Primary and secondary school - one mathematics. Non-school math

The teacher, since 1989, taught mathematics to kids for twelve years. From this work, many daily records have survived, and one article: "In Primary and Secondary School - One Mathematics" - a title that may attract a school methodologist. The only thing is that this teacher's name was Tatyana Mikhailovna Velikanova, and through the prism of her life, both the boring title and the article itself are seen in a completely different way.

It is impossible to tell about Tatyana Mikhailovna in brief.

For ten years, until her arrest in the fall of 1979, Velikanova was editor of the Chronicle of Current Events. More than an editor - more like an "executive director." What was it for her - a heavy burden, a feat? Tatyana Mikhailovna herself spoke about this simply: “For me and my friends, it was a way of life. In 69, I was 37 years old, and for the next ten years of human rights work, I felt like a completely free person, unlike my previous life. It was also a time for me to analyze and understand the regime under which my country lives. I received much more information about the life of my country than until now. And she reacted accordingly. "
Back in 1968, in August, when her husband Konstantin Babitsky and another "seven brave" at the Execution Grounds protested against the introduction of troops into Czechoslovakia, Tatiana Mikhailovna was nearby. To see and testify. During the interrogation, she also told everything that she saw - about the beating of people by the Chekists - although they expected another from her, condemnation of her husband's actions. But Tatyana Mikhailovna repeated both during the investigation and at the trial that she approved of her husband's behavior. Investigator: - "But you have three children!" “That's why,” Velikanova answered.

And the indictment read: "in particular, on the basis of the testimony of the accused's wife ...".
For Tatiana Mikhailovna “The most difficult thing was to learn how to cope with the system of mutual responsibility imposed on the entire population of the USSR. The fate of his relatives, the careers of his colleagues, the fate of his friends up to their arrest depended on the behavior of a person, regardless of his wishes. It was a total hostage system ... "
Velikanova made her choice.

Tatiana Mikhailovna never testified again. Both at her investigation and at the trial - she was silent. Only when asked to say the last word she said: "The farce is over - well, it's over".
Further - four years of the Mordovian camps, the "small zone" in Barashevo (about this - in the book of her fellow prisoner Irina Ratushinskaya "The Color of Hope is Gray"). And a link to Central Asia, to Orwell's stopping time, to God-forgotten places: Shetpe, Tauchek, Beyneu ... One of those who visited her in exile, Viktor Rezunkov, recalled: “For three days I tried to understand how such a fragile woman could resist the Council of Deputies, which, like a scorched desert, surrounded everyone, silently, lifelessly and, it seemed, forever. Twenty years later I did not understand ... Even in exile, the authorities were afraid of her. No pathos, no loud slogans - God forbid! Only deeds and faith, deep conviction in their righteousness ".

She even freed herself so that she remained free. Tatiana Mikhailovna refused to sign the pardon decree, and remained in exile for several "extra" months. And then she returned herself - herself, without anyone's mercy or permission.

And - to school, "for the rest of my life" ...

Here is what Yuliy Kim said in September 2002 at Memorial when he said goodbye to Tatyana Mikhailovna: “If our society had developed as it should, in its post-Soviet period, and would have been able to overcome its eternal sin of ingratitude and give everyone what he deserves, then our funeral service would not have taken place here. Maybe in Red Square. Maybe she would not have been enough then for people who would come to pay their last debt, to accompany Tanya on her last journey. "
Probably, her grateful students understood this. They now have to envy. But what should we do - after all, Tatyana Mikhailovna has left good deeds, and by no means teachings. An example remains - but who can have such heights of spirit? Although, on the other hand, this was not given from above, but it was the result of working on oneself. As Sergei Kovalev noted, “Tatyana Mikhailovna was a very passionate person, a person of high limits, and her remarkable restraint, noble simplicity is the result of passionate, direct, conscious self-education”.
… From Tatyana Mikhailovna there was only one article about teaching mathematics, published in 1996 with a circulation of 600 copies. However, if you look closely, you can find there a lot of important things for those who left high school long ago.

