The District’s fourth- and eighth-graders made significant gains on national math and reading tests this year, posting increases that were among the city’s largest in the history of the exam.

Students at the city’s public charter and traditional schools also showed more improvement than nearly every state on the 2013 National Assessment of Educational Progress, an exam the federal government has administered every two years since the early 1990s. Results of the tests, known as the Nation’s Report Card, were released Thursday morning.

Even with the gains, the city’s scores — which have long trailed the rest of the nation’s — remain at the bottom of state rankings, with achievement gaps between white students and their black and Hispanic classmates being among the country’s largest.

The improvement comes amid a period of rapid change that has turned Washington into a closely watched experiment in urban education. Charter schools have expanded, now enrolling 44 percent of the city’s public school students; preschool has become available to every child; demographics have shifted; the city has adopted new academic standards; and the traditional school system has gotten rid of teacher tenure, instituting evaluations that tie job security and pay to student test scores.

That range of variables makes it difficult to pin down the root of the better test results, but District leaders said they demonstrate that the city’s school improvement efforts are working.

“We’ve made a number of revolutionary changes in our system,” Mayor Vincent C. Gray (D) said Thursday at a news conference in Southeast Washington. “We are seeing now the results of the investments that have been made in our children.”

The performance of D.C. students on annual citywide standardized tests has been controversial, as allegations of cheating have lingered for several years. A set of local D.C. tests that showed large, across-the-board gains this year triggered questions after revelations about how local officials measured student achievement.

D.C. education leaders embraced Thursday’s positive results on the national exam — generally regarded as cheat-proof — as evidence that the gains demonstrated on local tests this year are real and have now been independently verified.

“This unequivocally shows that we don’t have to cheat. . . . Our children are achieving more than they have previously, and we’re catching up with the nation,” D.C. Schools Chancellor Kaya Henderson said. “It confirms that the reforms that we put in place are working. When you raise the bar for teachers and you raise the bar for kids, they rise to the occasion.”

The District’s performance has been improving for more than a decade, according to NAEP results, with steady growth in math and more fitful gains in reading.

Between 2011 and 2013, eighth-graders broke more than a decade of stagnation in reading and posted bigger score gains than in any other two-year period, climbing six points to 248 on a 500-point scale. The national average was 266.

Only 17 percent of D.C. eighth-graders scored well enough in reading to be considered proficient, which the U.S. Education Department defines as “solid academic performance” on skills appropriate for that grade level. Thirty-six percent of eighth-graders nationwide were deemed proficient in reading.

In math, eighth-graders posted a five-point gain, and the proportion of proficient students climbed from 17 percent to 19 percent. By contrast, 65 percent of eighth-graders scored proficient on the city’s annual math exam, the D.C. Comprehensive Assessment System, demonstrating a wide gulf between expectations on the two tests.

Fourth-grade math proficiency jumped from 22 percent to 28 percent. In reading, proficiency increased from 19 percent to 23 percent.

Black and Hispanic students made gains, and achievement gaps between them and white students narrowed slightly in some subjects and grade levels. But the gaps widened or remained the same in others.

“The gains are real, they’re sustained and they’re touching all groups of District students,” said Scott Pearson, executive director of the D.C. Public Charter School Board. “But as much as we celebrate the progress we made, there’s still a lot more ways to go.”

The U.S. Department of Education administered the exam to a representative sample of students in the city’s traditional and charter schools, and the results reflect the combined performance of those students. Charter school students, on average, have performed better than traditional school students on annual city tests.

Federal officials plan to issue a report this year that will show how D.C. traditional schools fared compared with other large school systems. The District’s results on the national test were released alongside those of each state, a less-meaningful comparison because Washington is entirely urban.

The District was one of just three jurisdictions in which student performance grew at both grade levels and in both subjects. The other two were Tennessee and schools run by the Defense Department. The District’s improvements from 2011 to 2013 were the largest in three categories and the second-largest in a fourth category.

Average scores in Maryland and Virginia were higher than the District’s and national averages, but neither state showed statistically significant gains or losses between 2011 and 2013.

Education Secretary Arne Duncan, who appeared alongside city leaders at Thursday’s news conference, praised them for proving wrong the “Chicken Little pundits” who said that Gray would not continue the changes begun under former Mayor Adrian M. Fenty (D). “D.C. is literally — literally — helping lead the country where we need to go.” Duncan applauded city policies favored by the Obama administration — including universal preschool and the adoption of merit pay and Common Core State Standards

D.C. Council member David A. Catania (I-At Large), the Education Committee chairman who has sparred with Gray over school policy, said he was “delighted to see the improvement and celebrate these accomplishments.” But given the District’s low proficiency rates, he said, “we have a long way to go.”

The demographics of test-takers in the District has shifted over the past two decades, with the proportion of white and Hispanic students growing while the proportion of black students has fallen. White students now account for 10 percent of fourth-graders, up from 8 percent just two years ago, while the proportion of black fourth-graders fell from 77 to 73 percent during the same period.

Education researcher Steven Glazerman said that it’s not possible to tease out what caused the higher scores because different students take the test each time it is given.

The “NAEP is not very well designed to answer the ‘why’ question,” said Glazerman, a senior fellow at Mathematica Policy Research who coined the term “misnaepery” to describe the misuse of NAEP scores to defend — or undermine — certain policies. “We’re all just speculating,” he said.

It is nearly impossible to track the performance of poor children because the method for identifying low-income students in the District has changed since 2011, the last time the NAEP was given.

A child’s poverty status is measured by his or her eligibility for a free or reduced-price lunch. Until last year, children became eligible for free meals by turning in forms showing household income. Now, if 40 percent of children in a D.C. school are in foster care, homeless, or receiving welfare benefits, every child in the school is deemed eligible for free meals.

The change in the District is a test of a new federal policy meant to ensure that more hungry kids have access to free meals. It means that some children who are not actually poor, but who attend high-poverty schools, are probably now included in the low-income category, said Jack Buckley, commissioner of the National Center for Education Statistics, which administers the NAEP.

That change is “masking whatever is actually happening,” said Buckley, who said his office is concerned about and working to address the inability to track the progress of poor children. He cautioned against drawing conclusions about the progress of the District’s poor children based on the 2013 test results.

Those results show that the proportion of children eligible for free meals rose significantly at both grade levels and that they made some gains over 2011. But the gap between them and their more affluent peers, who were not eligible for free meals, grew significantly.