Today, New York City begins negotiating a new teachers union contract. In importance, this task may outweigh Mayor Bloomberg’s entire school reform. The math and reading curricula instituted throughout the public schools by Schools Chancellor Joel Klein can be undone with a gesture of the hand. But the provisions written into this contract will require something far more substantial to be broken should the city someday deem itself to have erred in any one of its concessions.

The president of the United Federation of Teachers, Randi Weingarten, dropped a tantalizing morsel on the table yesterday — a potential loosening of the union work rules that have choked the school system like a noose these many years. Aside from the basics, such as salaries, pensions, and health care, the city and the union also haggle quite a bit about the rules determining what schools can and can’t ask teachers to do. The situation is so bad that education expert Sol Stern, author of “Breaking Free: Public School Lessons and the Imperative of School Choice,” dubbed the UFT agreement the “we-don’t-do-windows” contract.

Among the things teachers can’t be asked to do under the contract: walk children to a school bus, patrol the lunchrooms or the hallways or the yards, cover extra classes in an emergency, come in more than one day before classes begin at the start of the year, attend more than one staff meeting a month, and attend a staff meeting during lunch. The contract also governs the lengths of classes at every school, the amount of preparation time teachers get before classes, the process for teachers’s performance to be reviewed, and the process for teachers to be transferred from school to school. The seniority system is a particular hassle for principals unable to get rid of unfit senior teachers and forced to accept the incoming seniority transfers of unfit teachers from other schools.

Ms. Weingarten’s proposal, so far as it can be made out — the union is keeping things vague, at the moment — is to allow the teachers at a small number of schools to opt out of some of the work rules in exchange for more control over their schools. She says that she is willing to include as many as all of the schools in one of the 10 regions to be included in the venture. However, in a union document, she says that “provisions covering salaries, pensions and other benefits, safety, due process and other matters required by law and to guarantee fairness” are off the table.

Any move by the union to loosen the work rules is an encouraging one, particularly when it comes from Ms. Weingarten. But it’s doubtful how much flexibility the city would be gaining under her scheme. When Ms. Weingarten says salaries are off the table, does she mean both in the downward and upward directions? Would participating schools be unable to institute any form of pay-for-performance? If not, why not? Bonuses for outstanding performance could be a grand experiment for the city and could entice more teachers to demand that their schools sign up. Furthermore, if the structure of the school day — presumably including its length — is on the table, a principal presumably would need to be able to offer some monetary incentive to get teachers on board with any innovations.

We already know what can be accomplished when a school truly is freed from the constraints of the UFT contract. The Knowledge Is Power Program Academy in the South Bronx, established as a charter school in 2000, meets from 7:25 a.m. to 5 p.m. during the week and for four hours on Saturdays; under the UFT contract, teachers work only a little more than six hours a day, five days a week. KIPP has a 213-day school year, with three weeks in the summer, compared to the 180 days that most public schools have under the standard contract. The result: KIPP Academy, with a disadvantaged student body, ranked 17th in New York City in the eighth-grade reading scores released in May, with 72% reading at or above grade level; that is opposed to an average of 32.5% in New York City.

Less rules sounds nice. But if the rules that matter stay in place nothing will be gained. A lock-step pay system based only on years on the job, a seniority transfer system that prevents principals from getting the teachers they want, a grievance process that makes it impossible to fire incompetent teachers — all are major impediments to improving our schools. The extent to which Mayor Bloomberg and Chancellor Klein demand freedom in these areas. It will be a measure of their political courage; the extent to which the UFT concedes will be a measure of its good faith.