Education officials have increasingly relied on the Teaching Fellows program to find teachers for hard-to-staff subjects like math, science, and special education. But with more than half of the new teachers quitting within a few years, some critics say the $16-million-a-year hiring strategy amounts to filling a leaky bucket.

The Teaching Fellows program was launched four years ago, when Harold Levy was schools chancellor, to recruit and train talented lawyers, stockbrokers, advertisers, other professionals, and recent college graduates to be teachers. The program has been successful at finding new educators, attracting eight applicants for each of its roughly 2,000 slots a year. Keeping them, however, has been a major challenge.

During a fellow’s first two years, the city pays the teacher an extra $8,000 to obtain a master’s degree and teaching license. That doesn’t count the price of advertising the program in subways, newspapers, and Web sites, or providing extensive mentoring to recruits. Still, many fellows quit as soon as their subsidized education ends, if not before.

“From the perspective of the long term it’s not such an excellent strategy, only because retention rates are so low,” the chairwoman of the City Council’s Committee on Education, Eva Moskowitz said last week. “It creates a real problem. … Unfortunately, it’s likely that these rather talented people won’t be there in a year or two.”

This year, 40% of the city’s new teachers in math and special education and 21% in science were hired through the fellows program.

When the program began four years ago, many fellows were assigned to teach in elementary schools, which are relatively easy to staff. But over time, most fellows have been assigned to teach specific subjects in middle and high schools. As fewer fellows have been routed to elementary schools, more have been sent to fill deficits in certain subject areas.

Last year, according to the city’s Department of Education, 55% of the fellows took positions in subject areas that have teaching shortages. This year, more than 70% of the 2,000 fellows hired were placed in such areas.

“Fellows are trained primarily in critical shortage fields, such as math, science, and special education,” said the chief executive officer of the department’s division of human resources, Elizabeth Arons.

But the teachers union says that hiring people who are destined to leave at high rates after a few years is shortsighted. The president of the United Federation of Teachers, Randi Weingarten, said the city should retrain committed teachers, rather than pour money into grooming new teachers who are likely to quit.

Ms. Weingarten said she suggested that idea in the last round of contract negotiations, but met opposition from the Bloomberg administration.

“There are a lot of people who say, ‘I want to make a difference in the lives of kids,’ ” she said, comparing the Teaching Fellows program to the Peace Corps. “But the issue is that they come and they leave because it’s a job that a lot of people don’t want to stay at anymore.”

While critics share the same complaints about the program, they don’t back the same solutions.

Ms. Moskowitz said she thinks the city should fill hard-to-staff subjects by paying teachers extra – an idea supported by City Hall.

The teachers union has vehemently opposed any kind of differential pay scale, insisting instead that all teachers with the same seniority receive the same pay, regardless of the subjects they teach.

Ms. Weingarten said raising pay for all teachers across the board would encourage math and science teachers, as well as educators with expertise in teaching English-language learners and special education, to stick around.

The union has been locked in a bitter contract battle with the Bloomberg administration, and its president often argues that higher pay for all teachers would solve many of the problems in city schools.

“New York City has a big black mark saying don’t come and work here if you can work anywhere else,” Ms. Weingarten said last month in an interview. “It doesn’t treat its teachers well. It doesn’t support its teachers. It doesn’t pay its teachers well. So you’re not going to get people coming out of the ed schools, especially in these shortage areas.”

Some fellows contacted by The New York Sun said, however, that pay was not the deciding factor.

David Stern, who was hired straight out of Brown University to teach science at Washington Irving High School but left after one year to become a doctor, said additional hands-on preparation before the start of the school year might have led him and more of his peers to stay longer. He said higher pay probably wouldn’t have made a difference in his decision.

“I think the Teaching Fellows is a good start to a solution, but then you have to address the problem of Teaching Fellows leaving as often as they do,” Mr. Stern said, adding, “The high turnover definitely hurts the kids.”

Another former fellow, who asked not to be identified, said he was recruited to teach special education even though he had no background with children with special needs.

“I think I was as qualified as any other teaching fellow, but I just felt very overwhelmed,” he said. “I knew what I was getting into, but I still couldn’t believe the actual reality of the whole situation.”

More training in classroom management could help ease the transition for teaching fellows and make them stay longer, that ex-teacher said.

Philip Baccaro, who was hired as a fellow this year to teach math at the Bronx Guild School, said, “There are a lot of people out there in the corporate world who have a very strong background in math and can teach it right off the bat. It’s fulfilling a huge need, and I’m not sure how else it would be filled.”

Mr. Baccaro, a Harvard graduate, spent seven years as a financial consultant before applying. He said he’ll definitely stay until he receives his subsidized degree. “After that, I don’t know,” he said. “I don’t intend to be a teacher for the rest of my life, but I do plan on being in education for a while.”