartoon "in the country of unbearable lessons."

And yet schoolchildren think tensely, think. And the teacher sat in the corner as an outside observer and ... neither. And I would like, it would be possible to tell, direct the idea in the right direction. But the example is given: to figure out, do not rush and give the correct answer. And most importantly - to do all mental operations orally.

I am sure: suggest contemporary guys such an example, most of them would get immediately in the portfolios for calculators. They learned to think our modern schoolchildren strain. And who would not have been lazy (or at hand did not turn out to be "crutches for the brain"), he would most likely consider this example "in the forehead", i.e. Would perform consistently written actions. And thus complicated "life."

But everything is much easier and more interesting. See:

See, everything is simple. And if you know the property of some numbers that the sum of the squares of three consecutive numbers is equal to the sum of the squares of the next two consecutive numbers behind them, then it was possible to do without these calculations.

"This task is also good that it is not only the brain thumps, but also for many far-reaching, generalizations of coma," said S.A. Khachinsky.

AND Rachinsky tasks also have. But I will write about it later.

So, the main character today was the picture "". Recently, 195 years old, the most famous lesson of mathematics, who spent in the Peasant School of the Oleninsky County of the Smolensk Province Sergey Aleksandrovich Rachinsky in the peasant school. It was he who left the University Department to become a rural teacher. And thanks to him, Russia received a lot outstanding figures cultures and arts, among whom were Tretyakov, Nikolay Stepanovich And the author of the picture in this article Pictures Nikolai Petrovich Bogdanov - Belsky.

What impact was on the formation of these two legendary personalities S. A. Rachinsky, we will consider in the next article. And at the same time we will touch on the topical topic about the influence of the teacher's personality on the younger generation.

But if you were interested to get acquainted with the identity of S.A. Rachinsky and the picture "Oral account. At the People's School of S.A. Rachinsky "Artist N.P. Bogdanov-Belsky, press the buttons below and share this knowledge with friends.

This picture is called a "oral account at the Rachinsky school", and painted her the same boy who stands in the picture in the foreground.
He grown, graduated from this church-parish school of Rachinsky (by the way, friend K.P. Pobonyostsev, an ideologist of church-parish schools) and became a famous artist.
Do you know about whom?

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

"Verbal counting. In the People's School of S. A. Rachinsky, "painting by the artist N. P. Bogdanov-Belsky written in 1985.

On the canvas, we see an oral account lesson in a rustic school XIX. century. Teacher - face is quite real, historical. This is a mathematician and botany, Professor of Moscow University Sergey Aleksandrovich Rachinsky. Ages to the ideas of militarian in 1872 Rachinsky arrived from Moscow to his native village Tatevo and created a school with a hostel for rustic children. In addition, he developed his own teaching methodology to the interpretation. By the way, the artist Bogdanov-Belsky and himself was a student of Rachinsky. Pay attention to the task written on the board.

Can you decide? Try.

O Radian School Rachinskywho is still in late XIX. A century instilled the rustic guys the skills of the oral account and the basics of mathematical thinking. In the illustrations to the note - the reproduction of the paintings of Bogdanov-Belsky depicts the process of solving in the mind of the fraction 102 + 112 + 122 + 132 + 142365. The readers were asked to find the simplest and rational method of finding an answer.

As an example, a calculation option was given, in which it was proposed to simplify the numerator of the expression, which thus grouped it to the terms:

102 + 112 + 122 + 132 + 142 \u003d 102 + 122 + 142 + 112 + 132 \u003d 4 (52 + 62 + 72) +112+ (11 + 2) 2 \u003d 4 (25 + 36 + 49) + 121 + 121 + 44 + 4 \u003d 4 × 110 + 242 + 48 \u003d 440 + 290 \u003d 730.

It should be noted that this decision was found "honest" - in mind and blindly, while walking with a dog in the grove near Moscow.

For a proposal to send its solutions to more than twenty readers responded. Of these, slightly less than half are offered to represent the numerator in the form of

102+ (10 + 1) 2+ (10 + 2) 2+ (10 + 3) 2+ (10 + 4) 2 \u003d 5 × 102 + 20 + 40 + 60 + 80 + 1 + 4 + 9 + 16.

