It has been four years since Mayor Bloomberg did what his predecessors could not: He convinced Albany to abolish the Board of Education and give him control of the city’s massive school system.

Yesterday, on the anniversary of Governor Pataki’s signing the law giving Mr. Bloomberg control of the nation’s largest school system, the mayor received a mixed report card from the education community, union leaders, and academics on what he’s done with that power.

While most applaud Mr. Bloomberg for wrestling control from the board and credit him for taking risks on innovative programs, they say there is a lack of transparency and that the much touted test score spikes have not translated into students learning more.

The president of the teachers union, Randi Weingarten, pointed to Mr. Bloomberg’s announcement yesterday that he is giving more decision-making power to principals at certain schools as an acknowledgement that things have not been hunky-dory under the centralized system where all decisions are made at Tweed – the Department of Education headquarters.

Mr. Bloomberg’s deputy mayor for education, Dennis Walcott, denied that and said the new “empowerment” schools were a natural evolution of the vision to give principals more independence.

Mr. Bloomberg regularly talks about how he has taken on political forces to transform a dated public school system that was failing students. He ripped up the 32 districts that once existed and replaced them with 10 regions. He has tackled the politically thorny issue of social promotion and has battled with the teachers union over salaries and merit pay.

He points to rising test scores and the narrowing gap between white and minority students’ scores on standardized exams as proof that things are moving in the right direction.

“Over the course of the just four short years, we’ve succeeded in stabilizing what was a failing school system and putting it on the path to success,” Mr. Bloomberg told reporters yesterday at a school in the Bronx.

His success in toppling the board that existed for more than 30 years garnered national attention. In March, the mayor of Los Angeles, Antonio Villaraigosa, who is fighting for control of the school system in his city, visited with Mr. Bloomberg and praised his success as groundbreaking.

Those in the local education community say eradicating the culture of inertia has been good, but that they still have concerns.

Ms. Weingarten said she expected a “heated debate” before the mayoral control law sunsets in 2009. The union leader said that while the business community is thrilled that the mayor has taken control, those who use schools feel that everything is done by “fiat.”

“Schools are not corporations,” she said. “Schools are not businesses.”

The head of a new charter school in Harlem, Eva Moskowitz, said she supports mayoral control but that the Bloomberg administration has made “structural mistakes” and that the slight up-tick in test scores seemed to have more to do with the test than with improvements by students.

“There is a tendency for the administration to emphasize that things are getting better, and better, and better and hold press conferences to that effect, when the reality is much more complicated,” Ms. Moskowitz, who served as chairwoman of the City Council’s education committee until she was termed out of office in November, said.

A research professor of education at New York University, Diane Ravitch, another known critic of the administration, said that while control allows the mayor to “act quickly and decisively in a way that a school board never could,” the public is boxed out of the decision-making process.

A spokesman for the state Senate majority leader, Joseph Bruno, said the mayor is doing a good job. “We feel that mayoral control is a success and that the mayor is doing a good job,” the spokesman, Mark Hansen, said. Aides to the Assembly speaker, Sheldon Silver, did not return calls. He has been more critical of the mayor’s role.

Mr. Bloomberg said yesterday the biggest difference he’s made since taking over the schools is that the schools are now more focused on students.

Mr. Walcott said the administration has a proven record of results, ranging from test scores to new programs, but that it would not rest on its laurels.

Even though Mr. Bloomberg told voters to judge him on his progress in the schools, Ms. Ravitch said there are so many issues on voters’ minds that he does not have true accountability on this one.

“It’s too soon to say whether there have been any significant improvements,” Ms. Ravitch said. “The ultimate judge on these reforms is going to be the judgment of history.”

Mr. Walcott said: “If there had been negative results, the mayor may not have been re-elected. The bottom line is that this administration has produced results.”