Math’s is for everyone

On May 12, HSE celebrated Women’s Day in Mathematics at the New School site. We talked with Vlada Kazantseva, a mathematics teacher at New School, a graduate of the first class of the HSE Mathematics Faculty, about how today’s children relate to mathematics, how teachers differ from teachers, how to choose between career and motherhood, and why mathematics is a science for everyone.

Tell us why this year you decided to hold an event on the site of the New School? After all, at first glance, women in mathematics are not the most obvious topic for schoolchildren. How did this idea come about, why here, why so, why in this format?

– It so happened that several active women met, including Sasha Skripchenko, me, Liza Mishina, deputy director of our foundation. Sasha told us that there is such an event, May 12 – Women’s Day in Mathematics. Word by word, I wanted to expand this idea. After all, a woman in mathematics is not necessarily a scientist. Almost every person learned mathematics through a woman, simply because, according to statistics, there are more female mathematics teachers than men. And often the love of mathematics was instilled by women. We wanted to develop this idea, reconcile these two worlds and make a scientific-school conference.

In addition, the Higher School of Economics, and the Faculty of Mathematics in particular, is a place that is in some way looped around with school education. I myself went to work at the school after the Math Faculty of the HSE. And now the faculty of MSC has opened, which, together with the faculty of mathematics, began to prepare students of mathematics so that they would go to work in school and be cool teachers. They give us teachers, we give them students. It seemed to us that it was possible to combine these worlds and give birth to interesting collaborations in them.

Sasha Skripchenko suggested that Joan Birman could be taken as the hero of our meeting, because she has an interesting biography. She also asked Vladimir Shastin to tell about her work. Children prepared their reports on knot theory, in parallel we remembered the mathematics teachers, after that there was informal communication. I think this is important, because when people communicate like this, get to know each other, they have ideas, and then these ideas grow into something beautiful. In order to continue this, we created the “Mathematical Union” group. It is still closed and is only developing, but we plan to make it open not only for mathematicians. It is very important to talk about mathematics in such a way that people not only from mathematics, but also from other spheres could understand something, learn, feel that it is beautiful, cool, interesting.

A little more about the children’s part of the conference. Was there some sort of selection, or did everyone who wanted to make a report? How did the children choose topics, how did they prepare, together with the teachers, or on their own?

– We took Sosinsky’s book “Knots and Braids” as a basis, we gave it to the children, said that there would be a conference, you could take part. At our school, I addressed several children addressed to them, because I knew that they were interested in this, I also wrote to colleagues, acquaintances, they responded, brought their children. In particular, I really liked the team from school 179. First I sent them a book, they registered, then there was a long silence. And suddenly the day before, a girl from school 179 called me and said that she wanted to make a report. I asked which chapter, she replied that the whole book. Then I realized that the children are ready, they will come and do it. And so the first conference turned out. And I want to develop this, because I think it is important when children can live something, some kind of mathematical topic. This is a feeling, I know from myself, a feeling of pride,

Someone today suggested that men and women teach mathematics differently. If men somehow try to fulfill themselves, then women give more. What do you think about this from your experience?

– A very interesting idea. I didn’t think about it, it’s hard to say. I have a specific experience, I studied in the materiel class, and there they really taught us to achieve something, to develop. But on the other hand, I have always been comfortable with both male and female math teachers. When this idea was expressed, I tried it on myself as a woman teacher. I do not know if this is related to gender, but I really have a motherly attitude towards these children. If something doesn’t work out for them, I let it all through myself, I start to worry, I really want to help them, I very often arrange individual consultations with them. I am afraid to talk about gender, because I still think that most of the personality comes from. But speaking of me, I really always try to take care, to show that it’s not difficult that I’m around, I will help, I will lend a shoulder so that they are not afraid, but, on the contrary, rush into battle. So there really is something like that

Generations are compared at all times. Someone says that “the children are not the same now,” someone, on the contrary, believes that everything is always the same. How, in your experience, do children now relate to the study of mathematics, how are modern children different from the memories of your schoolchildren?

– It’s difficult to compare here, because I studied in the materiel class. At the New School, the children are different, of course, because these children do not take it on faith that it is interesting to do mathematics, and children who knew that this was the case by default went to the matclass. I like it when children have these discoveries that mathematics does not work according to the principle “the teacher said, therefore it is so”, that everything can be shown, that everything is logical, everything has origins. I like that thanks to mathematics, children have a sense of the base, that everything is logical, that if something suddenly breaks down, you just need to get to the bottom and everything can be fixed. And my favorite and most important achievement is that children begin to ask questions and thoughtfully follow what I am doing. Sometimes I make mistakes, sometimes on purpose, but often not, and they catch me by the hand, prove that there was a mistake.

But returning to the question of whether the children are different, in some ways, perhaps, they really are different. They are very modern, you need to be able to maneuver with them, because they are very bright, sharp-tongued, active. But I like their optimism. I really like modern children, I don’t understand why they are scolded. They are overwhelmingly optimistic, often very kind. Sometimes strange situations happen to them, just as it happened to all of us, but I like how they get out of them. They are thoughtful, they think a lot about human relations, more than we did in our time, they attach great importance to this, maybe something good will come of it.

