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The relationship between the city and the powerful United Federation of Teachers remained rocky throughout 2010. Mayor Michael Bloomberg received a mixed reaction when he spoke at a party celebrating the 50th anniversary of the teachers' union's in March.

"Some of you cheer, some of you boo," said the mayor.

A month later, both sides came together to end the infamous "rubber rooms," the holding pens for some 700 teachers accused of wrongdoing and awaiting decision on their cases.

"Together, we and the UFT have said, enough is enough," said Schools Chancellor Joel Klein.

"We've been talking about this, saying we need to get this fixed. This isn't working. It really isn't working for anyone. And we want a faster, fairer process," said UFT President Michael Mulgrew.

They agreed to speed up the hearing process and clear out the backlog of cases. Accused teachers were assigned to administrative work, although many said they were still doing a lot of sitting around.

The collaboration between the Department of Education's management and the union stopped when it comes time to balance the budget. The mayor threatened to lay off 4,400 teachers, but at the last minute said he would save the money by denying all teachers' raises for the next two years.

"Given the two options that faced the mayor, I think it's clear, from my point of view, he made the tough but right decision," said Klein.

"The mayor can propose it, but he can't impose it, and it's not something we've agreed to," said Mulgrew.

In terms of a contract, they didn't agree to anything at all. The last teacher contract expired in 2009 and 2010 passed with no new agreement.

On the first day of school, the union president broke tradition by not appearing with the mayor and chancellor to ring in the new year. They went on two separate school tours.

Some disagreements even made it to the courts. The union lawsuit that kept the city from closing 19 schools was not their only high-profile legal battle.

The UFT also took the city to court over its decision to release 12,000 teacher report cards, which would mean parents could look up individual teacher's grades by name.

The city said the reports are an important tool for parents, but the union said the reporters are often inaccurate and are never supposed to be public. A judge heard arguments in December, but no matter what she decides, the other side will almost surely appeal.