During both the summer and winter school vacations, Victor Shatalov, a teacher in Donetsk (Ukraine), travels to various parts of the country, often far from his home — to Murmansk, Petropavlovsk- Kamchatsky, Novosibirsk, Tashkent or Odessa. In recent years he has covered thousands of miles.

Listening to a seven-hour lecture on how to teach mathematics would not appear to be any great pleasure, but thousands of people gather to hear this ordinary schoolteacher speak. The doors of an auditorium in Leningrad (now St.Petersburg), which seats 1,500, were closed an hour before the beginning of one of his talks because the hall was overcrowded. It’s harder to get a ticket to a Shatalov lecture than to a famous guest performer’s concert. Surprising? Yes. But more, Shatalov hardly touches on general problems in education, he simply tells his listeners how he teaches, giving concrete examples in the process. For instance, he might take a topic in mathematics to which the school curriculum allots 12 hours and present it brilliantly in 20 minutes, closing with a joke: “Even if you try to forget it, you won’t be able to.” This is true. Whatever Shatalov explains once, you don’t forget — at any rate; his pupils don’t.

In the fall of 1971, after 20 years of experimenting with small groups, Shatalov took on a conventional class at an ordinary secondary school, School No. 13, in Donetsk. He began teaching his pupils mathematics, physics and astronomy, subjects which are traditionally the most difficult. It is also thought that progress in these subjects depends almost completely (if not entirely) upon a pupil’s natural abilities. However, Shatalov’s first large class, a poor one, was a challenge. The class’s annual grade point average in physics and mathematics was 2.7 (the Soviet school system employs a five-point grading system, with “five” being the highest grade. As a matter of fact, grade 2 means you know nothing). Shatalov was to teach this class for the three years that remained before its graduation. At the end of the second year, Alexander Semushin, a representative of the USSR Academy of Pedagogical Science, administered a 12-hour test covering the entire secondary school curriculum to Shatalov’s pupils. “My impression,” Semushin later told me, “was that I could have continued to examine any of the pupils in that class for 24 hours straight, yet he or she could have answered all my questions without difficulty.” Semushin openly presented two sets of problems, both easy and hard, to the pupils. Most chose the harder ones.

When Shatalov’s class graduated, only three of the 33 students had “threes”; the rest had higher grades. All 33 easily passed the entrance examinations to technical institutes in different cities. More important, three-fourths of these students are receiving stipends with bonuses because of their excellent academic progress. Remember that these pupils were thought to have no aptitude for mathematics!

Shatalov has worked this wonder more than once. Not long ago he taught a class in astronomy. He covered the traditional 35-hour course in 32 hours, and all the students received grades of “five.”

At first people refused to believe Shatalov. They insisted he was a charlatan, that he secretly chose the best pupils and gave them additional instruction, sat with them for hours. Later, when the results he was obtaining became obvious, people began to say that Shatalov had unusual teaching abilities and talents and even that he (I heard this myself from a very respected teacher) hypnotized his pupils, putting knowledge into their heads. Think of that. Hypnotized them!

But as the years went by, it became harder and harder to find fault with Shatalov’s teaching. However, until 1971 he was still the only person using his methods. In 1972, after attending a number of Shatalov’s lessons, a teacher with 20 years of experience said that she was ashamed to continue teaching in the old way and adopted the innovator’s methods. Soon there were 30 followers, then 300, 500, 1500. By the 1977-78 academic year 5,000 teachers in different parts of the country were using Shatalov’s methods. In addition, there are now schools where almost all subjects are taught in this manner. Today, when Shatalov travels to give talks, he is not alone but has a complete teaching staff accompanying him. One is teaching physics, another – geography; a third – history. Shatalov’s adherents admit that their results are not as brilliant as his, but their teaching skills have greatly improved. More importantly, all of Shatalov’s followers acknowledge that their students are growing academically, becoming more inquisitive, active, and developing confidence in their ability to graduate and earn a General Education Certificate, which will give them the chance to continue their studies at a school of higher education.