Mathematics in school is often presented as elitist, exclusive. They say that in order to understand it, you need to be, if not a genius, then at least a gifted child. What about this at the New School? Do you think it is necessary to get away from this, or let there be this isolation?

– It seems to me that you need to embrace all the facets. Indeed, we have a reputation for elite mathematics in Russia. There are math schools in which mathematics is very strong, and let it continue. I really want there to be another level. For children who are not such high school students, but good, strong, who can think consistently and solve problems of the required degree of difficulty, who strive to work. In general, I do not see any problem in order to be able to do math for creative children. To translate, for example, the same nodes into mathematical language, after all, it is very beautiful and unexpected, and I am sure that many children will succeed much better than solving quadratic equations, for example. This is not enough. Because the program is aimed at the fact that absolutely all children need to be taught to solve quadratic equations, and the children resist it, because it is not theirs. I want every child to have an opportunity to study mathematics at an accessible pace and volume, because mathematics develops creative thinking, creativity, consistency of thought, and the ability to distinguish fakes from non-fakes. So I want different mathematics for different children, but I don’t know how to do it yet.

It is known that with each next rung of the career ladder there are fewer women in mathematics. If the teachers of mathematics at school are mostly women, then the professors are mostly men, and there is still only one woman among the winners of the Fields Prize. Gradually, they are eliminated along this ladder. In your opinion, is there a pattern here? What is it? Or is it not a problem at all, it just happens that way?

– This is a difficult question, because here, as always, everyone has different experiences, and based on this experience, people draw conclusions. For example, my experience is that I have chosen motherhood as my main priority. I have two children, and I tried to be more involved in work than in school, but I didn’t like it. I wanted to be with children. They say that children prevent women from building a career, but this is my deliberate choice. There were such moments that I did not understand if this was my choice. Sometimes, you take your child for the 105th time in a week somewhere and wonder why you received so many higher educations, and you work as a taxi driver. At this moment, it hurts terribly when you are in such a situation that is not resourceful. But I was lucky that my husband supported me when I went to work fully. We redistributed all responsibilities, I lived in this and realized that to be with children is my conscious choice. It was a great experience that helped me prioritize. It is good when a man, man or woman, does what he does in his life consciously and understands for what and what he refuses. I decided that nothing prevents me from raising my children a little, and if I really find it interesting to do science, then go to science, if it is interesting to do some kind of business, then grow myself up and do business.

They say that there are years gone by and so on, but I think that if you have enough motivation, then you can handle it. It is very important that this is not a trap, these female tasks, motherhood, etc., which are often drawn over a woman. If she likes, let her do it. There is a wonderful film “The Smile of Mona Lisa”. There was a teacher, played by Julia Roberts, and she has girls. One says that she will be a wife, then it turns out that she will not be a good wife, this is an imposed choice, not her decision. An important moment when you have the opportunity to sort it out and leave. Some women try their hand at motherhood in life, but they understand that they have ambitions, strength, and they find a way to combine children and career. And there was another woman in this film who shone, but at a certain moment she said: sorry, I like being a mother and wife better. And I want everyone to feel this freedom and understand that he just wants it.

I was lucky enough to communicate with the mathematician Claire Voisin, she, by the way, is a mother of five children, and I asked her similar questions. And she says the problem is that in school, mathematics is presented as a competitive tool, an element of selection. “Solve faster and more interesting than everyone else” – there is even something sporty about it. And boys tend to be more competitive, while girls choose quieter areas. Do you see this in school, and could this be the source of the fact that there are fewer women in mathematics than in other sciences?

– Here again, depending on what kind of experience someone has. Maybe you thought so in your childhood, you noticed it, you can draw such a conclusion, but there are a lot of components here. I’m one of those girls who love to compete. I think girls love competition too. If we talk about calm science, on the contrary, something was beating inside me, I didn’t want to be calm, I got the impression that mathematics is just a calm area where you can calmly engage in science. I had an amazing scientific advisor at HSE – Boris Lvovich Feigin, whom I remember with great fondness, who put into me that mathematics is very calm, reliable and good, you have to do it for fun, and not for something else. I hope to come back to this. I put this on my shelf. I’m waiting for my engine to burn out a little. So I don’t know it depends on girls and boys, and on the school, and on the teacher, a lot depends on what. I would like children who want to do calm mathematics, without a competitive element, so that conditions are created for them in which they can do it. And people who like to compete, let them have where they compete.

We talked a lot today about the fact that everything is individual and depends on personal experience. Could you give some advice to those girls, schoolgirls, who are interested in mathematics, but maybe afraid, who are told that mathematics is for boys?

– I would advise you never to listen to that something for someone. Do not allow this choice to be made for you. Mathematics, which girls “don’t need” – I also went through this. My mother filtered out such things, although many mothers told her: “where are you giving the girl, why do you need it.” Mathematics is for everyone, and if you like it, do it, and there is absolutely no confirmed fact that a woman, on an equal basis with a man, cannot do mathematics. I had students who were initially afraid that they would not be able to cope. It just seems that everything is complicated in mathematics. I would like these girls to find an adult who would help and support them. And of course, avoiding stories when you are told that it is not yours will not work. This is not true, no one can ever predict who will succeed, everything in life changes.

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