Students across New York State scored modest gains in the latest round of Common Core testing in English and math, the State Education Department reported Wednesday, though results were expected to be clouded by the large numbers of children in grades 3-8 who opted out of the exams.

In English, the percentage of test-takers scoring at the "proficient" level inched up to 31.3 percent statewide in 2015, compared with 30.6 percent in 2014 and 31.1 percent in 2013. In math, percentages rose to 38.1 percent in 2015, from 36.2 percent in 2014 and 31.1 percent in 2013.

Progress for black and Hispanic students held steady in 2015, though those students on average still faced a "significant achievement gap," the Education Department reported.

National Common Core academic standards were imposed in statewide testing two years ago, with spring testing in the 2012-13 school year.

"The transition to new learning standards is not easy, and success isn't instantaneous," Education Commissioner MaryEllen Elia said. "Teachers across the state are working hard to help students reach the high bar we've set for them."

Meeting Albany's test-proficiency standards, established in 2013, is no easy task.

New York ranks either at the top or near the top among all 50 states in the cutoff scores it sets for passing standardized tests in English and math, according to a study issued in July by the National Center for Educational Statistics, a research arm of the U.S. Education Department.

Some experts question whether this is a good thing. Diane Ravitch, a New York University researcher and former U.S. assistant secretary of education, has compared the standard to an A grade that is "unreasonably high" for a great many students.

New York State, in setting this yardstick, deliberately aligned its requirements with those used by the National Assessment of Educational Progress, or NAEP, a federal testing agency.

The idea was to compare student performance in New York against a mark that was lofty and unchanging -- the same approach used in Massachusetts, where student achievement is rated the highest in the country.

"Look, NAEP's the gold standard for career and college readiness," said Steve Sigmund, executive director of High Achievement New York, a Manhattan-based nonprofit advocacy group that supports Common Core curriculum guidelines. "So I think the fact that New York is the state that comes closest to this standard is the way to go."

This year's April testing brought the largest-yet incidence of student refusals to take the English and math tests -- a boycott driven by parents and teachers with origins on Long Island in the spring 2013 round of state tests. The grassroots revolt, the biggest in the nation, has grown each year.

The federal No Child Left Behind law requires that at least 95 percent of eligible students participate each year in state English and math testing. School districts and states that fall short of that requirement face potential penalties, ranging from tighter federal scrutiny of their testing procedures to losses of school financial aid.

The biggest U.S. school-aid program, known as Title I, provides New York State with about $1.1 billion annually, including $45 million for Nassau and Suffolk counties. Much of that assistance is targeted to students in low-income communities.

During the latest wave of test opt-outs in April, both federal and state officials suggested that financial penalties could be an option at some point down the road. Each side seemed to indicate, however, that the other side was responsible for taking action, and some statements were conflicting.

Dorie Turner Nolt, press secretary for the U.S. Department of Education, issued a statement expressing confidence that the New York State Education Department would "take the appropriate steps" to make sure students were tested.

"The U.S. Education Department has not had to withhold money -- yet -- over this requirement, because states have either complied or have appropriately addressed this with schools or districts that assessed less than 95 percent of students," the statement said.

Nolt added that her agency will need to formally review New York State's report on student participation rates before taking any action.

New York education officials, in their own statements, have emphasized the importance of the federal role in the ultimate decision.

"The U.S. Department of Education has made clear that when a district fails to ensure that students participate in required state assessments, the state education agency is expected to consider imposing sanctions on that district, including -- in the most egregious cases -- withholding programmatic funds," the state agency said.

During an interview in Buffalo, Merryl Tisch, chancellor of the state Board of Regents, said she personally believes imposing such penalties would be wrong.

"I am totally opposed to penalizing our students for a fight that the grown-ups are having," said Tisch, whose board sets statewide education policy.