A student at Birney Elementary School in Washington, D.C. (Marvin Joseph/The Washington Post)

Anthony A. Williams was D.C. mayor from 1999 to 2007 and is chief executive of the Federal City Council. Donald Graham is chairman of Graham Holdings and serves on the boards of the D.C. College Access Program and KIPP-DC charter schools.

District residents have to be confused after the release of apparently conflicting student test results this week. The new annual tests given to some D.C. students seem to show dramatic declines in the percentages of high school students scoring “proficient,” or working at grade level.

Meanwhile, results from the federal government’s National Assessment of Educational Progress (NAEP) tests, administered every two years, seem much more encouraging. The scores in many states went down, but not in the District. Reading results for D.C. fourth-graders increased by more than any other jurisdiction has recorded in the history of the test. And for the fifth time in a row — since the test is given every two years, that means 10 years of progress — the District’s scores have increased overall. In fact, in 2013, D.C. test scores went up as much as any state’s. (The District was tied with Tennessee.) This year, the same thing happened: In terms of progress, we’re No. 1 in the country again (tied with Mississippi). Such sustained advances are very rare. Not all of D.C.’s NAEP scores rose. Eighth-graders’ results, which showed large-scale improvement in 2013, stayed flat or went down two points.

So what do these apparently contradictory results tell us?

Neither of us is an educator, but we have each spent decades following public education in the District. We would agree with most residents that running the education system (now including traditional and charter schools) is perhaps the most important thing the D.C. government does. Citizens should want to know: How are we doing?

As recently as 2003, there was no doubt about the answer: Among cities participating in the federal NAEP tests, our results were the worst in the country, and they were a considerable distance behind the second-worst.

Residents made it clear to their elected officials that schools were their highest priority. And a new mayor, Adrian Fenty, persuaded our city council to do what it had been reluctant to do before: abolish the elected school board and let the chancellor of the D.C. Public Schools report to the mayor. This wasn’t an easy vote, and the council (then led by Vincent Gray, later a mayor with a strong education record) deserves credit for taking action. Fenty followed through by picking skilled change agent Michelle Rhee to be his chancellor.

Much of the progress within DCPS stems from that date (although to again give credit where due, NAEP scores began to increase under then-Superintendent Clifford Janey). The progress has been slow but steady ever since, and 10 years after we placed last, our results were better than 10 of the other 20 cities whose results were broken out.

Miles of improvement are still needed. As the NAEP tests show, only a minority of DCPS fourth- and eighth-graders are working at grade level. But D.C. students in every demographic category have improved (though not all demographics have improved equally). Educators tell us that when all the results are released, the number of students who are “proficient” on NAEP and the District’s assessment — now called PARCC, for Partnership for Assessment of Readiness for College and Careers — will be pretty similar. (This week’s PARCC release included only 10th-grade results.)

So if things are going so well, what do the PARCC results mean? And why are so few of our high school students “proficient”? There are two reasons:

First, this is a brand-new test. Apparently it’s next to impossible to compare the results with last year’s DC CAS, the District’s previous standardized tests, and say if they are better.

Second, the new test was deliberately made much more challenging, in order to give students a clearer idea of where they stand.

All states and the District are required to give some of their students proficiency tests so parents and voters can assess how schools are performing. This year, the D.C. schools decided to replace the old DC CAS tests with the much tougher PARCC. Many states did the same thing, in line with the state-initiated “common core” educational standards.

With PARCC, if you are “proficient,” you are definitely ready for college. College education means so much to the futures of DCPS and charter school graduates, every student needs to know whether he or she is truly prepared. Most states adopted the same proficiency standard the District did — a four on a scale of five. States that adopted a lower benchmark (a three means you are proficient in Ohio) were properly criticized for not being straightforward with students, parents and voters. No one gains by calling students proficient when they are not.

Here’s how we’ll be following D.C. school system results in the years to come:

The most important results are the ones produced by the federal government’s NAEP tests. We can use them to compare ourselves with other metropolitan areas and the states to determine whether we are getting better or slipping. This year’s results are very encouraging, most of all because they seal a decade of progress.

On the PARCC tests, since there seems to be no fair way to compare this year’s results with those of the past, the 2015 results establish a new benchmark and the goal is simple: improved scores, for many years into the future.

The District is fortunate to have the school leaders it does. Chancellor Kaya Henderson is in a class by herself — just look at the 10-year results from other cities. And the District’s amazing charter school leaders deserve to take a bow as well, including the Public Charter School Board and Executive Director Scott Pearson for closing many low-performing charters.

Michael Casserly of the Council of Great City Schools has just published research definitively describing how duplicative and poorly designed much of our testing has become. You can’t argue with his case. But NAEP and PARCC are the two tests we shouldn’t do without. And D.C. residents who long for continuing improvement from our schools will be watching the results of those tests in the years ahead.