Now that I have aroused the reader’s interest, it is time to probe deeper into Victor Shatalov’s methods. I warn, you, I’m not a mathematician. However, to me that is no obstacle because the vital element to Shatalov’s approach is not mathematics or physics itself, but that special “something” which he came to understand better than others — the workings of a student’s mind and heart.

**How Do Children Study?**

Thousands of books in many languages have been written on the subject of children’s study habits. Three years ago I asked my son, then an eighth grader, what would make students study better? He answered, “That’s simple. They must do their homework every day, that’s all.” However, for some reason he had no intention, as far as I could judge, of following his own simple rule.

Distinguished Soviet educator Vasily Sukhomlinsky’s reply to the question was approximately the same, except that his answer was more paradoxical: “For children to study well,” he wrote, “they must study well…”. There is no other way.

All modern talk about the need to first arouse a child’s intellectual curiosity, about the need to develop creative thinking and about the so-called problem technique in teaching is not applicable to the classroom situation, where at least some of the students don’t understand the subject that is being discussed at the blackboard, don’t have any (or enough) knowledge and, naturally, don’t want to study.

Intellectual curiosity (and, hence, the creative process) begins with an understanding of the material. This may seem trite, but I had to conduct experiments with 7,000 schoolchildren and write a book to help children and their teachers get to the bottom of the seemingly simple problem. As it turned out, many teachers, students and parents were sure that intellectual curiosity was something extraordinary; it either existed or it didn’t. “I don’t need mathematics”, “I don’t like mathematics”, and “I’m not interested in mathematics.” These conclusions seem final to children. “Sit down and study,” their parents command in reply. Certainly the child can sit down and stare at a book, but he cannot and will not study a subject that he doesn’t like and doesn’t understand.

But the origin of the dislike is simply that the student does not study every day, does not do his homework regularly, begins to fall behind the others in class and ceases to understand what the others are talking about. In addition, the student doesn’t study in the first place because the teacher, physically, can’t check each pupil’s complete knowledge at every class session.

The hullabaloo raised over programmed instruction using teaching machines and the sophisticated mathematical teaching theories boils down to one simple aim: to somehow check and evaluate a pupil’s knowledge — not just occasionally, but at every step, so that no gaps develop, so that he or she will say “I know” and “I understand.” That’s when the student will begin to say “I like.”

I have profound respect for teaching machines, the people who design them, the theories they are based on and the schools that spend money on them, but Shatalov is achieving the same results using more effective means and much cheaper ones, by the way.

No matter what is said about Shatalov, one thing is indisputable: he has ingeniously solved a problem that the schools have been struggling with for a long time. He developed a method to precisely evaluate how well each pupil understands the material taught at every lesson. It takes only 12 minutes from the beginning of a lesson for Shatalov to have gained exhaustive information on the knowledge of each of his 40 pupils. The pupils, in turn, receive a grade that they think they deserve.

If students know that they will be tested every day, they do their homework every day. Children begin to study regularly; next, to understand mathematics: then, to like the subject matter; and, as a result — Sukhomlinsky’s paradox — to do well.

The process may seem involved and vague to some readers, but it becomes clearer when you observe how the pupils in Shatalov’s classes study with real interest, with a love for science, with faith in their abilities, with self-confidence and pleasure, without being nagged or pushed, without any punishment or scoldings. Instead of being late or skipping classes, the students actually look forward to them. What particularly surprises visitors is that Shatalov’s pupils don’t try to copy from each other, no matter what the circumstances. They all work independently, something the ordinary teacher finds hard to believe.

**Pulsing Knowledge**

Shatalov says that his method contains 200 new discoveries in the area of teaching, but its core is a peculiar kind of outline or, as he puts it himself, “a page of reference signals.”

