Supplementary mathematical education in Russian schools
(A. Smirnova, https://www.herzen.spb.ru/news/08-02-2016_1/)
“The share of male students in school is integer number percent from total number of students. After New Year vacation a boy and two girls have entered the school as new students. But the share of male students in school remains integer number percent. Please prove that total number of students in previous year was not less than two hundred.” (A. Solynin)
This is the problem from mathematical Olympics of Saint Petersburg city in 2016-2017 for 6th class (see http://www.pdmi.ras.ru/~olymp/2017/problems/c_68_17.pdf (in Russian)). It means that 12-year old children have to solve it along with five more problems and orally explain the solution to high commission in order to win the competition.
Russia is one of the world-leading countries in mathematics nowadays. The system of mathematical education in Russia has very deep structure and because of that talented students start to learn required professional skills even at school. Let us briefly explain how this system works.
At the 30’ years of XX century famous mathematician Boris Delaunay (the Delaunay triangulation is called after him, by the way) introduced the basics of this system. He suggested to start the Leningrad (Saint-Petersburg nowadays) School Olympics in Mathematics and the first one was held in 1934. The main goal of this Olympics was to select talented students among others and after that suggest them to continue their mathematical studies at one of the specified mathematical clubs in Leningrad. These clubs were supervised by professional mathematicians who regularly provided some specific problems for students to solve and then met with them in order to check their solutions. The main feature of these studies was that the student had to orally explain their solution to one of the tutors and it strongly raised the students’ level of mathematical culture. Also the studies included some theoretical courses (mostly from university program) on different subjects from abstract topology to the combinatorics and graph theory.
This system was spread throughout the whole USSR and it evolves and continues to function presently. Saint-Petersburg, Moscow, Kazan, Sochi, Kirov, Omsk and Novosibirsk are the leading cities in this educational process nowadays. Such a big number of cities is also one of the main reasons why we have so many talented mathematicians in Russia.