© Abramson Math, 2022

Psychology and mathematics — two scientific foundations for Abramson’s unique method.

The creator of a revolutionary math teaching method, Yakov Abramson, found his calling by accident which turned out to be life-changing.
“It was in spring, an early Saturday morning,” remembers Yakov, “I was playing ball in the yard with other kids. Suddenly we saw our friend Dima going somewhere all dressed up and in a white shirt!
“Where are you going dressed up like that, Dima?” we asked.
“I am going to apply to a math school while you poor fools keep kicking the ball in the sandlot!”

Obviously, we kicked a ball at him to make him go faster, and he went away. I told the guys that I had to go home, turned a corner, and ran after Dima — I was intrigued because that was an adventure, something new in my life.
I went there as I was — wearing kicks and sweats. I was given a pen, a sheet of paper, and a sheet with math problems. I solved what I could, wrote it down, gave my sheet with answers away, and forgot about it. A month later, there was a commotion at our house — we received an official letter that I got accepted to the sixth grade. Nobody knew that I had applied!”
Thus a sixth grader Abramson became a student of the famous Moscow school number 2 (currently a lyceum “Second school”). This school has always been academically oriented. There was no factory in its vicinity; instead, there were several institutions of the Academy of Sciences of the USSR. In the mid-20th century in the USSR, schools were required to organize industrial training for students. The then director of the school Vladimir Ovchinnikov approached the Institute of Precision Mechanics and Computer Engineering with a request to help them organize training for the specialization of a radio fitter that was rare at that time.

Among Yakov Abramson’s school teachers were some well-known Moscow educators and simply outstanding personalities: Z.M. Fotieva, V.I. Tatarsky, V.M. Polonsky, and others.

Yakov Abramson
“In my school,” Yakov says, “there were many interesting people who significantly influenced me and my choice of profession as a teacher.
Professor Tatarsky from the Institute of Atmospheric Physics taught us a special course on oscillations and waves. He did it in such a way that I could understand the physical effects of the differential equations that he derived to describe the oscillation processes. However, I didn’t even know basic calculus by then!
Our geography teacher, Alexey Makeev, whom we called “Fantômas”, spent 15 years in GULAG. Apart from his main subject, he taught us orienteering. When we asked him: “Why would we need that?” he answered evasively: “It may come in handy.”

This attitude toward the subjects that seemed unnecessary at first was something that I will remember for the rest of my life.

Valentin Polonsky left a deep imprint on me. He taught us chemistry for some time. He was a person with a sense of humor, embracing life and everything interesting in it. He was also interested in psychology. We also had a teacher of “dances and good manners”. It was a bald and fat David Shlifer, who was as old as the 20th century itself. In his classes, we rarely danced, mostly we used to listen to his stories. It turned out, for example, that cuffs of the shirt had been used to write down names before the revolution. Or that at a ball, if a gentleman would ask a girl to dance for the third time, he had to be introduced to her parents and get their permission. The third time meant that he was romancing her.

This old man from “the times before” always introduced his stories by saying something like “as your grandmother probably used to tell you,” presuming that everybody’s grandmothers were empresses’ ladies-in-waiting or at least had graduated from an Institute for Noble Maidens.

His example taught me that you can get fascinated by a subject that you see as unnecessary if it is presented interestingly, and a teacher can create an inspiring atmosphere in class.”
Yakov never considered himself to be an outstanding student. Math was really hard for him. Here is what he remembers about his years in school:
“I didn’t have any great achievements in school. I was an average student among some really bright and talented kids.

We had a lot of different math classes… About fifteen hours a week, if you include special courses. We had a huge amount of homework. Every day I had to spend two-three hours doing it, and that’s only math. I had to ditch other subjects (apart from physics).

Looking back right now, I can say that I received a significant and valuable skill — to single out what is important and necessary and to save my strength and resources. As they say — no living man all things can.”
As Yakov Abramson started his last 10th grade, he had to choose where to continue his education. Should he apply for the Faculty of Mechanics and Mathematics, for which his school was specifically preparing its students; or should he go for the Faculty of Psychology of the Lomonosov Moscow State University, where his grandfather, the famous Piotr Galperin, was a department chair. It was quite tempting to continue a family tradition. Besides, the prospective student Abramson was more interested in psychology, while mathematics frightened him with a perspective of having a very difficult five years at the university.

