SCHOOL REFORM in the District is working. That is the unassailable message of test scores released Thursday by federal education officials. Students at every level improved in reading and math, and the improvement exceeded the national average. Tremendous gains in the past two years show that there has been no lessening in the intensity of school reform under Mayor Vincent C. Gray (D) and Schools Chancellor Kaya Henderson.

“A pretty remarkable story” was the apt summary by Education Secretary Arne Duncan, who joined D.C. officials in celebrating the results of the 2013 National Assessment of Education Progress (NAEP). This respected report card showed gains for District students of double digits in math and of nearly 10 points in reading since 2007, when the reforms began. Striking gains were achieved since 2011: five points in fourth-grade reading; seven points in fourth-grade math; six points in eighth-grade reading; and five points in eighth-grade math.

The NAEP results include both the traditional school system and public charter schools. While a significant achievement gap persists between minority students and white students, all subgroups of students, save English-language learners, improved. And while D.C. students still trail the national average, the steady, fast improvement puts them on pace to catch up.

In other words: The reforms started during the administration of former mayor Adrian M. Fenty (D) and schools chancellor Michelle A. Rhee, and sustained and refined under Mr. Gray and Ms. Henderson, are working. They are based on high standards, rigorous evaluation of teachers, an investment in pre-kindergarten and school choice.

The NAEP is the gold standard or, to use Mr. Duncan’s description, “irrefutable.” The naysayers against reform have been many and often vitriolic. They have included critics who didn’t like Ms. Rhee’s style; supposed experts who doubted that poor, black children could learn and insisted that poverty must be eradicated first; union leaders more concerned with sinecures than with results; and politicians advancing their own agendas. They all should take note of these results. In some cases, they owe apologies for their slanderous suggestions that school officials were cheating. But we would settle for a bit more open-mindedness going forward.

Our country holds dear the idea that all children, no matter the circumstances of their birth, will have an opportunity to better themselves. For decades, the casual acceptance of rotten schools in the poorest precincts of this city robbed too many children of that chance. Now, day by day, year by year, the hard work of school improvement is helping to turn the theory of American opportunity into reality. The work is far from done, but these results show that the reformers are on the right track.