“In elementary school, the first and universally recognized goal is to teach elementary techniques and skills. The second is to ensure success for every student. Success or failure largely determines his entire future destiny. The third is to instill a taste and love for intellectual activity, to provide an opportunity for a creative, search approach. In middle and high school, one of the main goals is to teach people to understand that the world is complex, but not chaotic; that what we are studying is a complex but real model; that any model operates in a limited area, and it is highly desirable to know the scope of the model. "

After all, this is not only about children of six, seven or eight years old (Tatyana Mikhailovna once remarked - they say, it's a pity that babies cannot be taught mathematics ...) This is after all written about people in general. At the very least, you need to be able to do something and respect yourself for it. But more is possible - creativity and understanding. The question is how to go from small to large?
The first in her article - “The idea of \u200b\u200b'getting ahead' ... concepts and even sections of mathematics, which are given in middle and high school, should be introduced already in elementary school. This does not mean that you need to "pass" them earlier, you just need to start earlier. Propedeutics [abridged presentation - A.Ch.] of a complex on simpler material greatly facilitates the passage of this complex in the future ".

"Society is not ripe"? "The masses are not ripe"? Yah! If we do not raise serious questions, return to them again and again, then we will remain in the "sandbox".

Second - “The need to organize such types of child's activities and tasks in which the student's independent, searching activity can be manifested. Traditionally, most of the time is devoted to the study of rules and procedures, the role of tasks is illustrative. The problems themselves are very artificially constructed models, where all the necessary data is present, there is nothing superfluous, and the answer is always “good”... In life, everything is different - something is missing, and something superfluous deliberately distracts us from the main thing. And, although it is easier to solve "examples", it is much more interesting to "also" put ", find or find out the missing data, discard unnecessary ones, choose the necessary procedures and their sequence, be able to write it all down in a convenient way ..."

The "masses" are by no means an attentive audience, and not an instrument in the hands of the "leaders." And you should not seduce them with simplified models of being, where there is an answer for every question, and the right question has already been prepared for each answer.
How not to let yourself be isolated with these problems? Here is: “Work in small groups: to discuss within a group both the formulation, and methods of solving the problem, and methods of verification, and even divide the work among themselves when the problem requires many calculations, for example, trial. Discussion generates ideas, ideas evoke other ideas, the search is on! In successful cases, when observing the work of such a group, there was a feeling of the creative atmosphere of a small scientific team ".

After all, this applies not only to the school class, but also to those “classes” to which the “leaders” usually address. For a real, not a "leader" social movement, these "small groups" - "cells of civil society" are important. Consisting of units, a fragmented, atomized society, only that can become a "mass" - passive or obedient. The work of understanding is the work of communication.

And finally “To combine everything that can be combined; use all connections, analogies, oppositions ... the problem of the oncoming movement of two trains and the problem of filling a pool through two pipes from the point of view of mathematics is the same problem ", - people should learn to see their meaning behind the events:" if the teacher helps the student to see this community, his understanding and ability to solve such problems will rise to the next level ".
Then student "Not only gets knowledge, but also learns to learn, learns to approach a problem, a task - not only intellectual, but also emotional".

But one of the reasons for our "time in which we stand" is the inability to live in a changing world, full of problems and free from ready-made solutions.

"Primary school should lead to 'big' mathematics, or, more precisely, 'big' mathematics should start in primary school".

To live seriously, that is, freely, must begin even when it seems that there is no room for this freedom. Then you can feel "Completely free person, in contrast to the previous life".
Probably, and this can be taken from the lesson of Tatiana Velikanova.
Although, to be honest, I don't know what she would say to that. Maybe she would just look through her glasses - through and through, as she knew how - would have kept silent expressively, and turned to the students ...

VELIKANOVA, TATIANA MIKHAILOVNA(1932-2002), Soviet dissident, human rights activist.
Born February 3, 1932 in Moscow in the family of a famous Soviet hydrologist, corresponding member of the USSR Academy of Sciences. Almost all of the seven Velikanov sisters and brothers took part in the human rights movement to one degree or another.

Velikanova graduated from the Faculty of Mechanics and Mathematics of Moscow State University in 1954, worked as a teacher in the Northern Urals, then, since 1957, as a programmer-mathematician in Moscow.

She was present on Red Square in Moscow on August 25, 1968 during the "demonstration of seven" who protested against the invasion of Warsaw Pact troops into Czechoslovakia (one of the participants in the demonstration was her husband Konstantin Babitsky), but did not take part in the demonstration. At the trial, the demonstrators acted as a witness for the defense.