Sometimes he wanted to have a break from his studies. In the Soviet Union, there was no concept of a gap year that would allow people to try different activities after school to realize what they really wanted. There was, however, a necessity for it.
“I probably wouldn't have applied anywhere," Abramson recalls. “I was very tired after years of difficult studies in school. The idea of military conscription that I would have to face otherwise was for me quite abstract at that point and didn’t actually scare me.

But I was afraid to make my dear grandpa and grandma, who for some reason were seriously afraid of me being conscripted. So I had to apply, but where to? Math was pretty much the only subject that I mastered in school. And so the decisive factor was that if I were to apply to the Faculty of
Psychology, I would have to pass the exams in subjects that I was really bad at.

The exams for the Faculty of Mechanics and Mathematics were all in familiar subjects, and I would not have to feel guilt and shame. Besides, I wouldn’t want to be the “grandson of Piotr Galperin” for the rest of my life, so I chose the Faculty of Mechanics and Mathematics.”
Despite having made this choice, Yakov didn’t forget his passion for psychology and used it in creating his teaching method.

Studying at Moscow State University surprisingly turned out to be much easier than in school and way more interesting. There were also a lot of great professors able to inspire a student who influenced Abramson significantly. Among his mentors were I.R. Shafarevich, M.I. Vishik, V.A. Artamonos, and Y.S. Ilyashenko. But the biggest influence on Yakov had his scientific adviser E.M. Landis.
“Evgenii Landis was both a wonderful teacher and a person!” Abramson says. “For seven years, he wasn't just cut off from math; he was under unimaginable stress. He was conscripted in 1939 to fight in the Winter War and went through the whole Great Patriotic War, having demobilized only in 1946. Not everyone was able to get back to a peaceful life after such a trial. Landis managed to not only do that, but he also came back to math and defended two dissertations during the challenging post-war time. He was an incredibly kind and tender person who just radiated a sense of peace.
I felt bad that this great man had to supervise me, an average student. I was really embarrassed. And although I defended my graduate thesis on the ill-posed Cauchy problem and got an A, I didn’t feel that I had anything to do with it. For me, he is still an unachievable paragon both as a person and as a professional.”

Meanwhile, Yakov kept thinking that there was something wrong with the school math curriculum. He thought that the topic sequence was especially erroneous.
“Geometry, for some reason, begins only in the seventh grade,” Abramson notes, “although children have a geometrical experience since pre-school, a three-dimensional one! At the same time, children in the sixth grade have to be introduced to the formulas for the area of a circle and the length of a circle, as if it would be impossible to do later. But school is not over after the sixth grade…

And so school students have to see a strange “number Pi '', which is not even a decimal! So what is it then? Well, just “a number”, which is, you see, written as an infinite nonperiodic decimal fraction. Did you get it?

You can explain a periodic sequence and, consequently, a nonrepetitive sequence to children of this age, although nobody tries to do it. But to explain what is an “infinite decimal fraction”... I am not going to attempt. And nobody has to. The time will come, and everything will fall into the right place; you just have to wait. And there are many examples like that.``
The discussions about pedagogy that Yakov had heard at home since he was a child, and the desire to change the school math curriculum, and make it more logical and consistent, gradually led him to design his own method.

Яков Абрамсон
“When my grandfather Piotr Galperin was still alive, I wasn’t really interested in teaching,” admits Abramson, “although I read some of the books from his great library. But the year after my grandpa and grandma died, I started teaching on Sundays in math clubs held in the basement of the youth housing cooperative “Atom” at the Khoroshevskoye highway. It was going well enough, and children liked how I was presenting the material and the problems I was giving them. A couple of years later, two women co-organized a private school for their children in Krylatskoye District. They were looking for teachers, and a mother of one of the children I was teaching at “Atom” recommended me as a math teacher. That is how I began working as a math teacher.”
Abramson Math is more than 30 years old. More than 900 students have studied with it. Yakov Abramson has taught math to children from Russia, the USA, Canada, Israel, Bulgaria, Switzerland, and England. He constantly receives positive feedback from the students and their parents. What is probably more important, Yakov Abramson also has the pleasure of seeing his students achieve great results in mathematics, IT, and other spheres.

Remarkably the history of Abramson Math included the predetermination, family traditions built in by professor Piotr Galperin, and the happy chance embodied in Yakov Abramson’s friend Dima, who brought him to the math school.

