How to solve math problems

“We only teach that this mathematics! complains Irina, mother of 11-year-old Alice. — The daughter seems to know the formula, but still stumbles at every step. Sometimes it solves a difficult problem, but not a simple one. Controls are horror for the whole family. The child is all on his nerves, my husband and I have a headache. You never know if she will write for four or bring a deuce. Studying all weekend and no progress!”

I understand Alice very well. I remember how melancholy all these equations, functions and tangents evoked in me at school. Even the unloved chemistry and physics were closer to me: I could somehow correlate them with my own experience. But «a plus b divided by c» was infinitely far from my life.

Alice and I are no exception. In every class there are children for whom mathematics is a complete torment. And their parents are tormented by questions about how to relate to this and how they can help.

Do kids need math?

These problems are everywhere. In 2012, The New York Times began a discussion about whether children need algebra if one in four students in the United States does not graduate from school due to problems with this subject.

And in France, former Minister of Education and Science Claude Allegret, himself a geophysicist, has been seriously discussing the abolition of the teaching of mathematics in schools, since many children cannot cope even with elementary tasks.

“My daughter is not, she is a humanist, like me, she will go to the philological faculty,” 36-year-old Marina is sure. “The main thing for us is that in literature, Russian, history there are fives, and in mathematics — if only not a deuce.”

“This is a painful question: how deep do you need to know mathematics for those who do not seem to need it? — reflects the writer and mathematician Leonid Kostyukov. But who are the humanists? One-tenth — people of art, and nine-tenths — people of culture.

For people of art (artist, poet, actor), mathematics is probably not necessary for creativity. But people of culture — a historian, a philologist, an editor, a publisher, a journalist — cannot do without systems thinking. Namely, mathematics educates, disciplines the mind.

For the first time, I wondered if I was wrong to neglect mathematics when I began to write my dissertation. The topic was purely philological — but what anguish it cost me to organize all the huge factual material and convincingly substantiate my concept! Logical thinking was the problem. But since I still managed to complete my dissertation, then maybe I’m not as hopeless in terms of logic as it once seemed to me and my parents?

Most difficult subject?

If a child has difficulty with mathematics, we always have an answer ready: it means that there is no mathematical ability. And with that, we kind of close the topic: no, there is no trial. In other words, we easily agree: mathematics is so difficult that not everyone can cope with it. And we console ourselves with the fact that in other disciplines our child is quite (or perfectly) in time.

Leonid Kostyukov, an experienced tutor, is sure that he teaches one of the easiest subjects: “The mathematics course is incredibly elegant, beautiful, and logical. Very little needs to be learned, much more needs to be understood. If I don’t remember the formula, but I remember where it comes from, I can quickly deduce it. There is no such possibility in any other school sciences.”

In his opinion, if a child has time in other subjects, there is no reason for him not to cope with mathematics. “If, for example, he is good at English, it means that everything is in order with his logic, because the English language is arranged very logically. Moreover, objectively it is more complicated than the language of school mathematics. This means that this child should be able to do well in mathematics.” So why is this not the case in practice?

When problems snowball

“Mathematics gives the purest and most direct experience of truth,” said the German physicist, Nobel Prize winner Max Laue in his book Pages from the Life of Landau. And in every class there are children who are familiar with this experience, who experience pleasure, for example, from a beautiful solution to a problem.

“As a rule, these children are active, curious, ready to take risks, they are not afraid of problem situations, they love to make discoveries,” says child psychologist Elena Morozova. — And children who are afraid of mathematics often do not rely on themselves, they are too dependent on the opinion of their parents (teachers, classmates), they are not confident in themselves, they easily believe that they are slow-witted.

Any task leads such a child to a stupor: he is afraid of the very expectation that now it will be difficult and he will be insolvent. Fear can cause failure in other subjects as well.”

It grows gradually, like a snowball. For example, the child psychologist recalls, in the first grades, not all children still read well “and the condition of the problem may simply not be understood. In addition, they have not yet developed abstract thinking, it is difficult for them to imagine a picture: here is a train leaving point A, and here is another train leaving point B, here they meet. And the child deliberately refuses to delve into the problem: I won’t even try to do something about it.”

“If I missed Griboyedov in literature, this will not prevent me from studying Turgenev,” remarks Leonid Kostyukov. — But if I missed something in algebra, then I will have systemic problems. Other subjects represent a specific set of topics. Mathematics, by and large, is the development of one topic. But sometimes it turns out that not all older students know even the multiplication table for sure.

The reason is not math

“She has a bad relationship with the teacher”, “classmates laugh at him”, “she is worried that her father left the family” — there can be many reasons for poor performance in any subject. But are there reasons that cause difficulties with mathematics?

Educational psychologist Ann Sieti is sure that mathematical concepts can awaken the deepest feelings. «Condition», «required», «prove», «necessary but not sufficient» — all these words can unconsciously be associated with internal problems.

“What is only the notorious “X” — an unknown, behind which is unknown what is hidden,” she says. — Or another example: one of my students did not put brackets in her equations, forgetting to separate some numbers from others. And then it turned out that at home it was difficult for her to be alone in her room — that is, to perceive herself separately from other family members.

A child’s problems with mathematics are not related to his intellectual abilities, but to something inside him that prevents him from thinking clearly and understanding the teacher. That’s where so many disturbing emotions block the mind.

Don’t Learn, Understand

We admit: very often school failures drive parents out of themselves. We get angry, indignant and criticize a child who “does not try”, “does not want to understand” and generally “does not think well”. And experts are unanimous: the main task of parents is just the opposite — to reduce his stress and worries.

“A child should not be fixated on failures at all,” Elena Morozova emphasizes. “It’s better to say: yes, it’s not working yet, let’s think about how to help you.”

“Mathematics needs to be understood, to feel its integrity, unity. If you just cram, it will only be an extremely tedious and, most importantly, meaningless training for memory, ”warns Leonid Kostyukov.

“It is necessary not to hammer in, but to consistently lead the child to an independent decision,” continues Elena Morozova. — And when this insight happens, the child is amazed: “Wow, I could!” It turned out once, twice, a third — and gradually he begins to get involved, to feel his worth.

Of course, the best help here is a specialist — a teacher who can be asked for additional classes, or an experienced tutor. But parents themselves can try to make these discoveries together with the child.

Not necessarily after that the student will shine in the classroom and bring fives. Although grades do get better if you don’t focus on them, Ann Sieti notes: “After all, everyone has their own goals. For one, it is important not to be the worst in the class. Another dreams of becoming a veterinarian. The main thing is that children begin to feel better, get rid of anxiety and fear, and begin to enjoy doing math.”