The usual solution to problems of "too many adjectives and pre-modifiers" is to use a relative clause.
English usually puts adjectives before the noun, so "specialized school" is good. But "specialized maths school" or is awkward: its not clear if specialized is modifying "maths" or "school".
Relative clauses can be much "heavier", you can put a preposition to indicate the relationship that "maths" has. If you have adjective that is formed as a participle, consider using it as the verb in a relative clause:
Using "default" is okay, but "the local school" probably means the same, or it may be more natural to use the particular school name. (If I recall, Russian schools tend to be numbered rather than named)
I want to send my daughter to a school that specialises in maths, rather than School 10.
(A small historical aside) Now there is an compound phrase "Mathematics specialist school", in England (not even the UK) from an old government initiative to create specialised schools, but this refers to a particular scheme (that doesn't even exist anymore). At one point, about 15 years ago, nearly all schools picked a "specialism" because the government was offering extra money. Some might still use the term in advertising (even though the scheme has ended)