The city, though, disputes these conclusions. Dan Weisberg, the education department’s chief executive for labor relations, says that fewer than 30 teachers work full time in a classroom and that the vast majority of teachers in the pool are substitutes.  The union reached the amount that it says the reserve pool costs through a complex calculation. First, it said that hiring 471 entry-level teachers at $64,690 a year — instead of using the ones in the reserves — cost the city $30.5 million a year. Then, it said that by using the reserve teachers as substitutes, the city saved $11.8 million that it otherwise would have had to pay for substitutes. The total cost, the union concluded, was $18.7 million a year.  The union’s calculations do not consider the salaries of those in the reserve pool, which must be paid under the contract.  Randi Weingarten, the president of the union, said the city could have saved the $30.5 million it paid to hire new teachers by placing reserve pool teachers in different jobs. She also said that the city was obligated by the terms of the contract to give these experienced teachers priority, but that the department had not done enough to help them find new jobs.  “The simplest way to solve this problem is for the department to implement what they already have an obligation to do, which is to care about their employees a little bit and actually manage the process,” she said. “Basically what they say is ‘Tough luck, it’s up to you to find a job.’ ”  Mr. Weisberg disagreed with the numbers and said that the vast majority of reserve teachers eventually found permanent posts, and that it was “patently false that we are just letting these people sink or swim.”  Timothy Daly, the president of the New Teacher Project, dismissed the union’s methodology and said that the union was underestimating the cost in an effort to play down the issue.  “They want to do the accounting to make it look like the policy is not a problem,” Mr. Daly said, adding that the real question was, “Is it appropriate to allow teachers to receive tenure when they’re not in a classroom or to be placed teaching a class they are not licensed for?”  A version of this article appears in print on , on Page B3 of the New York edition with the headline: City and Teachers’ Union Disagree on Reserve Pool. Order Reprints| Today's Paper|Subscribe
The teacher’s union says city teachers who are not assigned to permanent classroom jobs still play a vital role in the school system.