Breaking Stalin's Nose
Nina Petrovna is the type of teacher you wouldn't wish on your worst enemy. She's a mean-spirited, suspicious, and frankly rabid Communist. She takes delight in casual cruelty, by taking every opportunity she can find to remind people like Vovka and Four-Eyes that they are of a lower order than the rest of the students, just because their parents have been thrown in prison.
She's also not above tossing out some good old-fashioned racial slurs:
"Stop rocking back and forth, Finkelstein. You're not in a synagogue." (13.19)
Yeah: she's a real piece of work.
It Wasn't Always This Way
At first, though, Sasha thinks she's the cat's meow; "She's nice and fair, but when necessary, she's firm. In my opinion, she's the best teacher in our school" (13.11). He becomes much less of a fanboy when Nina Petrovna mercilessly reveals to the class that Vovka's dad was executed, which was the reason for his (in her words) "hideous anti-Soviet behavior" (22.11). At this point, Sasha realizes that this is a load of tripe, since his own father has been taken away from him. Sasha even physically intervenes in this fight, which gives us a good clue that his opinion of her "fairness" is going south (22.15).
In the end, Nina Petrovna is falsely accused of breaking Stalin's nose, thanks to Vovka's trumped up evidence (he's hid the nose in her desk, you see). So, the system she so rabidly represents ends up turning on her. That's what we call irony, folks, and we couldn't be happier to see it rear its ugly head.