For two-and-a-half years Gotham’s teachers worked without a contract, as their union leaders struggled with the mayor and chancellor over terms for the new pact. The teachers were looking for a raise while the administration wanted to remove work rules that it claimed prevented the proper administration of the schools. As the mayor’s re-election campaign entered the final stretch, a politically expedient agreement was reached.

Both parties declared victory at a now memorable press conference that featured Chancellor Klein planting a kiss on the top of union boss Randi Weingarten’s head. But as the details now emerge it is clear that the union has, once again, outmaneuvered the mayor, who has no one but the chancellor to blame.

One of Mayor Bloomberg’s notable triumphs on the labor front was winning an initial contract that increased the time that teachers had to work by 100 minutes a week, a contract concluded shortly after the mayor took office in 2002.

Unfortunately, there was no clear plan on the part of the administration for the effective use of this bonanza. When Mr. Bloomberg learned that half of the time was to be used for “professional development” to train teachers and the other half for remediation of students in small groups, he went ballistic on the hapless former chancellor, Harold Levy. The mayor, correctly, wanted the time to go to the children for instruction.

But even three years later, Mr. Klein was similarly unable to make the best use of the opportunity to put this time to benefit students. Each new school year brought a fresh plan, culminating in an extension of each school day by a nearly invisible 10 minutes. The rest of the time, another 50 minutes a week, was squandered on the professional development schemes beloved by “progressive” educators.

The new contract was supposed to fix all of this. After all, the administration won yet another 50 minutes to be added to the teachers’ week. This raised the amount of extra time teachers would be required to work by a half hour a day under Mr. Bloomberg’s watch. But the implementation of the agreement makes things worse, because the majority of students will not be getting more class time with their teachers, but actually ten minutes a day less.

The remaining students, about a third of the school population, will be eligible to receive 37.5 minutes a day (only a bureaucracy and a union could come up with this) of remedial instruction four days a week, in classes no greater than 10.

However, since the school day officially ends earlier, attendance at these sessions is voluntary, not covered by the state compulsory attendance law. As we have seen with other elective tutoring efforts, such as summer school, many of the students who desperately need help simply won’t attend. Mr. Klein now recognizes this and has asked principals to impose sanctions, such as exclusion from recess activities on students who do not stay late.

And even for those who do, the 37.5 “extra” minutes is not all that it seems – since the basic school day has been shortened by 10 minutes, these children will only gain 27.5 minutes.

Meanwhile, if some students leave at 3 p.m. and others at 3:37:30, how is bus service provided? What about older siblings walking their younger brothers and sisters home from school? What about after-school programs, including compensatory tutoring programs mandated under the federal No Child Left Behind law? How do teachers dismiss departing children while simultaneously providing remediation to those who stay? What about under-performing schools where nearly all children need tutoring? What about after school enrichment programs for academically advanced students?

How did the bureaucrats running the Department of Education fail to see these pitfalls and negotiate this contract? At the least, tens of millions of dollars in increased transportation costs, perhaps as much as $100 million, will be diverted from the classroom.

It has been suggested that the reason for the problems lies with the new Byzantine leadership structure that has separated instruction from the “business end” of managing the schools. Two factions jockey for position, neither having a handle on the problems of running the entire entity that is the school system.

On one hand, career educators such as the deputy chancellor, Carmen Farina, concentrate on imposing a progressive (and expensive) pedagogy on teachers, while a cadre of MBAs, most of whom have no experience in K-12 education, come up with ways to increase the “productivity” of the system.

As soon as the terms of the contract were announced, veteran principals, retired principals, and superintendents immediately saw the problems sure to result. But this is the type of expertise that has been excised from the Department of Education.

In the past, Ms. Weingarten has been remarkably accommodating in agreeing to revise the usage of the extra time, making three separate deals. But with the new contract barely approved by teachers whose morale is at an all-time low, it is unlikely that she will agree to save management from itself this time around.