Yakov Abramson, personal experience stories

How we gave up lunch for math
Разговоры о педагогике, которые Яков слышал в доме с самого раннего детства, в сочетании с желанием исправить школьный курс математики, делая его более логичным и последовательным, постепенно привели его к созданию собственного метода.

Yakov Abramson
It was more than twenty years ago. I was living in the USA then. I wasn’t a certified teacher, which is a prerequisite to teaching underage students in American public schools. So I could only work as a substitute teacher. Usually, this is a low-paid job for retired teachers.
It doesn’t require not only any knowledge of the subject, but even active participation in the lesson. You just have to distribute the materials prepared by the regular teacher and collect the notebooks — that’s all. So I could have been a substitute for physics, chemistry, or English teachers, but I limited myself to math, where I could have shared some knowledge even if my English was far from perfect.

At 5:30 a.m. sharp, a phone would ring, and an automatic voice would notify me where the substitution was needed today. Using a paper map (there were no smartphones then), I had to orient myself and find the way to the school. It was good if it happened to be high school. It was easier there, they were almost adults, minding their own business: we don't touch you, and you don't touch us.

In middle school, there was usually anarchy — noise, hubbub, a lot of running around, and general mayhem. My role was not to let them kill each other and to at least try and control this horde. It is prohibited to leave children unattended in schools.

It was really boring to just sit at the table and doze off, although that was exactly what I was expected to do. Once I decided to teach an actual lesson instead of idly sitting around. But I failed to take into account that this class was the last one before the lunch break.

It has to be said that the lunch break is an important point in the US school schedule. Even before the dismissal bell, every free school worker headed by the director line up along the corridor that leads to the canteen. When the bell rings, all the doors open, and just like wild animals, school students rush out of them and run screaming, laughing, yelling, and pushing each other. The teachers try to follow them, quell them, put them in a column, and bring them to the canteen in a predetermined order transmitted by a speaker.

And so I am finishing the lesson, and the dismissal bell rings. But we haven’t finished solving one of the problems. All the students are at the blackboard, arguing loudly, and everyone is trying to share their ideas and write them on the board. One minute passes, then another and another… Suddenly the director comes in with two policemen, sternly glances over the class, and changes his countenance, his jaw drops down. “What’s going on here?” he asks either me or the students. “We’re solving the problem,” I answer. “We didn’t manage to solve it on time.”

You can understand why he was worried: the whole class was missing. Obviously, something is wrong!

“Fine,” the director says confusedly after a long pause, still not believing his eyes. Just in case, he reminded us, “Actually, it is a lunch break…” And he went away.

Luckily, there were no negative repercussions for me.
A ban for an explanation

Яков Абрамсон
My improvisations as a substitute teacher in American schools have not always gone unpunished. Once I was a substitute for a math teacher. I noticed that students in the class were solving a problem of how to draw a tangent line from a given point to a given curve.

I asked them how they were doing it. They were surprised, “You know math?” They did not expect that from a substitute teacher. “Well,” I said, “I am not sure if I know much, but I am interested in how you do it here. Maybe I will learn something new.” They showed me, and I realized that they had no idea how to solve this problem. I went to the blackboard and explained to them how to do it. The children turned out to be smart; they grasped it quickly and thanked me. But they were apparently sad to realize that they had been taught wrongly.
Shortly afterward, I realized that they had stopped inviting me for substitutions. I called the local department of education to ask what happened. I was told that I “had done something terrible in the classroom, and they had been investigating,” and that I had been suspended until the end of the investigation.

Sometime later, my phone rang again, and I was again invited to substitute for a teacher, just as if nothing had happened. I couldn’t help but ask the department what had been the issue, though.

“Nothing serious,” a girl in the department told me. “We got things straight. It wasn’t your fault. It was a misunderstanding. Please accept our apologies. But you don’t really have to actually teach our school students because that is not a part of your duties. You are not being paid for that.”
Pushing the boundaries is important for science, but not everywhere you are allowed to

Яков Абрамсон
This “initiative” of mine was also the reason for my short tenure at a community college. I was given a huge book to prepare for the classes. It was a textbook that I was supposed to follow. It was simply impossible to read: everything was explained in the simplest terms. Ninety percent of the content was milk-and-water diluted with bright pictures. It is actually typical for many US textbooks to overuse colors. All pages are colorful, and if you are not used to it, you get ripples in your vision.
I skimmed through this volume, made myself familiar with the contents, and thought that would be enough. First lesson — quadratic trinomial and quadratic equations. That is an easy topic given that all students are school graduates who have been studying for twelve years, and they should have covered this topic as well.

