The schools have graduated to a “different league,” proclaimed a triumphant Mayor Bloomberg in Harlem, announcing a meteoric rise in test scores at the end of June. But do these buoyant results and sparking celebrations around the state truly gauge student progress?

To many parents the mayor’s claim sounds like locker room boasting. “I think the numbers are dubious,” said Laurie Gluck, whose two boys attend M.S. 54 on the Upper West Side. “They represent that students are better test takers, but that doesn’t necessarily reflect substantive learning.”

Mr. Bloomberg favors upbeat estimates from state exams, such as the claim that 61% of the city’s fourth graders now are proficient readers. But, according to federal education officials, only 25% tested at the proficiency level after taking the National Assessment of Education Progress, a more reliable test, one year ago.

Similar disparities have surfaced in math and for older students, illuminating how low Albany sets its definition of proficient achievement. The federal NAEP exam is immune to the classroom drill-and-kill that now commonly precedes testing week.

Albany’s lowering of the bar in part stems from a surreal federal mandate. The education commissioner of New York State, Richard Mills, is eager to move students closer to the No Child Left Behind dictate that all will be proficient in reading and math by 2013. This adds to the intense pressure on mayors and state officials to claim miraculous progress.

Mr. Bloomberg’s asseveration of dramatic achievement growth feels dubious when placed in historical context. The mayor claims that the share of eighth graders proficient in math has climbed to more than 59% this past spring from 29% in 2002 — a 30-point climb in six years, twice the rise gauged by the federal assessment over the past 18 years.

Seventh-grade reading scores were up over last year statewide, but the performance of eighth graders inexplicably declined. A professor at New York University and a former Board of Education testing official, Robert Tobias, ventured that “the test is probably easier than it was in the past.” Just two years ago, after introducing new exams and watching scores drop in some grades, Albany warned against comparing results from prior years, cautions that were dropped last week when scores allegedly jumped upward.

Few doubt that youngsters statewide are acquiring basic literacy skills more effectively now than a decade ago. But when Albany lowers standards and mayors exaggerate progress, it’s no surprise that parents and employers remain skeptical over the schools’ true efficacy.

Inflationary pressure further comes from exams that are hyper sensitive to small gains by low-performing students. The policy aim is virtuous: to recognize children and teachers who succeed against the odds. But the mayor’s inference that city students are performing almost on the level of suburban districts stems from what’s become a politically pressured barometer of progress.

Claims by Mr. Bloomberg linking the rise in scores with both the influx of new dollars from the state and the city’s revamped accountability reforms may be premature. Only recently have new education dollars seeped into schools, spurred by the statewide Campaign for Fiscal Equity settlement. And new accountability reforms that include reform coaches, who are district experts or from nonprofit firms, are just beginning. School principals — whose job tenure now rests on student growth — may be penalized simply because tests scores climbed too early.

What’s key in moving forward is to depoliticize student testing. Senator Kennedy has introduced legislation that would force governors to publish federal test results alongside states’ scores. Multiple measures of progress are needed, and accented by the current debate over the city’s dismal high school graduation rates.

Given Mr. Bloomberg’s faith in competition — heavily backing new options, like charter schools — he should know that markets work only when parents can exercise choice based on sound information. Recent test results prompted a feeling of disbelief, not one of confidence.

The state’s schools may be inching toward the major leagues. But progress will stall — along with parents’ faith in earnest reform efforts — until an unbiased scorekeeper is found.

Mr. Huerta and Bruce Fuller, who co-wrote this piece, are professors of education at Teachers College, Columbia University, and the University of California, respectively.