Shatalov called attention to the fact that knowledge could exist in two forms: detailed and condensed. When a teacher explains a lesson, no matter what the subject, even the best pupils do not try and remember what he or she says word for word. That’s really unnecessary. A general scheme, a plan, a set of key concepts, a kind of code of the lesson takes shape in the pupil’s mind. The pupil’s trouble in this course is not that they memorize poorly, but that without skills for mental work they are able to draw up that scheme or plan, that set of key signals, or they compile it uneconomically or distort it.

Shatalov frees the pupils of this task, a task which is beyond the powers of many. For every topic he compiles an outline of reference signals, which consists of a notebook page listing the key words of the lesson, major — but very concise — conclusions, selected extracts of schemes and examples. These are set out in a definite order, color-coded, in all kinds of frames, with arrows signifying the links and connections. Even a physics teacher can’t decipher, can’t understand, such an outline on a physics theme until he listens to the detailed explanation by the person who compiled that scheme. After the explanation the outline comes to life. The abstruse words and symbols take on meaning. Also, since Shatalov has a sense of humor, the signs and arrows when understood are funny.

Thus, the teacher lectures on a subject (detailed knowledge). It then repeated according to the list of reference signals (condensed knowledge). Then the pupils analyze the material at home, using their outlines and textbooks (the knowledge is again detailed). The next day the pupils come to class. But now the reader can make the same discovery that Shatalov made: The students’ knowledge is checked in the condensed form, not in detail! Experience has shown that this takes no more than 12 minutes. The pupils write yesterday’s outline, just one page, by heart. Those who don’t understand the material or weren’t listening to the teacher or haven’t done their homework are absolutely incapable of coping with the task, even though it is simple — almost elementary — for any pupil who tried to understand, who listened to the teacher and then worked independently, no matter how limited his or her possibilities. Shatalov collects the written homework and, after a cursory glance, sorts it into piles according to grades: “fives,” “fours,” “threes.” He doesn’t correct any mistakes because immediately after learning their grades, the pupils go to the blackboard and, using their outline, repeat the lesson (knowledge is again detailed). That way the students themselves are given the opportunity to find their own mistakes. The teacher only marks their knowledge in passing, as it were, spending no special time on it, but by the end of the lesson all the students get a grade which seems just to them — some even get two marks. Those who could not do the task or did it poorly get no mark. There’s a blank next to their names in the grade book, “a hole,” as Shatalov puts it. These will have to be filled in later when there is greater accomplishment. The teachers see the gaps in their pupils’ knowledge all the time.

In practice this is all rather simple. Yet it’s this simplicity that frightens off certain scholars, those who have come to believe that a modern discovery cannot be understood, otherwise it wouldn’t be a discovery.

The teachers explain the material, then repeat their explanations by using the reference signals. They may repeat difficult points a third and a fourth time, and (I’ve witnessed this myself) the pupils’ interest in the subject does not decline on the contrary, it intensifies. There is no memorization and no fear of forgetting anything. Everything the teacher has written on the blackboard, the students take home with them in the form of reference signals. Before the war Soviet Psychologist Pyotr Zinchenko showed, by precise experiments, that to memorize and to understand were mutually exclusive mental processes, that the one who tried to understand and to memorize would not understand anything or memorize anything. “One must only understand!” says Shatalov. And his pupils, accustomed to the new methods, do not become frightened when they don’t understand something, and they don’t stop listening to him. They know that whatever they failed to understand will become clear with the second or third explanation.

Thus, we have the following process: The students come to class, write outlines from memory, are graded and listen to the teacher’s explanations on the blackboard. Then comes the new material. Knowledge is condensed, detailed, again condensed, again detailed — it pulses — and, finally, with the help of these procedures and multiple repetitions, it is grasped and remains in the student’s mind. That is the way Shatalov’s ideal is achieved. According to the innovator, a pupil should be able to answer your questions on the subject even “if awakened in the middle of the night.”

