The city’s schools, which just received their first letter grades from Mayor Bloomberg, next year could receive a whole new set of judgments — this time courtesy of Governor Spitzer.

To be considered to have met federal No Child Left Behind benchmarks, New York schools now must only prove to the state that their students are scoring at a certain level. The new formula being developed in Albany — called a “growth model” — would require they also show improvement from one year to the next.

The planning for the new model has been under way since Mr. Spitzer and state lawmakers ordered it earlier this year, but two developments this week are giving it new momentum.

The first came on Monday, from President Bush’s education secretary, Margaret Spellings, who announced she is now allowing all states to apply for permission to follow growth models. Previously just a small set of states had been eligible, as part of a pilot program.

The second came yesterday, in the form of a $6.2 million grant package state officials said was unprecedented. Individual schools and school districts often receive support from outside foundations, but support for large-scale efforts such as the one New York is moving ahead with are relatively rare.

The new growth model, plus a new data system to help track students’ test scores from year to year, are among the projects the grants will finance. (Another project will bring a former adviser to Prime Minister Blair, Michael Barber, to Albany as a paid consultant.)

The state education commissioner, Richard Mills, yesterday called the model the “next generation” of assessing schools’ quality in New York.

Under the current system, mandated by No Child Left Behind, schools that do not meet performance goals for at least two years in a row face consequences, such as forced restructuring, even if they show marked improvement.

Calling that kind of system simplistic, Mr. Bloomberg set out for his school grading system to focus on improvement instead, and 55% of the city’s report card grade is calculated based on how much test scores rise.

The difference in methodology explains, in part, why grades from the city this year are often at odds with state measurements. Six schools now slated for closure are in good standing under the state system, while 50 schools on the state failing lists received A grades.

It is not clear, however, that the state’s new model would resolve those conflicts. The new model will be implemented as soon as Ms. Spellings approves it, state officials said.

The grading system — based on a complicated formula that takes into account how much schools improve, how high their test scores are, and how those figures compare to schools with similar students — has come under criticism from everyone from principals of schools that received low grades to education professors.

A professor at New York University who has authored a study of the New York State accountability system, Leslie Siskin, yesterday praised the city for working to correct its report cards for next year, but said the grading system as it stands now would not pass muster with many experts.

Had they been consulted, she said, “Education researchers would have raised some questions. I think those questions are being raised, and I think the department is looking into them.”

A former director of the city’s testing system who is now a professor at NYU, Robert Tobias, yesterday characterized the report cards as “not yet ready for prime time.”

Mr. Tobias said he raised concerns about the report cards over the summer when city officials invited him to review the system, but he said few changes seem to have been made since.

He said he supports the idea of a growth model in general. But he listed many concerns with the city system, from its statistical models to the kind of tests they are based on, which he said were not designed to be compared across different school grades.

He called a growth model “a necessary condition” for measuring schools according to how much they help students improve. But, he said, “if the basic data that you’re working with, test scores, are based on tests that have not been built for the purpose of tracking longitudinal growth, it is not a sufficient condition.”

A state education spokesman, Jonathan Burman, said the tests indeed are not designed to be compared between grades, and he said there is no immediate plan for the state to write new tests that would do so.

He said the Board of Regents will consider asking for new tests in the 2010–11 school year.