Picture of Bogdanov Belsky Oral account decision. Lesson-excursion by painting N.P

When I come to the Tretyakovka with another group, of course, know that mandatory list paintings by which you can not pass. I keep everything in my head. From beginning to end, these pictures are built in one line must tell the history of our painting. With all the fact that it is not a small part of our national Property and spiritual culture. These are all paintings, so to speak, first order that cannot be frequent without the story would not be flawed. But there are also such as it would not be mandatory for display. And my choice here depends only on me. From my location to the group, from the mood, and also the presence of free time.

Well, here, the painting "oral account" of the artist Bogdan - Belsky exclusively for the soul. And I can't go past it. And how to go through, because I know in advance that the attention of our foreign friends it is from this picture to such an extent that it is simply impossible to stop. Well, not to catch up for them forcibly.

Why? This artist is not from the most famous Russian painters. His name knows mostly specialists - art historians. But this picture will force, however, will stop anyone. And the attention of the alien it will attract to no less.

Here we are standing, and for a long time we consider everything in it, even the most small parts. And I understand that I don't need to explain here much. Moreover, I feel like my words I can even prevent the perception of seen. Well, as if I started to give comments at a time when my ear wants to enjoy the melody who captures us.

And nevertheless, do some explanations still need. Even necessary. What do we see? And we see eleven village boys plunged into the mental process in search of a response to a mathematical equation, written on the board by their cunning teacher.

Think! How much in this sound! The thought in the Commonwealth with difficulty created a man. The best testimony of this revealed to us Rodnith by their thinker. But when I look at this famous sculpture, And I saw her original in the Rodna Museum in Paris, then in me she gives rise to some strange feeling. And, oddly enough, is a feeling of fear, and even horror. Some kind of animal power blows from the mental stress of this creature set in the courtyard of the museum. And I unwittingly see wonderful discoverywho prepare us in their painful thinking sweat it is sitting on the rock of the creature. For example, opening atomic bombs, threatening to destroy humanity itself along with this thinker. And we already know that this animal person will come to the invention of a terrible bomb that can erase everything alive on Earth.

But the boys artist Bogdan - Belsky, do not scare me at all. On the contrary. I look at them and feel how warm sympathy for them is born in my soul. I want to smile. And the joy feel, which sticks to my heart from contemplating the touching scene. The mental search, expressed in the faces of these boys, admires me and worries. And also makes thinking about and now.

The picture was written in 1895. And a few years earlier in 1887, the infamous circular was adopted.

By this circular, approved by Emperor Alexander III and received the ironic name "On Kukhigan Children" in the company, was prescribed to the study authorities to allow only secured children in the gymnasium and deflection, that is, "only such children who are on the care of persons who represent a sufficient way to properly over them home supervision and in providing them necessary for training activities facilities". My God, what a wonderful stationery syllable.

And further in the circular, it was explained that "with the steady observance of this, the rules of gymnasium and the deflection will be released from the receipt of kucher, lackers, cooks, pubes, small shopkeepers and such people.

Like this! And now look at these young rapid minds of nonsense in the laps and tell me, there are many chances of becoming "reasonable and great."

Although maybe someone is lucky. Because he was lucky with everyone with the teacher. He was famous. And he was also a teacher from God. Sergey Alexandrovich Rachinsky called him. Today it is almost and do not know. And he so deserved all his life to stay in our memory. Look at him more closely. So he sits surrounded by his lapot pupils.

He was botany, mathematician, and also a professor of Moscow University. But the main thing, he was a teacher not only by profession, but also through his spiritual warehouse, by calling. And loved children.

Having touched the scholars, he returned to his native village Tatevo. And he built this school, which we see in the picture. Yes, and with a hostel for rustic children. Because, let's say the truth, he took him to school not everyone. He himself selected not as an example of Lion Tolstoy, who took all the surrounding children to his school.

Rachinsky created his own technique for an oral account, which could, of course, learn not to learn. Only Favorites. He wanted to work with selected material. And sought the desired result. So let it not surprise you that such a complex task is solved by kids in the laps and shirts for the release.

And the artist Bogdanov - Belsky and himself passed this school. And could he forget his first teacher. No, I could not. And this picture is a tribute to the memory of your favorite teacher. And Rachinsky taught in this school not only mathematics, but still along with other objects painting and drawing. And he first noticed the boy to painting. And he directed him to continue to study this subject not somewhere, but in the Trinity-Sergiev Lavra, in the icon-painted workshop. And then - more. The young man continued to comprehend the art of painting in an equally famous Moscow School of Painting, Drainies and Architecture, which is on a meat street. And which teachers he had! Polenov, Makovsky, spinters. And then also repin. One of the pictures young artist "Future Inok" bought the Empress Maria Fedorovna herself.