Some may ask, “Don’t the children find the repetition dull?”

No, it’s not boring because the children, like all people, enjoy work followed by a result. They see that they are beginning to cope with even that “hateful mathematics,” and they become unafraid of any subject. Putting it theoretically, we can say that the same job will seem new to us if the final result, the goal, is changed. The first time they listen to the outline to understand; the second, to check their own knowledge. At home they analyze it to remember, and in class they write it to report back to the teacher. They listen to their classmates at the blackboard to check themselves and to be sure that the teacher gives them the mark they deserve. Each time there is another goal. It’s almost like doing something different. In the meantime the outline is in front of the pupil, and even those who have poor memory gradually retain it. In addition, Shatalov’s method develops a child’s memory more rapidly. Interestingly, the pupils develop the ability to pick out the most essential point in any text and mentally turn it into a concise and precise scheme, that is, they understand.

I sat in on a literature lesson in Shatalov’s class. The teacher is explaining Tolstoy’s War and Peace in the traditional manner, but the pupils were listening and compiling “Shatalovlike” outlines of reference words, arrows, circles and the like.

Gradually, the work with reference signals was simplified. Outlines were printed up in advance. The pupils only had to color them at home following a predefined color scheme. Progress became even more rapid.

No conflicts develop between students and teachers, between the students and their parents, between the parents and the teachers. Pupils go to school without fear that they will be called on in class about what they will asked. The students know exactly what to expect and soon stop worrying about grades. There are so many that an extra “three” or “four” is not really important. Even a “hole” is not especially serious: It means having to write the outline again. No arguments. No tension. Complete psychological comfort. All the psychologists who watched Shatalov’s classes had the same observation: the children were strangely relaxed; they had nothing to worry about.

Also, the teachers relax when they see how seriously the pupils are working. In addition, it’s easier for the teachers to make their explanations using an outline, particularly if they are inexperienced. They don’t founder, get confused or sidetracked.

They are not inclined to be long-winded, therefore, the pupils understand them better. In turn, the pupils, guided by their outlines, do not have to rack their memories to answer the teacher’s questions. They speak freely, relaxed. The teachers don’t have to strain to fish knowledge out of their pupils. They can devote more time and attention to the pupil’s speech and correct their use of mathematical terms. People who visit Shatalov’s lessons note that his pupils speak with greater ease than those in conventional classes. To give the children an opportunity to speak more and develop speech habits, Shatalov manages so-called “mutual control days,” when the pupils quiz each other. They enjoy this.

The excitement found in Shatalov’s classes is not based on their teacher’s infectious enthusiasm nor, of course, on any kind of hypnosis. Even the weakest students feel that they have the opportunity to do well, that they have every chance of getting a good grade, something they haven’t gotten since their first day at school. All they have to do is listen to the teacher’s explanation in class and study at home with the outline. Honestly, the thrill pupils get from the first “five” they have earned can’t be measured. The first impulse is to get a second “five.” That’s how the students gradually land in a cunningly set trap and begin to study mathematics, which not too long ago seemed unbearable and which now gives them so much pleasure.

It is not surprising that the school children become the most ardent advocates of these new methods. There are several cases, where the students themselves brought articles describing Shatalov’s methods to their teachers and asked, “Why don’t we study like that?” When the process of instruction and learning becomes reasonable and productive, pupils stop asking: “What do I need mathematics for?” or “Why do I have to study?” Why play basketball? To win. Why solve mathematical problems? To solve them.

By finding a single new method to perceive and present knowledge in condensed form, Shatalov solved several pedagogical problems that had seemed insoluble for the school system. He graphically showed children the mental activity involved in the study of theory (the dynamic process of condensing and detailing); he found a method to induce them to apply themselves to this purely mental activity and, at the same time, greatly simplified the teacher’s control over the pupils’ efforts. Professor Nikolai Siunov of the Uraisi Polytechnic Institute, an authority in the field of electrical machines, is successfully using Shatalov’s method with his students and calls it “the method of continuous control.” Other teachers talk of Shatalov’s “engineering” pedagogy.