This is M. Graph Lubarsky (Pushkino); A. Glutsky (Krasnokamensk Moscow Region); A. Simonov (Berdsk); V. Orlov (Lipetsk); Kudrin (Rechitsa, Republic of Belarus); V. Zolotukhin (Serpukhov Moscow Region); Yu. Letnofullova, student of the 10th grade (Ulyanovsk); O. Chizhova (Kronstadt).

Even more rationally, the terms (12-2) 2+ (12-1) 2 + 122 + (12 + 1) 2+ (12 + 2) 2 were presented, when the works ± 2 per 1, 2 and 12 are mutually destroyed, . Zlokazov; M. Lyechanova, Yekaterinburg; Schneider, Moscow; I. Gornostayev; I. Andreev-Egorov, Severobay Kalsk; V. Zolukhin, Serpukhov Moscow region.

Reader V. Idiatullin offers its way to transform sums:

102 + 112 + 122 \u003d 100 + 200 + 112-102 + 122-102 \u003d 300 + 1 × 21 + 2 × 22 \u003d 321 + 44 \u003d 365;

132 + 142 \u003d 200 + 132-102 + 142-102 \u003d 200 + 3 × 23 + 4 × 24 \u003d 269 + 94 \u003d 365.

D. Kopylov (St. Petersburg) reminds one of the most famous mathematical finds 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 blackboard. And if the students of Rachinsky knew the squares of the first fifteen - twenty numbers, the task was reduced to the addition of three-digit numbers. For example: 132 + 142 \u003d 169 + 196 \u003d 169 + (200-4). Hundreds, dozens and units are detached separately, and it remains only to calculate: 69-4 \u003d 65.

The task of Yu. Novikov, Z. Grigoryan (Kuznetsk Penza region), V. Maslov (Znamensk, Astrakhan Region), N. Lakhov (St. Petersburg), S. Cherkasov (P. Tetkino Kursk region .) And L. Zhevakin (Moscow), which also proposed a fraction calculated in the same way:

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

A. Shamshurin (Borovichi Novgorod region) applied to calculating squares of numbers a recurrent formula type A2i \u003d (AI-1 + 1) 2, highly simplifying calculations, for example: 132 \u003d (12 + 1) 2 \u003d 144 + 24 + 1 .

Reader V. Parshin (Moscow) tried to apply the rule of rapid construction to the second degree from the book E. Ignatiev "in the kingdom of the Smekalki", discovered a mistake in it, led his equation and applied it to solve the problem. IN general A2 \u003d (A - N) (A + N) + N2, where N is any number less than a. Then
112 \u003d 10 × 12 + 12,
122 \u003d 10 × 14 + 22,
132 \u003d 10 × 16 + 32
etc., then the components are grouped rationally, so the numerator in the end takes the form 700 + 30.

Engineer A. Trofimov (P. Ibresi, Chuvashia) produced very interesting analysis numeric sequence in the numerator and transformed it into arithmetic progression View

X1 + x2 + ... + xn, wherexi \u003d ai + 1-Ai.

This progression is fair approval

Xn \u003d 2n + 1, i well2n + 1 \u003d a2n + 2n + 1,

Where does the equality come from

A2N + K \u003d A2N + 2NK + N2

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

Finally, the correct answer was possible to obtain by estimates, and not accurate calculations. A. Polyshkin (Lipetsk) notes that, although the sequence of squares of numbers is not linear, you can take a square of the average number five times - 12, rounded it: 144 × 5≈150 × 5 \u003d 750. A 750: 365≈2. Since it is clear that the oral account must operate in integers, this answer is probably faithful. It was obtained in 15 seconds! But it can still be checked additionally, making an estimate "bottom" and "top":

102 × 5 \u003d 500,500: 365\u003e 1
142 × 5 \u003d 196 × 5<200×5=1000,1000:365<3.

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

The author of the notes "Said Prediction" G. Poloznev (Berdsk Novosibirsk Region) rightly noticed that the numerator must certainly be kathedenger, that is, equal to 365, 730, 1095, etc. Assessing the size of partial sums uniquely indicates the second number.

It is difficult to say which of the proposed methods of calculation is simple: everyone chooses its own on the features of its own mathematical thinking.

For details, see: http://www.nkj.ru/archive/articles/6347/ (Science and Life, Oral Account)

In this picture, Rachinsky and author are also depicted.