So we reviewed it, looked at the special cases, and that was the end of the class. However, I had a second class with them as well. According to the program, we were supposed to simply keep applying the formula to specific examples of equations — substituting numbers into the formulas. But that was not how I had taught math in Moscow! Well, I thought that I could take a little step beyond the program and dive a little bit deeper into the topic.

But this time, when I asked, “Is it clear?” Everybody was silent. It turned out that it had been my last class at this college. I was called to the dean’s office and told I was “too good for this college.” They said that seven students had filed a complaint against me because I had broken the rules and gone beyond the textbooks, which was too much for them, and they could sue me…

I was glad I avoided the worst and got off with a simple discharge. But I also got valuable experience.
Process is king!

Яков Абрамсон
Once I started teaching a new sixth grade at the “Intellectual” school and began to work with them in my usual manner. The time has come for the first test. I graded it and announced the results. After the lesson, a girl from the class came to me.

— Mr. Abramson, you broke my heart!

I thought, “Oh my god!” But she continued:

— I got an F for the first time in my life! In my previous school, I never had a C; even B’s were rare!

I calmed down myself and began to calm her down:

– “Don’t worry,” I said, “that’s all nonsense, all these F’s and C’s, they do not matter. Who will care in two years what grades you had in the sixth grade? And in five years? You’ll get used to it. The process is king!”
Perseverance is more important than quick success

Яков Абрамсон
It was a long time ago. I have been teaching a group of school students since the fifth grade. In the sixth grade, they had some newcomers. The “old-timers”, of course, had an advantage. Also, all children are different; they have various development speeds, and they differ in their speed of thought, and many other cognitive qualities, including mathematical abilities.
One girl from the newcomers was visibly lagging. It was clear that it was difficult for her, but she worked incredibly hard, was very diligent, and, as they say, ground away at her studies. Some of the other kids were making fun of her, and despite my best effort, I could not stop it.

Three years later, there was no major breakthrough. Of course, there was huge progress, but the girl's position within the group stayed the same. She still was the weakest, the last to understand the solutions to the problems, had a hard time solving problems in front of the class, while her classmates had already figured it out a long time ago, etc.

After the end of the eighth grade, I talked to her and suggested to stop torturing herself and change tracks within the school. I told her I was worried about her psychological condition, given her relations with other children. She followed my advice and changed tracks and soon the schools. I lost her trace and have never seen or talked to her again.

Many years later, I learned from my other former students that she had stayed in mathematics, graduated from the university with a relevant major, and became a mathematician! And one of her brightest groupmates, who was a very talented boy, prize-winner of math olympiads, winner of an international Olympiad in Computer Science, has graduated from the Faculty of Mechanics and Mathematics, defended his doctoral thesis, but has chosen a well-paying job in IT.

This is a good lesson to me and everyone who reads it — do not jump to conclusions, even if you are basing them on the long-term observations of children’s successes in school. Motivation and persistence could be more important factors in the long term than the quickness of thought and the ability to grasp abstract ideas at an early age.
“For light reading” — math for fun

Яков Абрамсон
In 2020 during the pandemic, when children did not go to school, we decided to not give them homework for the break. But the children themselves have asked me to give them “not-a-homework” then.
I could not resist. How could I, if they ask?

As a result after the break I received the notebooks:
  • With not-a-homework
  • That definitely was not given for the break
  • Not from Ivanon, Petrov, or Sidorov.
But the apotheosis of it all was when I learned that I am teaching “not-a-math”.
Once I was running late for a lesson — my taxi came later because of bad weather. When I reached the school, the lesson was already going on for seven minutes — my colleague helped me out. When I entered the classroom, and my colleague went away, the students sighed with relief.

I asked them: “Why are you smiling? The lesson is not canceled.” They replied: “Hooray! There will be no math!” I asked: “What do you mean no math? What do you think we are doing here?” It turned out that they thought that math was something they did with that other strict teacher, and my class was just problem-solving for fun and entertainment.

Mathematics is a source of enjoyment for me as well. Instead of barbecuing somewhere outdoors, I prefer to spend my holiday at some seminar talking with my colleagues and looking for new interesting problems.

The curriculum must be diverse, so it will not get boring for children. That is one of the secrets to making your subject interesting.