In this Feb. 12, 2015 photo, a student works on math problems as part of a trial run of a new state assessment test at Annapolis Middle School in Annapolis, Md. (Patrick Semansky/AP)

A majority of Maryland’s students failed to meet academic benchmarks on state standardized tests linked to the Common Core this year, a disappointing result for educators and state officials who had hoped to see major upticks as teachers and students become familiar with the exams.

New data released this week showed that many grade levels saw overall passing rates of about 40 percent in the second year of testing using PARCC exams, which are intended to measure readiness for college and careers. Maryland students in grades three through eight showed gains in math, but English scores remained flat.

“We’re sure not seeing a heck of a rise on these results,” said Chester E. Finn Jr., a member of the Maryland State Board of Education and president emeritus of the Thomas B. Fordham Institute. “Forty percent is nowhere near good enough, and the gains, where there are some, are small.”

State data showed that most grade levels saw improvement in math, with proficiency inching up nearly three points in seventh grade and almost eight points in third grade. Third-graders did best, with 44 percent meeting or exceeding expectations, and eighth-graders lagged, with just 22 percent meeting or exceeding expectations. There was little change in English scores in third through eighth grades, with 37 to 40 percent of students reaching performance targets.

On the high school level, student scores improved by more than four percentage points in Algebra 1, with 36 percent of students deemed college-ready, and English 10, with 44 percent reaching that level.

The results came with little official analysis; state officials said they would have more comment and more detailed data — including district and school results — in late September.

“We’re pleased that the math scores showed some improvement,” said Bill Reinhard, spokesman for the Maryland State Department of Education.

As with previous tests, there were stark gaps in achievement by race and ethnicity, as well as for students in special education and those learning English.

In third-grade reading, for example, 64 percent of Asian students reached benchmarks compared with 52 percent of white students, 23 percent of black students, and 22 percent of Hispanic students.

PARCC tests are given in seven states and the District, and they were meant to set common benchmarks that would allow for direct comparisons. Maryland is the fourth jurisdiction to release results, said PARCC spokeswoman Heather Reams. Rhode Island is expected to do so Thursday, and others are expected to follow in coming weeks, she said.

Maryland ranks in the middle of the pack among states that have released results. New Jersey’s scores were stronger overall, and New Mexico’s were weaker. Colorado did a little better in English and not as well in math.

Betty Weller, president of the Maryland State Education Association, the state’s largest teachers union, cautioned against drawing strong conclusions, noting that the tests are in their infancy.

“PARCC is still in the very early stages, so we don’t have a lot of trend data yet or strong validity at this point,” she said. “It’s hard to extract meaning.” Weller also said the test results come as “only one of many measures that assess how students are doing.”

Finn, of the Maryland State Board of Education, said Maryland tends toward complacency in evaluating its educational performance.

“There is a persistent narrative in Maryland that everything is hunky-dory and the state can just rest on its laurels,” he said. “But that’s just not right.”

More than 90 percent of Maryland students took the test online, using computers or tablets, state officials said. With the tests still relatively new, they are not yet linked to accountability measures such as teacher evaluations or graduation requirements.