Working in the rural school Sergey Aleksandrovich Rachinsky brought into people: Bogdanova I. L. - Infecticalist, Doctor of Medical Sciences, Corresponding Member of AMN USSR;
Vasilyeva Alexander Petrovich (September 6, 1868 - September 5, 1918) - Archpriest, the confessor of the royal family, shepherd-sober, patriot monarchist;
Syanka Nikolai Mikhailovich (December 10, 1906 - September 4, 1991) - Doctors of Technical Sciences (1956), Professor (1966), fell. The figure of Science and Technology of the RSFSR. In 1941 - Deputy. GL Designer on tank building, 1948-61 - beginning. OKB in Kirovsky z-de. In 1961-91 - Deputy. Previous State K-OSR for the use of atomic energy, Stalin's laureate and state. premiums (1943, 1951, 1953, 1967); And many others.

S.A. Rachinsky (1833-1902), a representative of the ancient noble family, was born and died in the village of Tatevo of the Belsky County, and there was a corresponding member of the Correspondent of the Imperial St. Petersburg Academy of Sciences dedicated to the creation of a Russian rural school. In May of last year, 180 years old since the birth of this outstanding Russian man, a genuine devotee (there is an initiative for its canonization as the Holy Russian Orthodox Church), a tireless detergent, forgotten by us by a rural teacher and a striking thinker, from which L.N. Tolstoy learned to build rural school, P.I. Tchaikovsky received the records of folk songs, and V.V. Rozanov was spiritually instructed in writing issues.

By the way, the author of the picture mentioned above Nikolai Bogdanov (Belsky-pseudonym, since the painter was born in the village of Shiki's Belsky County of Smolensk province) came out of the poor and was just a student of Sergei Alexandrovich, who created about three dozen rural for thirty years schools and to their own means helped professionally realize the most vivid students who became not only rural teachers (about forty person!) or professionally artists (three pupils, including Bogdanova), but also, let's say, the lawpower of royal children, as a graduate of St. Petersburg The Spiritual Academy of Archpriest Alexander Vasilyev, or the monk Trinity-Sergiye Lavra, like tit (Nikonov).

Rachinsky was built in Russian villages not only schools, but also hospitals, the peasants of the Belsky County were not different as "father of his native." Rachinsky's efforts in Russia were recreated by the society of sobriety, uniting to the beginning of the 1900s tens of thousands of people throughout the empire. Now this problem is even more updated, it has been involved in it now and drug addiction. It is gratifying that the sober-feeding path of the enlightement again picked up that the Society of Rachinsky's sobriety appears again in Russia, and this is not some "Alanon" (the American society of anonymous alcoholics, resembling the sect and, unfortunately, leaked to us in early 1990s ). Recall at the same time that before the October coup 1917, Russia was one of the most non-singing countries of Europe, yielding "palp trees" only Norway.

Professor S.A. Rachinsky

* * *

Writer V. Rozanov noticed that the Tatev School of Rachinsky became the parent school, from which "all new and new bees fly away and in a new place are creating a matter and faith of old. And these faith and the case were that Russian teachers of devotees looked at the teacher as a holy mission, to the great ministry to the noble goals of lifting spirituality in the people. "

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"Did you manage to meet in the modern life of the heirs of ideas Rachinsky?" - I ask Irina Ushakov, and she talks about a person who divided the fate of the People's Teacher Rachinsky: and his lifetime conviction, and post-revolutionary crop. In the 1990s, when it was just beginning to study the activities of Rachinsky, I. Ushakov often met with the teacher of the Tatev School Alexandra Arkadevna Ivanova and recorded her memories. Father A.A. Ivanova, Arkady Averyanovich Seryakov (1870-1929), was a favorite student of Rachinsky. It is depicted on the painting of Bogdanov-Belsky "The Patient Teacher" (1897) and, it seems, we see him at the table in the picture "Sunday readings in a rural school"; On the right, under the portrait of the sovereign, depicted Rachinsky and, I think about. Alexander Vasilyev.

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

In the 1920s, when the prayed people, along with the tempts, Ruschil along with the Barquish Manors and all the good dispensations of the nobles, the names of Rachinsky were desecrated, the temple in Tatev turned into a repair shop, the manor was looted. All teachers, Rachinsky pupils, are expelled from school.

