Mayor Bloomberg already handed out his letter grades to schools. Now, the president of the United Federation of Teachers, Randi Weingarten, is preparing her own report card system.

Ms. Weingarten had been among a chorus of objectors to Mr. Bloomberg’s grading system, which she said drew too heavily on standardized tests and not enough on other measures such as safety and the availability of art and music classes.

“New York City’s grading effort should not be the last word on how to assess schools,” she wrote in a column last month.

Now she is turning her words into action, or at least into a new UFT task force, which is charged with creating an alternate accountability system that could rival the one drawn up by Mr. Bloomberg’s Department of Education.

Ms. Weingarten’s criticisms of the so-called progress reports echo those made by teachers union leaders across the country. But her push to create an alternative accountability system appears to be unprecedented.

“I’m not aware of any teachers union local that’s done anything like this any place,” a senior fellow at the Washington, D.C.-based Fordham Foundation, Chester Finn, said. “Normally they just roll over and accept the state system or the district system. They grumble about it, but they live with it.”

The co-director of the Education Sector think tank in Washington, Andrew Rotherham, said an accountability plan produced by a teachers union could send an important national signal. “It would show that the producers are willing to be held accountable — and not just say they are, but actually put forward a meaningful proposal,” he said.

The UFT plan is still in its early stages, leaving many important details blank, from what union-produced grades would look like to whether the union even endorses letter grades.

But Ms. Weingarten’s past statements give some indication of her own preferences.

She has praised the education department’s emphasis on progress over absolute achievement — but denounced its reliance on just two years of test scores. She has praised the letters A, B, C, D, and F, saying “ratings help us make decisions” — but she also indicated support for giving more than one grade to each school. “Moving forward,” she wrote in the same recent column, “the progress reports should give more weight to conditions like class size and safety, access to advanced courses and the availability of enrichment activities.”

Told of Ms. Weingarten’s plans yesterday, critics of the city’s grading system said they welcomed new ideas.

“It’s important that DOE is open to suggestions for positive change, and who would know better than actually the people who are in the system?” the chair of the City Council’s education committee, Robert Jackson, said.

The executive director of the nonprofit Center for Arts Education, Richard Kessler, also praised the effort, which he called “a huge challenge to the DOE.”

A senior fellow at the Center for Educational Innovation, Harvey Newman, a supporter of the Bloomberg administration’s education initiatives, said the union should spend its energy advocating for teachers’ quality of life, not grading schools. “We welcome their next commentary on what’s going on in Iraq, what our next surge policy should be,” he joked. Mr. Finn said the quality of the plan will be crucial. “If they measure totally subjective soft teacher kinds of things – student happiness for example; self-esteem, for example – these would be not a good approach to accountability,” he said.