That is, he gave him Sergey Aleksandrovich the Puewemer to life. And how could I thank my teacher already taken by the artist? But just this very picture. This is the biggest thing that he could do. And correctly did. Thanks to him and we also have today the visible image of this wonderful man, Teachers Rachinsky.

Lucky, of course, the boy. Just incredibly lucky. Well, who he was? Open-up son Bathers! And what could he have a future, he did not get to the school of the famous teacher.

The teacher wrote a mathematical equation on the board. You can easily discern it. And rewrite. And try to solve. Once in my group was a teacher of mathematics. He diligently rewrote the equation for a piece of paper in the notebook and began to decide. And decided. And spent at least five minutes for at least five minutes. Try and you. And I don't even take it. Because at school I did not have such a teacher. Yes, I think that if it were even, I would not succeed. Well, not the mathematician I am. And to this day.

And I understood it already in the fifth grade. Let and I was still very small, but then I realized that all these brackets and stokers would not be suitable for me in any way in life. Do not come out any sideways. And in any way these tsiferki soul did not worry. On the contrary, only outraged. And I do not have a soul to them to this day.

I then unconsciously found my sweat in solving all these diquses with all sorts of bad badges and even harmful. And they did not cause anything other than quiet and unspoken hatred. And when all sorts of cosines with tangents came, then the complete darkness came. I was shown that all this garbage algebraic only broke me out of more useful and fascinating things in the world. For example, from geography, astronomy, drawing and literature.

Yes, I have not learned since what is catangers and sines. But there are no suffering and regret on this occasion. The absence of these knowledge, well, did not affect all of my already and not a little life. For me, today is a mystery, as electrons run with an incredible speed inside the iron wire on the terrible distances, creating an electric current. Yes, and that's not all. In some small fraction of a second, they suddenly can stop and run together back. Well, let them run, I think. To whom it is interesting, so let him do it.

But the question is not in this. And the question was that I didn't even understand in those small years, why was it to torment me what the soul rejected completely. And I was right in these my painful doubts.

Later, when I myself became a teacher, I found the answer to everything. And the explanation is that there is such a plank, such a level of knowledge that the public school should lay so that the country is not lagging behind in its development from others, going about the duals like me.

To find a diamond or a grain of gold, you need to recycle tons of empty breed. It is called dismissal, unnecessary, empty. But without this unnecessary breed and diamond with gold grains, not to mention nuggets, also not to find. Well, so I and me like and were this very demanded breed, which only needed to grow required country mathematicians and even math adderkind. But how could I know then about this with all my sweats to solve the equation that a good teacher wrote to us on the board. That is, I contributed to the birth of real mathematicians with its flour and complexes of inferiority. And from this obvious truth will not leave.

So it was, so it will always be so. And it is known for me today. Because I am not only a translator, but also a French teacher. I teach and quite accurately know that from my students, and in each group they are approximately 12, the language will know two many three student. The rest are sucks. Or a dust breed, if you want. For various reasons.

You are in the picture you see eleven enthusiastic boys with burning eyes. But this is a picture. And in life is not at all. And this will tell you any teacher.

Causes are different, why not. To be understood, I will give the following example. Moma comes to me and asks how much time I need to teach her boy french. I do not know what to answer her. That is, I know, of course. But I do not know how to answer, not offended by an assertive mother. And I need to answer the following:

Language for 16 hours is only on TV. I do not know the degree of interest and motivating your boy. There is no motivation - and put with your expensive diet at least three professors of tutors, nothing will come. And then there is such another important thingas abilities. And some of these abilities are, but there are no others at all. So genes, God or someone someone unknown decided to me. Here, for example, the girl wants to learn ballroom dancing, and God did not give her a feeling of rhythm, no plastics, nor, just about the horror corresponding to the figure (well, fat became or leaning). And so I want. What will you do here if nature itself got across. And so in any business. And in learning the language too.

But here, however, in this place I want to put a big comma to myself. Not so simple. Motivation is a movable thing. Today it is not, and tomorrow appeared. That is what happened to me. My first teacher of French, dear Rosa Naumovna, as if heavily wound up, learning that it was her subject would be the matter of my life.

