On May 12, the HSE celebrated Women in Mathematics Day at the site of The New School. We talked to Vlada Kazantseva, a mathematics teacher at The New School, a graduate of the first set of the HSE Faculty of Mathematics— about what modern schoolchildren think about mathematics, what is the difference between male and female teachers, how to choose between a career and family, and why mathematics is a science for everyone.
Why was it decided to hold the event at the site of The New School this year? After all, women in mathematics is not the most obvious topic for schoolchildren. How did this idea come around?
— It just happened that several active women met, including Sasha Skripchenko, myself, and Lisa Mishina, the deputy director of our charity foundation. Sasha told us that there is such an event as the Women in Mathematics Day. Word for word, we wanted to expand this idea. And after all, a woman in mathematics is not necessarily a scientist. Almost every person was introduced to mathematics through a woman, simply because according to statistics, there are more female math teachers than males. And for many people, 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 somewhat looped with school education. I became a schoolteacher after graduating Faculty of Mathematics. And now they opened a joint program with the Centre for Teaching Excellence, which began to train math students so that they would go to work at the 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 create interesting collaborations.
Sasha Skripchenko suggested that as the hero of our meeting, we can take Joan Birman because she has an interesting biography. She also asked Vladimir Shastin to talk about her work. The children prepared their talks on the theory of knots, at the same time we remembered the teachers of mathematics, after that there was an informal meeting. I think this is important because when people communicate like this, get acquainted, they have ideas, and then these ideas grow into something beautiful. To continue this, we have created the group “Mathematical Union”. 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 not only mathematicians, but everyone can understand something, learn something, feel that it is beautiful, cool, and interesting.
One more thing about the children's part of the conference. Was there some sort of selection, or did everyone who wanted could make a presentation? How did they choose the topics, how did they prepare, together with the teachers, or independently?
— We took Sosinsky's book “Knots and Braids” as a starting point. We gave it to the kids and suggested they participate. At our school, I addressed several children specifically, because I knew that they were interested in this, and I also wrote to my colleagues and friends, who responded and brought their children. I particularly liked the team from school #179. I sent them a book, they registered, and then there was a long silence. And suddenly, the day before a conference, a girl from that school calls me and says that she wants to make a presentation. I wondered which chapter she was going to report, and she said it was the whole book. Then I realized that the kids are ready, they will come and do it. So, that how the first conference went. And I want to develop this because I think it is important when children can live through some mathematical topic. It's a feeling, I know from myself, a feeling of pride. I did it, I did well, and I overcame this mathematical problem.
Someone said today that men and women teach mathematics differently. Men tend to prove themselves and women tend to give more. What do you think about this from your own experience?
— That is quite an interesting thought. I didn't think about it so it's hard to say. I have a specific experience, I studied in mathematical class, and they really taught us to achieve something, to develop. But on the other hand, I've always been comfortable with both male and female math teachers. When this idea was expressed, I tried it on myself as a female teacher. I don't know if this is related to gender, but I really have a somewhat motherly attitude towards these children. If something doesn't work out for them, I let it all go through me, I start to worry, I really want to help them and often make individual consultations. I wouldn“t say about gender, because I still think that most of it comes from personality. But indeed I personally always try to take care, to show that it is not difficult, that I am there, I will help, I will lend a shoulder so that they are not afraid, but on the contrary, they are eager to fight. So there really is something like this
At all times people try to compare generations. Someone says that ‘the children are not as we were’, someone, on the contrary, believes that everything is always the same. In your experience, how do children feel about studying mathematics now, how do modern children differ from the memories of your school days?
— It is difficult to compare because I studied in a mathematical class. In The New School children are different, of course. They do not take for granted the fact that math is an interesting thing to do, and in the mathematical class, there were children who thought that by default. I like it when children have these discoveries, that mathematics does not work as ‘it is true because the teacher said, that’. They discover that everything can be proven that everything is logical, everything has its origins. I like that thanks to mathematics, children get a sense of the foundation, that everything is logical, that if something suddenly breaks, you just need to get to the bottom of it and everything can be fixed. And my favorite and most important achievement is that children start asking questions and thoughtfully follow what I do. 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 children are different, in some ways, perhaps, they are really different. They are very modern, you need to be able to maneuver with them because they are very bright, clever, active. But I like their optimism. I really like how they are now, I don't understand why they are scolded. They are incredibly optimistic, often very kind. Strange situations happen to them sometimes, just like they've happened to all of us, but I like the way they come 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 out of it.
