In Montgomery County, 14 percent of elementary and middle schools fell short of key testing targets this year in reading or math, according to Maryland data made public this week. In Prince George’s County, the share that fell short was 24 percent. The statewide share was 15 percent.

Last year, far more schools in Maryland failed to meet academic benchmarks: about two-fifths statewide, records show. Failure rates were also higher last year in Montgomery and Prince George’s.

Behind the change in ratings lies a new accountability system, with more flexible federal rules allowing the state to create new academic targets. Maryland is one of 26 states, including Virginia, that have received a waiver from provisions of the 2002 federal No Child Left Behind law.

Under the new rules, many schools that did not meet what the law calls “adequate yearly progress” — leading to a label known as “failing AYP” — now are able to reach benchmarks known as “annual measurable objectives,” or AMOs.

Some education advocates say they have mixed feelings about the new targets, especially if they do not push schools to improve student achievement.

“This can be a good thing on the one hand,” said Natasha Ushomirsky, a senior policy and data analyst for the Education Trust, an advocacy group for minority and poor students. “But we want to be really careful about is [that] the progress of every student continues to matter.”

The federal law set a controversial target that all students should pass grade-level tests by 2014. For the past decade, the state has had a single standard for proficiency in place for each elementary and middle school to meet every year. If the schools did not meet the mark, they were threatened with sanctions. The standard applied to all students in a given school, as well as subgroups based on race, ethnicity, income and disability status.

But the federal waiver allowed Maryland to do away with AYP. Now, each school has been given five years to cut in half the number of non-proficient students at the school. The state still tracks the performance of subgroups of students. But its calculation that 85 percent of schools are meeting standards is based only on analysis of whether the overall population at a given school is making enough progress. In addition, the state no longer applies the penalties prescribed under No Child Left Behind — student transfers, for instance.

“The goal is that schools hit all these realistic and achievable targets in order to stay on track to 2017,” said William Reinhard, a spokesman for the state Department of Education. “But there are no sanctions.”

The new rules have created some confusion.

So much so that Prince George’s officials said Wednesday that 63 percent of its elementary and middle schools met academic targets this year.

It turns out, according to the state, that a little more than 76 percent, or 126 schools out of 165, in the county met the mark.

The change to the accountability system is the most significant in a decade.

“Everybody is confused,” Reinhard said. “We’re trying to make it less confusing.”

Peggy Harrington, supervisor of test administration in Prince George’s, agreed. “This is a learning curve for us,” she said.

Dana Tofig, a spokesman for Montgomery schools, said: “As we do with all data, we will look into these results and use it to start conversations about how we can improve teaching and learning for all students.”