*****
But back to the teacher Rachinsky. I confess that his portrait is interested in immeasurably more than the personality of the artist. He was a born nobleman and not a poor man. He had his own estate. And he had a headed head. After all, it was he who transferred for the first time the "origin of the species" of Charles Darwin into Russian. Although here is a strange, struck me fact. He was deeply religious man. And at the same time translated his absolutely disgusting soul to his famous materialistic theory

He lived in Moscow at the Small Dmitrovka, and was familiar with many famous people. For example, with lion thick. And it was Tolstoy who made him on the case of popular education. In his youth, Tolstoy was fond of the ideas of Jean Jacques Rousseau, the great enlightener was his idol. That, for example, wrote a wonderful pedagogical work "Emil or about the upbringing". I and not only read it, but wrote on it coursework At the institute. It's truth to say, Rousseau, as it seemed to me, put forward ideas in this work well more than the original. And the very thick fascinated the following thought of the Great Enlightenment and Philosopher:

"Everything comes out of the hands of the Creator, everything degenerates in the hands of a person. He forces one soil to feed the plants, treated on the other, one tree fruits the fruits characteristic of the other. It mixes and confuses climates, elements, seasons. He urges his dog, his horse, his slave. He overturns everything, everything distorts, loves disgrace, monstrous. He does not want to see anything as nature created - not excluding a person: and he needs to pull out a man, like a Horse for a player, you need to remake on your own way as he robbed a tree in his garden "

And on the slope of the years, Tolstoy and tried to implement the above mentioned remarkable thought. He wrote textbooks and benefits. Posted by the famous "ABC" wrote and children's stories. Who does not know the famous Philipper or the story about the bone.
*****

As for Rachinsky, then what is called, two kindred souls met. Yes, so that the inspired by the ideas of Tolstoy, Rachinsky left Moscow and returned to his family village Tatevo. And built according to example famous writer For your money school and hostel for gifted rustic kids. And then it became an ideologist of the church - parish school in countries.

This here's his activities on the Niva of the public enlightenment was noticed at the very top. Here, read what the Victorious Emperor Alexander III writes about him:

"You will remember to remember how a few years ago I reported to you about Sergei Rachinsky, a revealed person who, leaving the professorship at Moscow University, went to live in his estate, in the most remote 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 that are now a sample for the whole land. This is a wonderful person. Everything that he has, and all means of his estate, he gives to a penny on this matter, limiting his needs to the last degree "

But what does Nicholas himself write in the name of Sergei Rachinsky himself:

"Schools that are based on and led, consisting among the church-parish, became a nursery in the same spirit of educated figures, school schools, sobriety and good morals and a living 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 "

In conclusion, taking courage, I want to add to the statements of the two above mentioned speakers a few words from myself. These words will be about the teacher.

In the world there are a lot of professions. All living on Earth is busy to extend their existence. And above all, to find yourself something for food. And herbivore and carnivorous animals. And the big and smallest. Everything! And man too. But the person has the capabilities of such a plurality. Selection of classes is enomained. That is, the classes that a person aroused in order to earn money on bread, for life.

But from all these classes there is an insignificant percentage of those professions that can give complete satisfaction for the soul. The absolute majority of all other affairs are reduced to the routine, daily repetition of the same. The same actions of mental and physical order. Even in the so-called creative professions. I will not even call them. Without the slightest chance for spiritual growth. Stampuy one and the same nut all life. Or driving on the same rails in direct and figurative sense Prior to the condesception of your necessary work experience. And they can not do anything here. This is our human universe. It is arranged in life who can.

But, I repeat, some professions in which all life and the whole thing of life is based solely on mental needs. One of them is a teacher. FROM large letters. I know what I'm talking about. Since himself in this topic already long years. The teacher is both the Cross of Earth, and the calling, and flour, and joy all together. Without all this there is no teacher. And there are enough, even among those who in labor book In the column, the profession is written - teacher.

And to prove their right to be a teacher need every day, with the very second, when you crossed the class threshold. And this is sometimes so difficult. You do not need to think that only happy moments of your life await you behind this threshold. And it is also not necessary to count on the fact that you will meet the small folk folk all in anticipation of the knowledge that you are ready to invest in their heads and souls. That all the cool space is inhabited by an angel-like, disembodied cherubs. These cherubs know how to bite some times. Yes, and how hurts. This fault, you need to throw out of my head. Just on the contrary, it is necessary to remember that in this bright with huge windows, you will wait for the ruthless animals, which still have hard way To become human. And it was the teacher who must hold them along this path.

I clearly remember one such "Cherub", when during an internship for the first time appeared in class. I was warned. There is one boy there. Not very simple. And God to help you cope with him.

What time has passed, but I still remember him. If only because he had some strange surname. Noah. That is, I knew that Noak was the People's Liberation Army of China. But here ... I went and instantly calculated this asshole. This sixth grader, who was sitting on the last desk, with my phenomenon put one of his legs on the table. Everyone stood up. Except him. I realized that this NAK wanted to immediately declare this manner and everyone else about who had the owner here.

