Mayor Bloomberg’s political opponents and leaders of the education unions have been grumbling that when the mayor won control of the public school system, he politicized education and turned the schools chancellor into a political attack dog.

But as the first mayoral campaign in the era of mayoral control of the schools heats up, different views are being expressed high in the Bloomberg administration on whether mayoral control has inserted politics into education or removed it – and some education experts said giving the schools a dose of politics might do them good.

In a recent interview, the deputy mayor in charge of education, Dennis Walcott, said the new system allows politicians to debate politics and leaves educators to teach the city’s students.

“While the candidates will debate the issues, it frees the educators to educate the children and also keep the parents involved as well,” he said. “The politics will happen. Our job is to really stay away from the politics and make sure, one, the vision of this mayor and this chancellor get implemented, and to make sure, two, when necessary, to debate the issue but not get sidetracked.”

The chancellor, Joel Klein, who was sitting beside Mr. Walcott during the joint interview, had a different take on the question of whether mayoral control had politicized education.

“It only becomes a political issue once every four years,” he said. “It’s just the opposite.”

In the old days of school boards, Mr. Klein said, there was plenty of politics in education.

Later in the conversation, the chancellor changed his tack. Instead of saying the school system was less political under mayoral control, he said, “It should be politicized. It’s a mayoral election. You should have the people deciding these issues. In the old days, as soon as the fur started to fly, the chancellor was gone.”

Union leaders and lawmakers in New York City said Mr. Walcott’s version of mayoral control, in which the mayor engages in politics and the Department of Education teaches, does not correspond to reality.

The president of the principals union, Jill Levy, said that every time the chancellor holds a press conference about the positive impact the Bloomberg administration has had on education, he demonstrates that education is intertwined with politics.

“I think Joel Klein has stepped over the bounds in everything he does,” Ms. Levy said. Under the new system, she said, the chancellor is “a puppet of the mayor.”

The president of the teachers union, Randi Weingarten, said she was pleasantly surprised by Mr. Klein’s candor about the new role of politics in education, but she said the chancellor is being too positive about the impact of the new governance structure.

“What we’re seeing is a chancellor who is more political than any chancellor we’ve ever seen, whose main job, it seems these days, is to re-elect Michael Bloomberg, and that is so antithetical to what the notion of mayoral control is,” she said. “Mayoral control was supposed to insulate the school system from the politics, not bring the politics in.”

Ms. Weingarten said Mr. Klein wades into politics in a way previous chancellors did not, and she predicted he’d “rue the day” when he spoke out on television against two of the Democrats running against Mr. Bloomberg.

The chairwoman of the City Council’s Committee on Education, Eva Moskowitz, said Mr. Klein is correct that the new system politicizes education every four years, but she complained that officials are gearing up each day between elections for the next election. For example, she said, the education department’s day-to-day announcements are so full of “spin” that “It’s as if they are writing the commercials, the political commercials, for the November election.”

She also said the new system “has put policy decisions on the political clock.”

“Not every decision, but enough to be troubling, are being made based on the November election,” Ms. Moskowitz said. “I think that this is disappointing and troubling, but that’s not to say the department has not done some good things in education.”

Experts on mayoral control said it’s unclear if there is more truth to Mr. Klein’s or Mr. Walcott’s take on the impact of the new school governance system.

A senior fellow at the Institute for Educational Leadership in Washington, Michael Usdan, said education has always been political, but he said giving the mayor control of a school system “makes explicit what is implicit.”

Mr. Usdan, co-author of a book on mayoral control in various cities, “Powerful Reforms with Shallow Roots,” said the system has proved “extremely positive” in some cities, such as Boston, where the mayor has taken control of the budget and union negotiations, acting as a buffer to the superintendent, who is freed to educate.

As a general rule, he said, it’s best for school systems to avoid partisan politics.

“There’s not a right or wrong way of educating kids, or a Democratic or Republican way,” he said.

Another expert on mayoral control, Kenneth Wong, who is a professor in public policy, education, and political science at Vanderbilt University, called mayoral control a “double-edged sword.”

“On the one hand you have the elected officials accountable for educational performance,” Mr. Wong said. “That’s a good thing. But it’s a question of how the mayor handles that power. The use of power sometimes may create a situation where the outsiders do not have enough voices.”

He said that making politicians accountable for education policy can help improve schools, but that typically a mayor should be careful not to make all decisions in-house without having outside researchers analyze data and assess policies.

“The first few years you see mayoral control meaning that City Hall would try to control a lot more policy in terms of staffing and policy and assignment of contracts and programs,” Mr. Wong said. “After a few years, I think, it is important to think about how to continue to broaden the support on the part of the schools and the teachers, the parents, and the community. There may be a need to move the pendulum back a little bit to incorporate some of these elements of input.”