She became actively involved in human rights activities after her husband's arrest, in the second half of 1968. Her signature is on many human rights petitions. In May 1969, she became a member of the first Soviet independent human rights organization - the Initiative Group for the Protection of Human Rights in the USSR (IG); participated in the preparation of most of the documents of the IG.

For many years Velikanova was an active participant in the publication of the human rights bulletin "Chronicle of Current Events"; after the arrest of its editor Natalya Gorbanevskaya, she assumed the main organizational and managerial functions - storing and replenishing the archive, collecting and organizing incoming current materials, searching for apartments for work, distributing work among the participants in the issue, organizing their meetings for joint text editing, printing the first typewritten print run release. She remained the main organizer of the work of the Chronicle until her own arrest.

Velikanova took part in a meeting of dissidents in January 1973, at which a decision was made to suspend the publication of the Chronicle; but in the fall of the same year she was one of the initiators of its renewal. October 30, 1974 Velikanova took part in a press conference at the apartment of Andrei Sakharov, dedicated to the announcement of this date as the Day of Political Prisoners in the USSR.

In the 1970s, Velikanova's Moscow apartment gradually became one of the centers where information about political persecution in the country flocked. She was fired from her job in 1976; her apartment was searched several times. She was arrested on November 1, 1979. She was charged with the texts of IS's appeals to the UN, issues of the Chronicle, as well as contacts with foreign publishers of the bulletin. On August 29, 1980, the Moscow City Court sentenced her for "anti-Soviet agitation" to 4 years in camps and 5 years in exile.

Even before the trial, a public committee for the protection of Tatyana Velikanova was organized in Moscow.

In her dissident activities, she followed the principle of non-cooperation with state bodies. In particular, she refused not only to testify on the merits of the case, but also from any procedural actions (for example, she refused to sign the interrogation protocols - since, in her opinion, all activities aimed at suppressing dissent are illegal). She is one of the few who managed to consistently adhere to these principles during their own investigation and trial.

After the completion of the camp term, which she served in the women's zone of the Mordovian political camps, Velikanova was sent into exile at the end of 1983 in the Mangyshlak region (Western Kazakhstan). In May 1987, during the Gorbachev campaign to release political prisoners, she was informed of a pardon, but for another six months she refused to accept the pardon and remained at the place of exile.

After returning to Moscow, she worked at school, taught mathematics and Russian in elementary grades.

Alexander Daniel

Introduction

Tatiana Mikhailovna Velikanova (February 3, 1932 - September 19, 2002, Moscow, Russia) - Soviet dissident, member of the human rights movement in the USSR, one of the founding members of the first human rights organization in the Soviet Union, the Initiative Group for the Protection of Human Rights in the USSR.

1. Biography

In 1954 Velikanova graduated from the Faculty of Mechanics and Mathematics of Moscow State University, worked as a teacher in a rural school in the Urals. Since 1957 in Moscow, employee of the computing center, programmer.

Velikanova's husband, linguist Konstantin Babitsky, was among seven participants in a protest against the invasion of Warsaw Pact troops into Czechoslovakia on August 25, 1968, and was exiled for 3 years to the Komi ASSR.

In 1969 Velikanova became one of the founding members of the first human rights organization in the USSR, the Initiative Group for the Protection of Human Rights in the USSR. In 1970 Velikanova took over the main organizational functions in the preparation of the main periodical of Soviet human rights defenders "Chronicle of Current Events" - a typewritten newsletter, published since 1968. For nine years under her leadership, about thirty issues of "Chronicle" were published. In May 1974 T. Velikanova, S. Kovalev and T. Khodorovich openly assumed responsibility for distributing this publication.

On November 1, 1979, Tatyana Velikanova was arrested on charges of "anti-Soviet propaganda." In August 1980, the Moscow City Court sentenced her to 4 years in prison and 5 years in exile. She served her sentence in Mordovia, and exile in Western Kazakhstan (Mangyshlak region). Velikanova's imprisonment is described in the story "Gray is the Color of Hope" by Irina Ratushinskaya.