**A Remedy for Fear**

There is no more skeptical a person than a teacher who is told about the fantastic achievements of another teacher. And I’m sure that if I were addressing an audience of educators alone, I would by now have been interrupted by shouts: “That’s great, but what about problem-solving? How does he teach children to solve problems?”

The quality of Shatalov’s teaching is the amazing flexibility. As soon as he approaches problem-solving, he changes completely, as if all his principles have been replaced by those quite opposite! When studying theory, there are marks at every step, continuous control to induce strict study discipline. In problem-solving he gives them unheard-of-freedom and no marks — only assistance and benevolent consultation, to nurture self-confidence and to liberate creativity. If pupils know their theories, the solution of a problem depends 90 per cent on their self-confidence.

Remember, Shatalov’s pupils are average students, and one may come across children in his classes who haven’t solved a single mathematical problem in their lives. They panic in the face of any mental effort.

In practice the stronger pupils tackle and solve problems of a complexity no ordinary teacher would ever think of giving them, while the weaker pupils are elated — an unprecedented feeling — when they solve their first mathematical problem and soon rise to the level of average. The point is that there should be no need for students to copy each other’s work or fit their solutions to some given answer; they should not be striving for good grades, but for hard problems. What you begin to get is an atmosphere of sporting excitement: Who chose and solved the most difficult problem? The class turns into a group of interested mathematicians.Shatalov begins from afar. He solves standard problems in the classroom — only listen and try to understand — and then he gives his pupils the same problems to solve at home. They don’t look the same, but they are, and he gives marks for their “repeated” solution at home. He believes that in the initial period an independent analysis, if the solution worked out in the classroom, is a large-sized achievement. Then he gives each of his students 100, then 150, diverse problems. He does not divide the class into “strong” and “weak” students. “To me” he tells them, “you are all the same, and I have equal faith in you. Here are a hundred problems for each of you. Choose those you feel you can handle, solve them and bring the answer in for checking. If you solve 50, and the toughest at that, good for you! If you only solve one, the simplest, you won’t be scolded either.” The answers are not graded, as there are no marks for the solution of problems at the blackboard. Complete freedom and ease!

Under normal conditions the weaker students would soon be disillusioned — a written test! It can’t consist of obviously simple problems, and so failure follows, a grade “two,” “I’m no good.”

Despite the disapproval of the school’s administration, Shatalov gives no written tests — considering them harmful — until he is absolutely sure that all his pupils will do well. His first test is given; then he walks up and down the aisles and gives help or prompts if he finds it necessary. Also, he gives the pupils good grades, for what was the initial stipulation: to work with the help of the teacher. This he adheres to. Six months later his pupils begin to solve standard problems, also with the teacher’s help if necessary. Only then does the independent solution of problems begin. Finally, he gives his pupils nonstandard problems to solve on their own.

Now, what do students really need from their teachers? The list of desired qualities could be endless, but the first should be confidence, confidence that with that particular teacher pupils will surmount all difficulties and learn the subject. Shatalov is indeed capable of teaching anybody. He does his utmost to support a pupil’s faith in his or her eventual success. And – faith in those very creative abilities, which sometimes raise up to extraordinary force, though many accuse him of standardizing academic abilities and performance. He does use standard outlines and does achieve a certain standard level of knowledge and skill. But if the choice is between standard knowledge and standard lack of knowledge — after all, if that’s the alternative — then I’m for the former, and I don’t think alone.

By Simon Soloveychik

1980

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This translation of S.Soloveychik’s article found from the document of Stan Hartzler VIII.Psychology of Learning H Affective Outcomes http://classappcogpsych.com

Revised by Aigul Aubanova