Under the Obama administration’s education policies, thousands of elementary and secondary schools are being held accountable for the academic performance of students who had been “invisible” under No Child Left Behind, the Bush-era federal education law, Education Secretary Arne Duncan said Thursday.

Duncan’s remarks came during a Senate committee hearing about No Child Left Behind waivers the administration has issued to 34 states and the District of Columbia since 2012.

In addition to unleashing “great innovation and creativity” on the part of the participating states, the waivers have pulled in “hundreds of thousands” of students whose standardized test scores hadn’t been counted toward accountability plans for schools, Duncan said.

No Child Left Behind, signed into law in 2002, required schools to sort children into groups by race, language ability, disability and poverty status and report test scores for each group.

But a blemish in that law created unintended consequences, Duncan told the Senate panel: If a school had a statistically insignificant number of particular students — such as from a specific racial group — the school was not required to report their scores.

“I don’t think any of the people who wrote No Child Left Behind knew this, and I didn’t realize it,” Duncan said. “But there were hundreds of thousands of children across the states who were not a part of the accountability. They were invisible.”

With the Obama waivers, schools that lack a statistically significant number of students in a particular category can combine them with other student groups for the purposes of evaluation, creating “super subgroups.” In Kentucky, for example, schools are allowed to combine black, Latino, American-Indian, low-income students and English-language learners.

“These children are no longer invisible, and there are so many thousands of additional schools now where adults have to be accountable for their learning,” Duncan said. “This is a very significant step in the right direction.”

Still, civil rights organizations are concerned that there are risks associated with super subgroups, in that some states undercut the impact those students have on the data.

Some states, including Indiana, award “bonus points” for academic growth of students in the super subgroup, as well as for growth among a school’s top-performing students, testified Kati Haycock, president of the Education Trust, an organization dedicated to closing the achievement gap. That can allow schools to meet accountability standards even when their weakest students don’t improve.

Thursday’s hearing was the first time lawmakers questioned Duncan about the waiver program, which began a year ago.

President Obama and Duncan issued waivers to free states from the requirements of No Child Left Behind, saying they were forced to act because Congress had failed to revamp the 11-year-old law, despite broad, bipartisan agreement on Capitol Hill that it is in need of an overhaul.

Governors, school administrators and teachers across the country had been clamoring for relief from the law, which they said was outdated and punitive. The waivers freed the states from some of the law’s toughest requirements, including that schools prepare every student to be proficient in math and reading by 2014 or risk escalating sanctions.

In exchange for relief, the Obama administration required states to adopt education policies it favored, including teacher and principal evaluation systems linked to student achievement, upgraded academic standards and aggressive turnarounds of the lowest-performing schools.

At Thursday’s hearing, Sen. Lamar Alexander (R-Tenn.), the ranking Republican and a former education secretary under George H. W. Bush, acknowledged that Obama stepped into a power vacuum created by Congress, but lamented it all the same.

“This is like a Washington version of the old game that children used to play called Mother May I,” Alexander said. “You say ‘Mother may I?’ and if you do the right thing, you get to do it, and if you don’t, you’re out of the game.”

Duncan said that when Congress rewrites No Child Left Behind, which expired in 2007, the waivers will no longer be valid.

It is unclear when or if Congress will act.

Last year, the House and Senate education committees passed legislation to update the law, but the bills — approved with bipartisan support in the Senate but by only Republicans in the House — clashed in terms of the federal role in education. The proposals never advanced.

Ten groups representing governors, state education officials and others sent letters to Congress on Monday urging reauthorization of the nation’s main federal education law. The groups said that the waivers are a stopgap measure and that the country needs a uniform, permanent solution.

“Waivers will work for some states, but will not work for all,” wrote the groups, including the National Governors Association and the Council of Chief State School Officers. “Moreover, waivers only provide temporary relief from specific provisions of the law, and in exchange require new criteria of states, school districts and schools not formally authorized in No Child Left Behind or by Congress.”

One of the panelists at Thursday’s hearing asked Congress to delay reauthorization.

Andrew Smarick, who helped write New Jersey’s waiver plan as a deputy education commissioner in that state, told the Senate panel that he is worried that Congress will roll out a new education law just as the waivers are taking root.

“They are making plans aligned with what is needed in their communities,” Smarick said, referring to the states that received waivers. “There’s much to be learned by these waivers that are doing relatively remarkable things.”