In Poland there are no ‘specialized mathematics schools’. There are,
however, a few schools with good mathematical traditions, in particular,
with many laureates of various mathematical olympiads. I can only say a
few words about one such school in Wroclaw, in which I have had classes
for one and a half year.
Let me start from the fact that secondary school education lasts three
years. There are classes of several specialties, one of them is
mathematics (or mathematics + computer science?). During the first
semester of the first year, students have 5 hours of mathematics per
week with a school teacher, where they learn a standard material for
mathematical classes, and, additionally, they have 2 hours with a
professor from the Mathematical Institute of the University of Wroclaw,
where they learn more advanced material, mainly related to the
mathematical olympiads. In the second semester, only the best students
continue these extra 2 hours with the professor, and the rest has all 7
hours with the teacher. The best among the second year students form a
special mathematical class and they have still 5 hours with the teacher
and 2 hours with the professor, and similarly with the third year
students. If I remember well, these students attend with their original
groups to the other classes (physics, literature, …).
I do not claim that this is a tradition, because I do not know if this
was like that before I started to teach there. I have an impression that
it changes every year.