Rests at home in the manor Rachi (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), talks about the attitude towards the rural enlightener Rachi Ober-Prosecutor of the Sacred Synod KP. Victoryosseva, which on March 10, 1880 he wrote to Jesarevich's heir to the great prince Alexander Alexandrovich (read, as if about our days): "The impressions of the Petersburg are extremely severe and irreparable. Live in this time and see at every step of people without direct activities, without a clear thought and a solid solution engaged in small interests of your I, immersed in the intrigue of your ambition, accurate money and enjoyment and idle-chatting, - just handle the soul ... good Impressions come only from the inside of Russia, from somewhere from the village, from the wilderness. There is still a spring spring, which breathes even freshness: from there, and not from here our salvation.

There are people with the Russian soul, who make a good deed with faith and hope ... Still, it is still gratifying at least one such one ... the friend of my Sergey Rachinsky, a truly good and honest person. He was a professor at Botanist at Moscow University, but when he was tired of the raised straight and intrigue between professors, he left the service and settled in his village, away from all railways ... He truly became the benefactor of the whole locality, and God sent him people "From the priests and landlords who work with him ... There is no chatter, but a matter and true feeling."

On the same day, the heir to Zesarevich replied to the victoriousness: "... how you envy people who can live in the wilderness and bring true benefit and be far from all the abominations of city life, but especially St. Petersburg. I am sure that there are many similar people in Russia, but they do not hear about them, and they work quietly, without phrases and boasting ... "

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

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N.P. Bogdanov-Belsky. Verbal counting. In the folk school S.A. Rachinsky, 1895

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"May man" Sergey Rachinsky passed from life on May 2, 1902 (under Art.). Dozens of priests and teachers, rectors of spiritual seminaries, writers, scientists have come to his burial. For a decade, more than a dozen books were written about the revolution about the life and activities of Rachinsky, the experience of his school was used in England and in Japan.

Many saw the picture "Oral Account in the People's School." The end of the 19th century, the folk school, board, an intelligent teacher, poorly dressed children, 9-10 years old, are trying to decide with enthusiasm to decide in the mind of the task written on the board. The first decided to tell the teacher's response to the ear, whisper, so that others do not lose interest.

Now let's look at the problem: (10 in square + 11 in square + 12 in square + 13 in square + 14 in square) / 365 \u003d ???

Heck! Heck! Heck! Our children at the age of 9 will not solve such a task, in any case in the mind! Why are the chumas and barefoot rustic children in a wooden school from one room taught so good, and our children teach so badly?!

Do not rush to resent. Close to the picture. It doesn't seem to you that the teacher looks too intelligent, somehow in a professorship, and dressed with a clear complaint? Why in school class such a high ceiling and a robing oven with white tiled tiles? Did the village schools and teachers looked like this?

Of course, they looked wrong. The picture is called "oral account at the People's School of S.A. Rachinsky." Sergey Rachensky - Professor Botanists Moscow University, a person with certain government connections (for example, a friend of the Ober-Prosecutor of the Synod of victoryossev), the landowner - in the middle of life threw all things, went to his estate (Tatevo in the Smolensk province) and started there (of course, for Your account) Experimental Folk School.

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

The Pedagogical theory of Rachinsky was very original, and it was somehow different with each other. First, the basis of education for the people Rachensky considered the training of the church-Slavic language and the law of God, and not so much explanatory as consistent with the memorization of prayers. Rachinsky firmly believed that a certain amount of prayer who knows a certain amount of prayer will certainly grow by a highly moral person, and the sounds of the Church-Slavic language themselves will have improving morality impact. For practice in Rachinsky, recommended the children to hire a psalter over the dead (SIC!).

Secondly, Rachinsky believed that the peasants are useful and need to be quickly considered in the mind. The teaching of the mathematical theory Rachi was interested in a little, but he set up an oral account in his school very well. The disciples firmly and quickly answered how much passing from the ruble should be given to the one who buys 6 3/4 pounds of carrots at 8 1/2 penny per pound. The construction of the square shown in the picture was the most difficult mathematical operation studied at his school.

Finally, Rachinsky was a supporter of very practical teaching of the Russian language - from students did not need any spelling skills, nor good handwriting, theoretical grammar did not teach them at all. The main thing was to learn how to read and write, let the knot and not too correctly, but it is clear that the peasant can be useful in everyday life: simple letters, petitions, etc. Still in the school of Rachinsky, some manual work was taught, children sang choir, And on this all education and ended.

