Fewer than half of Montgomery County students in grades 4 to 8 reached proficiency on state tests in math this year, but Maryland’s largest school system posted a string of gains in English.

In neighboring Prince George’s County, fewer than a quarter of students reached proficiency on math tests in most grades. In English, students in grades 3 to 5 did better than the year before and those in high school slipped.

Testing data for Maryland’s 24 school systems, released Tuesday, provided a look at how students fared during the third year of rigorous exams that reflect Common Core state standards.

Statewide, officials touted progress in English, with statistically significant increases at most grade levels. They called math performance mixed.

“These results provide educators with critical information on student performance which can be used to strengthen classroom practices,” Karen Salmon, state superintendent of schools, said in a statement. “When combined with other academic evidence, teachers are able to build instruction around the unique needs of each student.”

The data showed persistent racial and ethnic achievement gaps — a long-standing concern in Montgomery County. Superintendent Jack Smith has called efforts to narrow such differences in a system with more than 160,000 students “a moral imperative.”

In Montgomery, results for Algebra 1 showed gaps of more than 40 percentage points between black and Hispanic students and their white and Asian counterparts. About 23 percent of black students and 18 percent of Hispanic students reached the target on Algebra 1, compared to 69 percent of white students and 70 percent of Asian students, the data showed.

Montgomery school officials did not have immediate comment on the data released late Tuesday afternoon.

The state tests, known as PARCC exams, for the Partnership for Assessment of Readiness for College and Careers, are scored on a 5-point scale. Scores of 4 or 5 show students have met or exceeded expectations. They are widely viewed as a measure of whether students are on a path to college and career readiness.

In math, 54 percent of Montgomery’s third graders hit the proficiency mark. But in grades 4 to 7 and in Algebra 1, proficiency rates in Montgomery ranged from 31 percent to 48 percent. In Prince George’s, the rates for grades 3 to 7 and Algebra 1 were 14 to 25 percent.

One of the largest jumps in performance in Montgomery came in English 10. About 64 percent of students earned the highest marks — an increase of more than 16 points from a year earlier. Scores also climbed more than 9 points in English 7, which Maryland officials said was an area of particular improvement statewide.

Montgomery students did best on the geometry exam: About 85 percent earned the top scores. It had not been widely taken in Montgomery a year earlier, according to state data.

Both Montgomery and Prince George’s students made progress on English exams given to younger students. Prince George’s showed gains of 2 to 4 points across grades 3 to 5. But the county lost ground on the high school level, dropping 4 points in grade 10 and about 9 points in grade 11.

In an analysis that combined grade levels in Prince George’s, school district officials said that overall nearly 26 percent of students in grades 3 to 5 met or exceeded expectations in English, reflecting a 2.5-point increase over a year earlier.

“It is encouraging to see our youngest learners, who have been taught to higher standards the longest, showing the most growth,” Kevin Maxwell, chief executive of Prince George’s schools, said in a statement. “Our teachers and students continue to become familiar with the rigorous demands of the PARCC assessments as we prepare all students to enter college and the workplace.”

Prince George’s posted a 9-point proficiency gain in grade 7 math, to nearly 14 percent. The county ticked down 7 points in grade 8 math, with less than 10 percent of students meeting the goal.

Prince George’s officials said there was an anomaly for grade 8 because so many high-achieving students took the course previously and moved on to the next subject. With more than 132,000 students, Prince George’s has the state’s second-largest school system.

Considered more difficult than the previous generation of state tests in Maryland — called the Maryland School Assessment (MSA) — PARCC exams require persuasive writing, critical thinking and problem-solving.

State officials said 14 school systems showed increases in performance in English grades 3 to 8 and English 10. The share of students earning the highest scores on English 10 was up across virtually all demographic groups, but achievement gaps continue, the state said.