Notes

1. Irina Ratushinskaya... Gray is the color of hope - lib.ru/MEMUARY/RATUSHINSKAYA/ratush_gch.txt. Overseas Publications Interchange Ltd. 1989; ISBN 1 870128 41 9
2. Velikanova T.M. Primary and secondary school - one mathematics - sch57.msk.ru/collect/velik.htm. - Methodological collection of 57 schools

Categories: Persons by alphabet, Repressed in the USSR,

Tatiana Mikhailovna Velikanova,

The teacher, since 1989, taught mathematics to kids for twelve years. From this work, many daily records have survived, and one article: "In Primary and Secondary Schools - One Mathematics" - a title that may attract a school methodologist. The only thing is that this teacher's name was Tatyana Mikhailovna Velikanova, and through the prism of her life, both the boring title and the article itself are seen in a completely different way.

It is impossible to tell about Tatyana Mikhailovna in brief.

For ten years - until her arrest in the fall of 1979 - Velikanova was the editor of the Chronicle of Current Events. More than an editor - more like an "executive director". What was it for her - a heavy burden, a feat? Tatyana Mikhailovna herself spoke about this simply: “For me and my friends, it was a way of life. In 69, I was 37 years old, and for the next ten years of human rights work, I felt like a completely free person, unlike my previous life. It was also a time for me to analyze and understand the regime under which my country lives. I received much more information about the life of my country than until now. And she reacted accordingly. "

Back in 1968, in August, when her husband Konstantin Babitsky and the other "seven brave" at the Execution Grounds protested against the introduction of troops into Czechoslovakia, Tatyana Mikhailovna was nearby. To see and testify. During the interrogation, she also told everything that she saw - about the beating of people by the Chekists - although they expected another from her, condemnation of her husband's actions. But Tatyana Mikhailovna repeated both during the investigation and at the trial that she approved of her husband's behavior. Investigator: - "But you have three children!" “That is why,” Velikanova answered.

And the indictment read: "in particular, on the basis of the testimony of the accused's wife ...".

For Tatiana Mikhailovna “The most difficult thing was to learn how to cope with the system of mutual responsibility imposed on the entire population of the USSR. The fate of his relatives, the careers of his colleagues, the fate of his friends up to their arrest depended on the behavior of a person, regardless of his wishes. It was a total hostage system ... "

Velikanova made her choice.

Tatiana Mikhailovna never testified again. Both at her investigation and at the trial - she was silent. Only when asked to say the last word she said: "The farce is over - well, it's over".

Then - four years of the Mordovian camps, the "small zone" in Barashevo (about this - in the book of her fellow prisoner Irina Ratushinskaya "The Color of Hope is Gray"). And a link to Central Asia, to Orwell's stopping time, to God-forsaken places: Shetpe, Tauchek, Beineu ... One of those who visited her in exile, Viktor Rezunkov, recalled: “For three days I tried to understand how such a fragile woman could resist the Council of Deputies, which, like a scorched desert, surrounded everyone, silently, lifeless and, it seemed, forever. Twenty years later I did not understand ... Even in exile her power They were afraid. No pathos, no loud slogans - God forbid! Only - actions and faith, deep conviction of their righteousness ".

She even freed herself so that she remained free. Tatiana Mikhailovna refused to sign the pardon decree, and remained in exile for several "extra" months. And then she returned herself - herself, without anyone's mercy or permission.

And - to school, "for the rest of my life" ...

Here is what Yuliy Kim said in September 2002 at Memorial when he said goodbye to Tatyana Mikhailovna: "If our society had developed as it should, in its post-Soviet period, and would have been able to overcome its eternal sin of ingratitude, and give everyone what he deserves, then our funeral service would not have taken place here. Maybe on Red Square. Maybe it was not enough. then it would be for people who would come to pay their last debt to take Tanya on her last journey. "

Probably, her grateful students understood this. They now have to envy. But what should we do - after all, Tatyana Mikhailovna has left good deeds, and by no means teachings. An example remains - but who can have such heights of spirit? Although, on the other hand, this was not given from above, but it was the result of working on oneself. As Sergei Kovalev noted, "Tatyana Mikhailovna was a very passionate person, a person of high limits, and her remarkable restraint, noble simplicity is the result of passionate, direct, conscious self-education.".

… From Tatyana Mikhailovna there was only one article about teaching mathematics, published in 1996 with a circulation of 600 copies. However, if you look closely, you can find there a lot of important things for those who left high school long ago.

