Third-grade students at Carlin Springs Elementary School work on a math lesson on Sept. 11, 2014 ,in Arlington, Va. Third-gradestudents had a pass rate on the state’s standardized math test of 95 percent, a gain of 47 percentage points from two years ago. (Amanda Voisard/For The Washington Post)

As Virginia’s English-language learners fell further behind in state test scores this year, one poor, largely Hispanic school in Arlington County again recorded big gains in scores after ramping up test preparation for the second year in a row.

Some grades at Carlin Springs Elementary had double-digit increases in their state test passage rates after a concerted effort to prepare disadvantaged students for the exams and closely track student performance on practice tests. The repeat success suggests that the school’s efforts might be paying off, boosting scores among groups of students whose success on standardized tests has proved elusive.

Virginia published statewide passage rates for the Standards of Learning (SOL) exams Tuesday, and the annual tests that measure students’ performance across all subjects showed gains in almost every category. After Virginia increased the level of difficulty of its tests in recent years, scores had fallen, but the gains in the 2014-2015 school year reflect an upward trend attributed in part to teachers and students becoming accustomed to the more rigorous tests.

“Schools are adjusting to the new standards and the new framework for the test themselves,” said Steven R. Staples, the state’s superintendent of public instruction.

The state uses the SOL — a state-specific way of measuring how well students understand Virginia curriculum requirements — instead of the Common Core State Standards, the national standards embraced by the Obama administration. But Virginia officials have said that the SOL is as, or more, rigorous than the Common Core and tracks it closely in many ways.

Virginia Gov. Terry McAuliffe (D) also praised the results, noting a five-point overall statewide gain in reading and math and two-point increases in writing, science and history.

“I am so proud of the dedication shown by teachers, students, and the administrative staff of these schools in pursuing academic success,” McAuliffe said.

The statewide scores also got a bump from a new state law that allowed elementary and middle school students who failed the exams by slim margins to retake them with a parent’s permission. With every test, an average of 4 percent of students across the state were able to convert failing scores to passing ones with the retakes, boosting passage rates.

That was true across Northern Virginia, where large districts made modest gains or tallied roughly the same as last year’s.

“The legislation that we proposed and that I signed into law not only gives students a second chance, but more importantly, gives them the opportunity to demonstrate mastery of the material,” McAuliffe said in a statement. “By joining bipartisan legislation with the hard work of local school divisions, we are well on the way to preparing all of our students to succeed in the new Virginia economy.”

The state also scaled back testing this year amid concerns that Virginia students were being overtested, with a barrage of SOL exams along with local course testing. The state eliminated two history exams for elementary and middle school students, a fifth-grade writing exam and science and history exams for third-graders.

While nearly every category of Virginia student made gains or stayed the same in the 2014-2015 school year, passage rates for English language learners slid in three subjects: English writing, history and math. The state touted progress in closing the achievement gap between white students and Hispanic and black students, particularly since the introduction of the harder tests three years ago.

But the success at Arlington’s Carlin Springs stood out. In two years, the passage rates for third-grade math jumped 47 percentage points, with 95 percent of third-graders passing in the 2014-2015 school year. They even outperformed their peers in the largely wealthy, high-achieving Arlington school district, where 84 percent of third-graders passed.

Passage rates on the third-grade reading tests at Carlin Springs rose to 81 percent, and students performed far better than those two years ago, when less than half of the third-graders passed. There were similar jumps for fourth-graders, whose passage rate went up 35 points on the reading exam and 21 points on the math exam from the previous year.

Carlin Springs has the highest rate of students who receive free- and reduced-price meals in Arlington, and about 70 percent of its students are Hispanic. Both groups have traditionally lagged behind their affluent and white peers and behind the rest of the district.

Arlington schools as a whole saw notable gains in reading and math scores, with 86 percent and 87 percent of students districtwide passing those subject tests. Passage rates for other subjects remained largely the same but still far surpassed state averages.

Arlington’s superintendent, Pat Murphy, did not respond to requests for comment about Carlin Springs on Tuesday, but he said in a statement that countywide success is consistent, and he praised “students and families for their dedication to learning and academic excellence.”

“I am extremely proud to see the progress that has been achieved,” Murphy said. “This year’s impressive results are due to the committed leadership in all of our classrooms and throughout every school in our county.”

The test-prep and academic support for struggling students at Carlin Springs could serve as a model for other struggling schools, though teachers and administrators have been cautious because the approach was implemented only two years ago. The most recent success provided another year of data, and the dramatic improvement continued.

Amid the school’s recent success, though, there has been some ambivalence. Current and former teachers, reflecting on last year’s progress, said they worried that they were spending too much time on test preparation and putting too much pressure on students.

Loudoun County also reported improvement in scores for students with limited English proficiency, a group that has trailed behind state averages. The district as a whole, one of the most affluent in the country, has among the highest test scores in the state. This year, English language learners in Loudoun — about 6,700 students, or 10 percent of the school district — beat or matched state averages in all four subject areas.

Fairfax County saw gains similar to those experienced statewide, and county students did better than state averages. This year, 85 percent of students districtwide passed reading tests, up from 81 percent last year, and the passage rate for math rose two points, to 83 percent.

But the district, one of the largest in the country, has seen explosive growth in the number of poor and immigrant student it serves, and passage rates for students with limited English proficiency slipped. English writing scores for the group dropped from 59 percent in 2014 to 53 percent this year, though there were increases in some areas for minority groups.

“We are particularly encouraged to see the increases posted by black and Hispanic students, especially in math and reading, and we will continue to work to close these achievement gaps,” said Deputy Superintendent Steve Lockard.

Staples told reporters Tuesday that administrators across the state have said that many students now enrolled in their districts not only speak little English but also cannot read or write and have little formal schooling before enrolling.

“The children we’re getting now who are English language learners are not only learning English, but they’re engaging in literacy for the first time,” Staples said. “We’re getting children who haven’t been getting education even in their native language.”

Prince William County, the second-largest district in Virginia with about 85,000 students, tracked closely to state averages on all exams. Like the state, it had a smaller percentage of English language learners passing SOL exams. But the district highlighted its progress with black students, who beat state averages across all subjects.

The Alexandria school system, one of Northern Virginia’s smallest and most-challenged districts, made gains in several subjects but still trailed behind its neighbors, with districtwide passage rates ranging from the high 60s to the high 70s. In math and reading, passage rates climbed five points from last year, to 69 percent and 71 percent respectively.

The Jefferson-Houston School, which failed to meet state accreditation standards for three years running, saw double-digit gains across many grades and subjects. This year, 73 percent of fifth-graders passed the state math exam; just 32 percent passed the year before. But fourth-graders performed far worse on the math exam this year, with just 30 percent passing.