Sit down, children, - I said. All sat down and began to wait for the continuation with interest. Noahka's leg remained everything in the same position. I approached him, not knowing what I do and what to say.

What are you so the whole lesson and will you sit? Very uncomfortable posture! - I said, feeling how the wave of hatred for this income is rising in me, removed to break my first lesson in life.

He answered nothing, turned away and made the bottom lip move forward in full contempt to me. And even spat in the side of the window. And then I'm not thinking about what I do, I grabbed a collar and a kick under the ass knuckled him from the class in the corridor. Well, the young was still hot. In the classroom there was an extraordinary silence. As if it were completely empty. Everyone looked at me. "In Giving" - someone whispered loudly. The desperate thought flashed in the head: "Everything, in school I have nothing more to do! The end!" And heavily wrong. It was only the beginning of the pre-trial path of my school.

Ways of happy peak joyful moments and brutal disappointments. At the same time, I remember another teacher. Melnikov from the film "Let's live to Monday." There was a day and an hour when he was postgraded deep depressuha. And it was from what! "We will see here a reasonable, good eternal, but the Belen grows - thistle," he said in the hearts one day. And I wanted to leave the school. Always! And did not go. Because if you are a real teacher, then this is for you forever. Because you understand that in any other business you will no longer find yourself. Do not express yourself in full. He took - terpi. Great duty and high honor be a teacher. And it was exactly that Sergey Alexandrovich Rachinsky understood this, who he himself had a goodwill for his whole life from a black chalkboard.

P.S. If you still tried to solve this equation on the board, then the correct answer will be 2.

Famous Russian artist Nikolai Petrovich Bogdanov-Belsky wrote unique and incredible life history In 1895. The work is called "Oral Account", and in full version "Verbal counting. IN folk school S. A. Rakinsky. "

Nikolai Bogdanov-Belsky. Verbal counting. In the folk school S. A. Rachinsky

The picture is written by oil on the canvas, it depicts a rural school of the 19th century during an arithmetic lesson. Schoolchildren decide interesting and complex example. They are in deep thoughtfulness and search faithful solution. Someone thinks at the board, someone stands on the sidelines and is trying to compare the knowledge that will help with solving the problem. Children are completely absorbed by the search for a response to the question, they want to prove to themselves and the world that they can do it.

Nearby is a teacher, the prototype of which Rachinsky himself is - the famous botanist and mathematician. No wonder the picture was awarded such a name, it is in honor of Professor of Moscow University. On the canvase depicted 11 people of children and only one boy quietly whispers to the teacher in the ear, possibly the correct answer.

The picture shows a simple Russian class, children dressed in peasant clothes: lapties, pants and shirts. All this very harmoniously and concisely fits into the plot, unobtrusively carrying the world to the knowledge from the simple Russian people.

The warm color scheme carries the kindness and simplicity of the Russian people, there are no envy and falsehood, there is no evil and hatred, children from different families with different sufficient gathered together for the adoption of the only right decision. This is very lacking in our modern lifewhere people are accustomed to live quite differently, not believing, with the opinions of others.

Nikolai Petrovich devoted the picture to his teacher, the great genius of mathematics, who knew well and respected. Now the picture is in Moscow in Tretyakov Gallery, Be sure to take a look at the feather of the Great Master.

opisanie-kartin.com

Nikolai Petrovich Bogdanov-Belsky (December 8, 1868, D. Shiki, Belsky County, Smolensk Province, Russia - February 19, 1945, Berlin, Germany) - Russian Mobile Artist, Academician of Painting, Chairman of the Queenji Company.

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 Aleksandrovich Rachinsky (1833-1902), Botanist and Mathematician, 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.

On the chalkboard, an example is written that students need to be solved:

The task shown in the picture could not be proposed to students standard elementary school: In the program of single-class and two-class primary folk schools, it was not envisaged to study the concept of degree. However, Rachinsky did not follow a typical training course; He was confident in the excellent mathematical abilities of most peasant children and considered it possible to significantly complicate the program in mathematics.

Solving the problem of Rachinsky

The first way to solve

In order to solve this expression, there are several ways. If you at school taught the squares of numbers up to 20 or up to 25, then most likely it will not cause much difficulty. This expression is: (100 + 121 + 144 + 169 + 196) divided by 365, which is eventually transformed into a private 730 and 365, which is equal: 2. To solve the example of this way you can use the skills of care and the ability to keep in mind several Intermediate answers.

