Most of the furniture in classrooms is indeed purchased and owned by the school. Particularly the furniture that the students are using.

That said - it is definitely not uncommon for teachers to also purchase some items themselves. My daughter, a teacher, purchased a stool to use herself at the front of the class. A couple of my sisters, who teach elementary, purchased pillows and beanbags and small fake lazyboy-style chairs for classroom reading nooks. One of them also bought her own rocking chair she would sit on to read to the students when she was teaching 1st grade.

So I'd be curious if the item that was broken was the teacher's or the school's. If it was the teacher's, it makes sense for the teacher to collect money to fix or replace it. If it was the schools, then it makes much less sense for that to happen.

I'm also kind of curious as to why the teacher wouldn't involve the parents. $3 isn't much - but it's kind of weird to assume a kid that age has his own money when he obviously isn't old enough for a job. A quick explanation to parents in a note or email would go a long way.