School maths is often presented as an elitist, exclusive subject. They say that to understand it, you need to be, if not a genius, then at least a gifted child. How is it going at The New School? Do you think it is necessary to change it or let there be this separation?
— It seems to me that you need to include all the possible shapes and forms. Indeed, we have developed a reputation for elite mathematics in Russia. There are math schools where the math is very strong, and let it go on. I really want there to be another level. For children who are not such outstanding, but are good, strong, who can think consistently and solve problems of a certain degree of difficulty, who strive to work. In general, I do not see any problem to be able to do the math for creative children. Translating, for example, the same knots theory into mathematical language 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 teaching all children in a row to solve quadratic equations, and children resist it because it is just not for them. I want every child to have the 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 math for different children, but I don't know how to do it yet.
It is known that with every new career level there are fewer and fewer women in mathematics. So that math teachers at school are mostly female but you can hardly find a female high school professor, and among the winners of the Fields Prize, there is still only one woman at all. 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 chose motherhood as the main priority. I have two children, and I tried to have a more time-consuming job than at school, but I didn't like it. I wanted to be with my kids. They say that children stop women from building a career, but this was my conscious choice. There were times when I didn't know if it was really my choice. Sometimes, you ride a child somewhere for the 105th time in a week and think why you would get so many degrees to work as a driver mom. At this point, it is very annoying when you are out of your resources. But I was lucky that my husband supported me when I went to work full-time. We redistributed all the responsibilities, I tried this and realized that being with the children was my conscious choice. It was a great experience that helped me set my priorities. It is good when people, a man, or a woman, do what they do in their lives consciously and understand what they sacrifice. I decided that there was nothing stopping me from raising them up a little, and if I was really interested in doing science, then go to science, if I was interested in doing some business, then do business. They say that you lose years and so on, but I think that if you have enough motivation, then you can catch up with it. It is very important that this is not a trap, these women's tasks, motherhood, etc., are often drawn over a woman. If she likes it, let her do it. There is a wonderful film Mona Lisa Smile. There was a teacher, played by Julia Roberts, and she had girl students. 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 is that you can sort it out and leave. Some women try their hand at motherhood in real life, but they realize that they have ambitions, strength, and they find a way to combine family and a career. And there was another woman in this film who was brilliant at studying, but at a certain point, she said that she preferred to be a mother and a wife. And I want everyone to feel this freedom and understand that they just want it.
I was lucky enough to talk to the mathematician Claire Voisin, who, by the way, is a mother of five children, and I asked her similar questions. And she says that the problem is that in school mathematics is presented as a competitive tool, an element of selection. Solve it faster and more interesting than anyone else — that is even some kind of a sport. And boys are more likely to compete, 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 math than in other sciences?
—And again, depending on personal experience. Maybe you thought so as a child, you noticed it, you can draw such a conclusion, but there are a lot of components here. I'm the kind of girl who likes to compete. I think girls like competition, too. If we talk about quiet science, on the contrary, I just had something inside, I did not want to be calm, I had the impression that mathematics is just a quiet area where you can safely do science. I had an amazing supervisor at HSE – Boris Feigin, whom I remember with great warmth. He taught me that mathematics is very calm, reliable, and good, you need to do it for fun, and not for anything else. I hope to get back to that. I left it for later. I'm waiting for my engine to burn out a little. So I don't know, it depends on the girls, and on the boys, and on the school, and on the teacher, a lot of things. I would like to see children who want to do calm math, without a competitive element, have conditions 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 personal experience. Could you give advice to those girls who are interested in mathematics, but maybe afraid of doing it, who are told that mathematics is for boys?
— I would advise them to never believe that something is for someone. Don't let them make that choice for you. Math that is ‘not for the girls’ — I also went through this. My mother filtered out such things, although many mothers told her: ‘why do you let your daughter there, she doesn‘t need it’ Mathematics is for everyone, and if you like it, do it, and there are absolutely no confirmed facts that a woman cannot do mathematics as well as a man. I've had female students who were afraid they wouldn't make it at first. It just seems that everything in mathematics is complicated. I would like these girls to find an adult who would help them, support them. And of course, you can't avoid stories where people tell you that it's not yours. This is not true, no one can ever predict what someone will succeed in, everything in life changes.