On June 27, as a final salute to the school year, Mayor Bloomberg told business leaders about the advances that had been made in test scores that were, according to him, “most importantly closing the racial and ethnic achievement gaps in the classroom.”

His words were echoed by Chancellor Klein, who, in talking about narrowing the gap, calls education this generation’s civil rights movement.

At the state level, the regents chancellor, Robert Bennett, issued one or two sentences on the educational status of 1.2 million students. The press releases that accompany the annual English and math test results often include this quote from him: “Closing the achievement gap is the Regents’ highest priority.”

Two mandates of the No Child Left Behind Act, which was enacted in 2002, have placed enormous emphasis on improving and measuring the basic skills of all students.

By the 2013-2014 school year it is expected that, with few exceptions, every elementary and middle school student will be proficient in English and math. Additionally, there will be no appreciable differences among the various groups of students, which translates into elimination of the gap.

Taking these objectives to their logical endpoint means that in six years everyone will pass the test’s threshold of proficiency, regardless of race, gender, economic background, or other diversities. In this vision, all gaps are bridgeable and on deadline, too.

Five years into NCLB, with six to go and the law up for re-authorization this year, it’s time to peer into the gap and see how information about its closure has been reported. To date the gap has been treated too simplistically.

Its existence goes unacknowledged in press releases when test data do not show greater gains made by minorities compared to white and Asian students. When greater increases are made by African American and Hispanic students, however, these results are highlighted and headlined. It is these apparent victories that need to be examined.

For example, the state’s May 22 press release of English test scores did not mention the gap. Mr. Klein did not explain what happened to the gap in city’s English test results, which were confounded by a change in test population. The test results reveal that minorities did not gain ground.

On the other hand, on June 12, Mr. Bennett and the commissioner of education, Richard Mills, celebrated narrowing the math gap in grades three through eight when the gains of minorities increased more than those of the other groups.

The level of proficiency in math for minorities rose nine points between 2006 and 2007 — to 55% from 46% for African Americans and to 61% from 52% for Hispanics. This surpassed the six-point gain for whites, whose achievement went to 82% from 76%. Asians increased four points to 89%.

So, what’s wrong with the state and city’s account of the shrinking gap? The problem is that no consideration is given to each group’s starting point.

Intuitively we understand the issue. If Jill is making $100,000 a year and she gets a 6% raise, her salary increases by $6,000. When Jack is making $50,000 and gets a 9% raise, his salary increases by $4,500. It’s true that 9% is more than 6%, but Jill has $1,500 more at the end of the year. Their initial $50,000 difference in salary has actually widened to $51,500 now. So is the gap smaller or larger?

The nine-point math test score increases made by minority groups are seen in a different light when they are gauged against the distance that must be covered to reach the top.

African Americans, who were at a 46% proficiency level in 2006, had to move up 54% in order to reach 100%. That leaves a lot of room to grow. The nine-point gain they achieved in 2007 — not a small accomplishment — represents their closing of the gap by 16%. This is their actual gain — a ratio of nine to 54.

Applying this ratio method to the statewide results for the other groups yields approximate gap closing values of 19%, 24%, and 26% for Hispanic, white, and Asian students, respectively.

From this perspective, whites and Asians closed their gaps more than Hispanics and African Americans since their gain ratios are higher.

Both the state and the city have used simple year-to-year gains in the performance of ethnic groups to show the gap closing. They’ve done this without regard to each group’s starting point and the distance each must cover to make full progress. Had both factors been weighed, the news about closing the achievement gap would have been much more sober.

Moreover, the mayor and chancellor then compare the closing of the math gap between 2002 and 2007. This ignores the State Education Department’s admonition that results for the math tests conducted after 2005 “cannot be directly compared to results from previously administered assessments.”

The truth is non-partisan. In this era of accountability, it is time for us to evaluate exaggerated claims about the achievement gap and close the rapidly expanding credibility gap.

Mr. Smith, a retired Board of Education administrative analyst, is writing a book about New York’s testing program called “Failing the Test.”