Having been in public school for most of my life I can say unequivocally: yes. It is not uncommon for teachers to purchase books and classroom supplies out of pocket since there simply is not enough funding.
Most estimates I've seen of funding for New York students is $25k to $30k a year though. I would think that's more of a sign of incredible corruption and mismanagement and not that there isn't enough money to go around.
To compare, Stuyvesant High School, the best in NYC, is $18k per student.
I would argue the point that Stuyvesant is the "best" but I don't disagree with your point. The problem is that a lot of the money ends up in the schools with the rich kids and for a lot a lot of students and schools they never see anywhere near that type of money.
Stuyvesant, like most good schools, raises a good deal of private funds. That actually accounts for good deal of the difference in resources between schools.