Rachinsky was a real enthusiast. The school has become his life. Kids in Rachinsky lived in the hostel and were organized in the commune: they performed all the work on the economic maintenance of themselves and schools themselves. Rachinsky, who did not have a family, spent all the time from the early morning to late evening, and since he was very kind, noble and sincerely attached to the children, his influence on students was huge. By the way, the first deciding the task of the child Rachinsky gave the gingerbread (in the literal sense of the word, he did not have a whip).

School classes themselves occupied 5-6 months a year, and at the rest of the time Rachinsky individually engaged with older children, preparing them for admission to various educational institutions of the next step; The initial folk school was not directly related to other educational institutions and it was impossible to continue learning without further training. Rachinsky wanted to see the most advanced from his student teachers of primary school and priests, so he prepared children mainly in spiritual and teacher seminary. There were also significant exceptions - first of all, this is the author of the painting, Nikolai Bogdanov-Belsky, who Rachinsky helped to get to the Moscow School of Painting, Scary and Architecture. But, oddly enough, to conduct peasant children in the trunk path of the educated person - Gymnasium / University / State Service - Rachinsky did not want.

Rachinsky wrote popular pedagogical articles and continued to enjoy certain influence in the capital's intellectual circles. The most important was to familiarize with ultravyoli victorious. Under a certain influence of the ideas of Rachinsky, the spiritual department decided that there would be no sense from the Zemskaya school - the liberals of children would not be taught - and in the mid-1890 began to develop its own independent network of church-parish schools.

Some of the parish schools were similar to the Rachinsky school - there were many church-Slavic languages \u200b\u200band prayers in them, and the rest of the items were respectively reduced. But, alas, they were not transferred to the advantages of the Tatev school. The priests of school business were interested in little, managed schools from under the stick, they themselves did not teach themselves in these schools, and teachers hired the most third-time, and paid them noticeably less than in Zemsky schools. The peasants of the parish school were nevilubilized, as they realized that it was almost not taught helpful there, they were not interested in the prayers. By the way, it was the teacher of the church school that came from a parlia of the spiritual estate, turned out to be one of the most revolutionized professional groups of that time, and it was through them that the socialist propaganda was actively penetrated into the village.

Now we see that this is a common thing - any author's pedagogy, designed for deep involvement and enthusiasm of the teacher, will immediately reach the mass reproduction, falling into the hands of disinterested and sluggish people. But for that time it was a big bummer. Church-parish schools, by 1900, who were about a third of the initial folk schools, were unims to everyone. When, since 1907, the state began to send big money to primary education, there was no question about conducting church schools across the Duma, almost all the means left the Zemes.

A more common Zemskaya school was very different from Rachinsky school. To begin with, the land considered the law of God completely useless. It was impossible to abandon his teaching, for political reasons, so the zemstvo as they could kill him. The law of God taught the parish priest who paid little and did not pay attention to him, with the relevant results.

Mathematics in the Zemstvo school was taught worse than Rachinsky, and in a smaller volume. The course ended on operations with simple fractions and a nonmetric system of measures. Before the exercise, the training did not reach, so that students of an ordinary primary school would simply not understand the task shown in the picture.

Education to the Russian language Zemskaya school tried to turn into world studies, through the so-called explanatory reading. The technique was that the dictation learning text in the Russian language, the teacher also additionally explained to schoolchildren, as stated in the text itself. Such palliatively, the lessons of the Russian language also turned into geography, environmental studies, that is, that is, all those developing items that did not find a place in a short year of a class school.

So, our picture is depicting not typical, but a unique school. This is a monument to Sergey Rachinsky, a unique person and teacher, the last representative of the cohort of conservatives and patriots, to which it was still impossible to attribute the famous expression "Patriotism is the last refuge of the villain." The mass folk school was in economic attitude to be much poorer, the mathematics course in it was shorter and easier, and teaching is weaker. And, of course, students of an ordinary primary school could not only decide, but also to understand the task reproduced in the picture.

By the way, how do schoolchildren solve the task on the board? Only direct, in the forehead: multiply 10 to 10, remember the result, multiply 11 to 11, fold both results, and so on. Raczynski thought that the peasant is not on hand supplies, so he taught only verbal techniques accounts, omitting all the arithmetic and algebraic transformations, requiring calculations on paper.

For some reason, the picture shows one boys, while on all materials it can be seen that Rachinsky studied children of both sexes. What it means is incomprehensible.