"In elementary school, the first and universally recognized goal is to teach elementary techniques and skills. The second is to ensure success for every student. Success or failure largely determines his entire future destiny. The third is to instill a taste and love for intellectual activity, to provide an opportunity for a creative, exploratory approach. In middle and high school, one of the main goals is to teach us to understand that the world is complex, but not chaotic; that we study models of the complex, but real; that any model operates in a limited area, and it is very desirable to know the limits of the model's application. "

After all, this is not only about children of six, seven or eight years old (Tatyana Mikhailovna somehow remarked - they say, it's a pity that babies cannot be taught mathematics ...) This is after all written about people in general. At the very least, you need to be able to do something and respect yourself for it. But more is possible - creativity and understanding. The question is how to go from small to large?

The first in her article - "the idea of" getting ahead "... concepts and even sections of mathematics, which are given in middle and high school, should be introduced already in elementary school. This does not mean that they need to be" passed "earlier, you just need to start earlier.[abridged presentation - A.Ch.] complex on a simpler material greatly facilitates the passage of this complex in the future ".

"Society is not ripe"? "The masses are not ripe"? Yah! If we do not raise serious questions and return to them again and again, then we will remain in the "sandbox".

Second - "the need to organize such types of child's activities and tasks in which the student's independent, search activity can be manifested. Traditionally, most of the time is devoted to the study of rules and procedures, the role of tasks is illustrative. The tasks themselves are very artificially constructed models where all the necessary data are present, there is nothing superfluous, and the answer is always "good" "... In life, everything is different - something is missing, and something superfluous deliberately distracts us from the main thing. And, although it is easier to solve "examples", it is much more interesting to "also" put ", find or find out the missing data, discard unnecessary ones, choose the necessary procedures and their sequence, be able to write it all down in a convenient way ..."

The "masses" are by no means an attentive audience, and not an instrument in the hands of the "leaders." And you should not seduce them with simplified models of being, where there is an answer for every question, and the right question has already been prepared for each answer.

How not to let yourself be isolated with these problems? Here is: "work in small groups: to discuss within a group both the formulation and methods of solving the problem, and methods of testing, and even divide the work among themselves when the problem requires many calculations, for example, trials. Discussion generates ideas, ideas evoke other ideas, the search is on! In successful cases, when observing the work of such a group, there was a feeling of the creative atmosphere of a small scientific team ".

After all, this applies not only to the school class, but also to those “classes” to which the “leaders” usually address. For a real, not a "leader" social movement, these "small groups" - "cells of civil society" are important. Consisting of units, a fragmented, atomized society can only become a "mass" - passive or obedient. The work of understanding is the work of communication.

And finally "to unite everything that can be combined; to use all connections, analogies, oppositions ... the problem of the oncoming movement of two trains and the problem of filling a pool through two pipes from the point of view of mathematics is the same problem," - people must learn to see behind events, their meaning: "if the teacher helps the student to see this community, his understanding and ability to solve such problems will rise to the next level".

Then student "Not only gets knowledge, but also learns to learn, learns to approach a problem, a task - not only intellectual, but also emotional".

But one of the reasons for our "time in which we stand" is the inability to live in a changing world, full of problems and free from ready-made solutions.

"Primary school should lead to 'big' mathematics, or, more precisely, 'big' mathematics should start in primary school.".

To live seriously, that is, freely, must begin even when it seems that there is no room for this freedom. Then you can feel "Completely free person, in contrast to the previous life".

Probably, and this can be taken from the lesson of Tatiana Velikanova.

Although, to be honest, I don't know what she would say to that. Maybe she would just look through her glasses - through and through, as she knew how - would have kept silent expressively, and turned to the students ...

Monument to Tatyana Velikanova (1932-2002), one of the founders of the first Soviet human rights organization. Installed at the Khovanskoye cemetery in Moscow.

Tatiana Mikhailovna Velikanova (1932-2002) - Soviet dissident, one of the founders of the first Soviet human rights organization. A graduate of Moscow State University taught at a rural school, then returned to work as a programmer in Moscow. In 1968 Velikanova's husband was arrested - linguist K. Babitsky, after which an initiative group of human rights defenders was organized. Under the leadership of the group, the famous bulletin was published and distributed in samizdat "Chronicle of current events"... In 1980, this led Velikanova to a camp and exile, from where she returned only seven years later, to perestroika.

Tatyana Velikanova died on September 19, 2002, and was buried in Moscow. Next to her lie the mother of Evdokia Ilinichna Afanasyeva (1887-1972) and her sister Ksenia Mikhailovna Velikanova (1936-1987).

The grave of the human rights defender is marked with a modest