Leaders of the city’s teachers union are counting on a state panel to give them a better contract than one they could otherwise extract from the Bloomberg administration. It is a roll of the dice. These commissions have sometimes backed the teachers, recommending double-digit raises, while on other occasions they have suggested teachers get just a fraction of what they are asking for.

“The panel is supposed to provide a reasonable solution to the bargaining impasse,” the city’s former director of labor relations, Robert Linn, said. “The city’s argument is that they have formed a pattern with one union and that should apply to all the others. Generally the union says that they have circumstances that justify more money than the pattern allows. That same argument has been fought out for decades.”

Mayor Bloomberg has offered the unions representing municipal employees a raise of 3% to 4% this year, adding that any increase above that would have to be paid for with workplace efficiencies. That bargaining pattern was set with the huge District Council 37 earlier this year, and Mr. Bloomberg has insisted that other city workers unions follow suit. The teachers are banking on being able to do better by going to a fact-finding commission.

The teachers union has had mixed results with fact-finding commissions.

In 2001, teachers wanted a 22% raise. Mr. Bloomberg, when he came into office, offered them about 6%. The state fact-finding panel recommended that the teachers receive a 15% raise over 27 months, as part of a contract that would lengthen the school day by 20 minutes.

In 1993, the teachers fared worse. A report by the state’s Public Employment Relations Board offered a framework for an acceptable settlement that had the then-president of the United Federation of Teachers, Sandra Feldman, telling her members they needed to greatly lower their salary expectations. The board had called for a retroactive raise of 8.5% over 39 months. That gave teachers one-quarter of 1% more than the contracts approved by other city unions. They had asked for a 25% raise.

“Once the union decides to go to fact-finding it becomes a very public fight,” said a former policeman and negotiator for the police union, Harry Greenberg. “And that puts pressure on both sides to get it done.”

The public sniping has already started. Last week, the union representing about 1,250 physicians agreed to a new contract along the mayor’s lines, giving some doctors raises of more than 10% in exchange for longer work hours. Mr. Bloomberg used the opportunity to take a shot at teachers.

“So far, the teachers union has not come up with any of the savings to come up with monies to pay them over the pattern or the reforms we think are necessary to improve the school system,” the mayor said.

The president of the teachers union, Randi Weingarten, saw it differently. She said the city had walked away from the contract negotiations.

“We made a proposal and they never came up with a counterproposal,” Ms. Weingarten said. The two sides had discussed a 14% pay increase but couldn’t agree on how to pay for it.

The tension is about more than compensation. Mr. Bloomberg has pledged to reform the teachers’ 200-page, $9.5 billion contract, which covers everything from workloads and assignments to evaluations and promotion. The contract affects more than 134,000 employees of the Department of Education, of whom about 109,000 are teachers.

The teachers have been working without a contract since May 31, 2003. Some education researchers and political leaders said the work rules in the contract make it harder for principals to run good schools. Because the two sides are no closer to agreeing on those work-rules issues than they were months ago, the teachers union decided to turn to fact-finding.

“Either side has the right to bring wages, hours, and working conditions to the table,” said Mr. Linn, who is president of Linn & Green, a labor-relations consulting firm. “They are also allowed to bring up managerial things, like class size. The only thing that is really off the table are things like pensions.

“The teachers have nearly always accomplished substantial things toward their needs in these fact-finding procedures,” he said. “They have been able to use elements in their contract to justify increases.”

The fact-finding panel has its basis in the Taylor Law, a labor-relations statute covering most of the public employees in New York State. The law was enacted after the 1966 transit workers strike, which shut down the city for 12 days, at an estimated cost of $100 million a day. Three days after the strike was resolved, the governor, Nelson Rockefeller, appointed a Public Employee Relations Committee to “protect the public against the disruption of vital public services by illegal strikes, while at the same time protecting the rights of public employees.”

The committee was led by a University of Pennsylvania professor, George Taylor, and its recommendations became law in 1967. It was the first comprehensive labor-relations law for public employees in the state, and among the first in America. Among other things, it established impasse procedures to resolve collective-bargaining disputes and established the Public Employment Relations Board, known as PERB, whose members are appointed by the governor with the consent of the state Senate.

The Taylor Law has four ways to break impasses.

The first is mediation, the stage at which the city and the teachers are now, and the second is fact-finding, which is essentially a hearing with testimony from witnesses, briefs from both sides, and eventually a nonbinding recommendation for settlement. The fact-finder’s report is made public five days after it is issued – which, in theory, puts pressure on the parties to reach agreement.

“It isn’t just like a trial, because the rules of evidence are relaxed, but it is conducted like a hearing, with a record and that sort of thing,” said Mr. Greenberg, who is a partner at the law firm of Solomon, Richman, and Greenberg. “If they come out with a report that everyone agrees with, they can just adopt it – that is the contract. And while it can’t be imposed, both sides get boxed in publicly because the fight is in the paper when the recommendation is released.”

If the two sides still cannot agree, the next step is a legislative hearing. The governor’s office submits a copy of the fact-finding report with the agency’s own recommendations to the legislature. There are public hearings, and in extreme cases lawmakers can impose a solution. Usually the parties are able to agree before it reaches that stage.

Reaching an agreement with the teachers union is important to the Bloomberg administration. With an election coming in November, Mr. Bloomberg would rather have that potent union fighting for him instead of against him. Ms. Weingarten has been careful to say she hasn’t decided whom her union will endorse in the next election.

Mr. Bloomberg is having to walk a careful line. He could be criticized for ceding too much to the teachers union, and he doesn’t want to appear to have rolled over to their demands just before a campaign in which he will have to remind New Yorkers of multi-billion dollar budget holes as far as the eye can see.