The second way of solving

If you at school did not teach the values \u200b\u200bof the squares of numbers up to 20, then a simple method based on the use of the reference number can be useful. This method allows you to simply and quickly multiply two any numbers, smaller 20. The method is very simple, you need to add a second unit to the first number, multiply this amount by 10, and then add a piece of units. For example: 11 * 11 \u003d (11 + 1) * 10 + 1 * 1 \u003d 121. The remaining squares are also:

12*12=(12+2)*10+2*2=140+4=144

13*13=160+9=169

14*14=180+16=196

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

Third way to solve

Another way to use the simplification of a fractional numerator, based on the use of the formula of the sum of the sum and square of the difference. If you try to express squares in the fractional numerator number 12, then we obtain the following expression. (12 - 2) 2 + (12 - 1) 2 + 12 2 + (12 + 1) 2 + (12 + 2) 2. If you know the square of the sum of the sum and the square of the difference, then you will understand how this expression can easily lead to mind: 5 * 12 2 + 2 * 2 2 + 2 * 1 2, which is 5 * 144 + 10 \u003d 730. In order to multiply to 5, it is enough to simply divide this number 2 and multiply by 10, which is 720. Then this expression is divided by 365 and we get: 2.

Fourth solution way

Also this task can be solved in 1 second if you know the sequence of Rachinsky.

Rachinsky sequence for account in mind

To solve the famous Rachinsky task, you can also use additional knowledge of the laws of the sum of the squares. We are talking It is about those amounts called Rachinsky sequences. So mathematically, it can be proved that the following sums of squares are equal:

3 2 +4 2 \u003d 5 2 (both amounts are 25)

10 2 +11 2 +12 2 \u003d 13 2 +14 2 (amount equals 365)

21 2 +22 2 +23 2 +24 2 \u003d 25 2 +26 2 +27 2 (which is 2030)

36 2 +37 2 +38 2 +39 2 +40 2 \u003d 41 2 +42 2 +43 2 +44 2 (which is 7230)

To find any other sequence of Rachinsky, it is enough to simply make the equation of the following type (note that always in such a sequence to the right of the amount of summable squares permanently than the left):

n. 2 + (n.+1) 2 = (n.+2) 2

This equation comes down to square equation and easily solved. In this case, "N" is 3, which corresponds to the first sequence of Rachinsky, described above (3 2 +4 2 \u003d 5 2).

Thus, the solution of the famous example of Rachinsky, it is possible to produce in mind even faster than it was described in this article, just knowing the second sequence of Rachinsky, 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 is undoubtedly equal to two.

Also, the sequence of Rachinsky can come in handy and to solve other tasks from the collection "1001 task for the mental account" of Sergey Rachinsky.

Evgeny Bujanov

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 he knew a certain amount of A prayer The child will certainly grow by a highly moral person, and the sounds of the Church-Slavic language will already have improving moral impact.

Secondly, Rachinsky believed that the peasants are useful and need to be quickly considered in the mind. Teaching mathematical theory Rachinsky was interested in little, but he put 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 with children early in the morning Until late in the evening, and since he was very kind, noble and sincerely tied to 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).

Ourselves school lessons occupied 5-6 months a year, and during the rest of the time Rachinsky individually engaged in older children, preparing them for entering various educational institutions of the next step; The initial folk school was not directly related to other educational institutions And after her it was impossible to continue learning without further preparation. 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, lead peasant children in the trunk path educated person - Gymnasium / University / public 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. Priests school business It was not interested in little, managed schools from under the stick, did not teach themselves in these schools, and teachers hired the most third-time, and they 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, starting in 1907, the state began to send primary education Greater money, there was no question about spending a subsidy to church schools through the Duma, almost all the means left the land.

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 consisted that dictation text text In Russian, 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 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 famous expression "Patriotism is the last refuge of the scoundrel." 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. Rachinsky believed that the peasant does not happen at hand of written accessories, so he taught only oral receptions Accounts, lowering all arithmetic and algebraic transformations requiring calculations on paper.

P.S. 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 I could not figure it out.

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. "

* * *

"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)

* * *

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

* * *

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

* * *

"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.

Surely, everyone who studied at school (especially in Soviet times) remembers the 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. At the People's School of S. A. Rachinsky. "

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 person, 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 S.A. Khachinsky 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 many famous personalities, created 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 a 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 a very new life into a whole generation of peasants ... He became truly benefactor, founding and leading, with the help of 4 priests, 5 folk schools, which are now a sample for the whole land. 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 of outstanding figures of culture and art, among whom were Tretyakov, Nikolay Stepanovich And the author of the picture in this article Pictures Nikolai Petrovich Bogdanov - Belsky.

What influence has been 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.

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