Games for young mathematicians

Games for young mathematicians

Children from all over the Republic are welcomed through the doors of this Dagestani summer mathematics school.  The children in this class are the cream of the crop—exceptional in their persistence and willingness to overcome difficulties as well as in their love of mathematics.   A large circle of seemingly ordinary girls and boys is gathered around mathematician Igor Fedorenko.  He has glasses on his friendly face and is wearing shorts and a green t-shirt.   This is the second year for this summer mathematics school in Dagestan.  The idea for it originated with the Nadezhda Centre for Extra-Curricular Education of Schoolchildren in Makhachkala.  The month before, the same sort of activities took place in the town of Agvali in the Tsumadinsky district.  Many of the students there asked to be included in the second round.  The school lasts two weeks with instruction involving four groups for four hours each day.  Basically, it is a mathematics-oriented summer camp.  Apart from instruction the children play volleyball, tennis and chess.

In July and August the weather is fine with fresh air and quiet.  Labazan Gadzhiev, director of the boarding school for gifted children in Mekhelta, provided a place to stay for the children and instructors.

Seven instructors—two of whom, Igor Fedorenko from Krasnodar and Leonid Popov from Moscow, were invited from outside the region—work with 33 teenagers at the summer school.

Igor Fedorenko is director of the Krasnodar Bernoulli Mathematics Centre.  For the last twenty-five years it has offered extra-curricular activities in mathematics and programming.  Children start when they are in the fourth and fifth forms, and typically half of them will continue through the eleventh form and then enroll in Moscow universities.  Out of sixteen graduates from the Bernoulli sessions last year, fourteen enrolled at either Moscow University, the Higher School of Economics, or the Moscow Institute of Physics and Technology; of the remaining two, one went to the University of Mannheim in Germany and one continued his studies in the Kuban region.

Since its founding in 2007, the Nadezhda Centre for Extra-Curricular Education of Schoolchildren has been associated with the Bernoulli Centre.  The Nadezhda Center is not state-run, and parents pay a nominal tuition fee.  The bulk of the funding for Nadezhda is provided by the Ziyavudin Magomedov PERI Charitable Foundation.

‘I’ve known a good many of these children—Ramazan, Aishat, Ismail, Rustam—for several years’, says Igor Vladimirovich.  ‘Of course, the achievements of the Dagestani centre do not compare with the one in Krasnodar.  But in fact the purpose is not only to win olympiads and enroll in prestigious universities. It’s also to develop intellectually aware children.  We always tell them, “Your success in the olympiads doesn’t matter to us.  It’s much more important that you are involved in the study of mathematics and are working on something serious.”’

‘This is Team Mathematic s Dagestan’, the instructors quip.  The children here really are from all the cities and many regions of the Republic.  They will notice someone at the olympiads and invite him here.  However, there is no pressure.  The parents decide whether their child should come or not.

‘That’s a principle’, Igor Vladimirovich explains.  ‘In the fifth and sixth forms all children have a way with mathematics—I am certain of that.  Who is handling a child is very important.  We do not have qualifying events, or aptitude tests, or pop quizzes along the way, or even graduation exams.  The main goal is for children to have the desire to study mathematics.  At the first session I say right off: “Children!  There is no need at all to get into mathematics at any point in your lives.  It’s difficult, boring, and uninteresting.”  The reaction is just the same as yours—they can’t believe it.  And, lord be praised, then they are making a deliberate choice, once we have told them honestly that it will be hard.  The child will wonder why he should take on such a frustrating thing.  Why should she not take up dancing, literature, or history that comes easily to her?  In reality, the child will be just about as capable with anything he commits to.  There are a lot of personal aspects to this, and we foster willingness in children to study, patience, and the ability to overcome obstacles.  Today they got their first homework assignments.  It will take them until tomorrow morning to get them done.  They’ll have to sacrifice volleyball and break time while they work their way through the problems.  We put children in a position where they either study independently or lose to everyone else.  And then comes the moment of truth—to keep up with the others or give up.  Handling choices makes a huge contribution to a child’s character.’

After the session the children play in the yard, some at ping pong and others at a kind of draughts where black and white stones take the place of the usual round pieces.  After break time in the evening in one of the classrooms instructor Leonid Popov will be waiting for anyone who would like to go through the problems, and he has no doubt that there will be someone.  Next morning these children will be going over the assignments for international olympiads with Igor Fedorenko.

The Nadezhda Centre holds sessions in mathematics for children during the school year according to a special programme.  It does not make use of anything that the Ministry of Education has chosen for schools.  ‘The school programme has a number of inconsistencies.  Ours is formed from the viewpoint of the community of professional mathematicians.  We are not bound to a schema the way that school teachers are’, say the teachers.

Asker Askerov , director of Nadezhda, thinks that mathematics education in the Republic is in a difficult position:

‘In the ‘90s institutions of higher education would graduate just about anyone who came.  Because of that the schools are manned mostly by a mature generation of teachers, and there are almost no young teachers.  There is only one way out of this situation—find the children who are math “standouts” and work with them at a centre.  We are in fact quite insignificant in the educational scheme of the Republic, although we accomplish quite a lot in conveying mathematics to children.  Almost all the prize winners in the Republic’s olympiads are our students. The results so far in national olympiads are not very impressive, although two children placed in the Moscow mathematics olympiads—Khadzhimurad from Makhachkala (with a second place certificate) and Zamir from Derbent (with a third place certificate).  And the Moscow one is really considered more demanding than the nationals.  And this was the very first time that children from Dagestan competed in the Moscow olympiad.’

A while ago it was a big thing when any of our schoolchildren made it to the Russian finals in mathematics, but now it is nothing special.  Mathematicians love counting.  And they see their goal with mathematical precision—in the near future to have two or three Dagestani prize winners in the national olympiads.

On a school desk in a classroom I come across a sheet of problems that the students have solved.  ‘A hungry Baby and Karlsson ate a cake and are full. When he is hungry, Karlsson weighs less than a full Baby.  But a full Karlsson weighs as much as two hungry Babies.  Which is heavier?  The cake or the hungry Baby?’  I wracked my brains for a long time over the solution.  Can you come up with the correct answer?