Until now two major educational institutions have been in lead in national and international Olympiads. These two are Kazakh-Turkish High Schools for gifted children and Zhautykov Republican Specialized Physics and Mathematics Boarding School.
As I am from KTL myself, I can easily tell the difference between philosophy of these two schools. First of all, according to "stereotypes", KTLs have more gocus on religion. That's not true! Preparation requires a lot of time, diligence and patience. Both schools can provide students with these desired factors. Both schools prepare really clever pupils. That's obvious when you see the winners of the last 10 years. The matter is that at KTL, students are taught by upper-class students, who have a lot experience at Olympiads. Other methods are by and large the same.
Winners raised the priorities. For example, 5 years ago Golden Medal at IMO seemed unaccomplishable until the student of RPhMS won it two times in succession! The same applies to all the international Olympiads.
Recently, Nazabayev Intellectual Schools have been opened. As far as I am concerned, it will add extra competitiveness among students as there a lot of gifted students too.
Kazakhstani pupils are certainly getting more and more clever, which makes everyone happy!