KANSAS CITY, Mo. — Five more states have been granted relief from key requirements of the Bush-era No Child Left Behind law, bringing the total to 24 states given waivers, the Education Department said Friday.

Arkansas, Missouri, South Dakota, Utah and Virginia will be freed from the No Child Left Behind requirement that all students test proficient in math and science by 2014, a goal the nation remains far from achieving.

In exchange, the states and all others granted waivers must develop accountability plans that set new targets for raising achievement, advancing teacher effectiveness, preparing all students for careers and college and improving the performance of low-performing schools.

“We all understand that the best ideas don’t come from Washington, and moving forward, these states will have increased flexibility with federal funds and relief from NCLB’s mandates, allowing them to develop locally tailored solutions to meet their unique educational challenges,” Education Secretary Arne Duncan said in draft remarks released to The Associated Press.

Democrats and Republicans agree the No Child Left Behind law is broken but have been unable to agree on how to fix it. The law has been praised for shining a light on the performance of minorities, low-income students, English language learners and special education students but also has led to an increasing number of schools being labeled as “failing” and subject to a prescribed set of interventions — even if just one of these groups didn’t meet learning targets.

Critics of the law also say it has had the unintended effect of encouraging instructors to teach to the test and has led schools to narrow their curriculums.

Duncan and the White House have pushed for a comprehensive reauthorization of the Elementary and Secondary Education Act, but there has been little movement in Congress over the past two years. After Duncan warned that 82 percent of schools could be labeled “failing” — a figure many said was inflated, but nonetheless agreed to be rising — the Obama administration announced last year that states could apply for waivers. Republicans have charged that the president with overreaching his authority and imposing his vision for education on the states.

Iowa’s waiver request was rejected last week. Iowa Education Department Director Jason Glass said the state’s application met all the U.S. Education Department’s requirements, except on teacher evaluations. In order to receive a waiver, states must have teacher evaluation systems that include at least three performance levels and factor in student progress, among other elements.

Iowa lawmakers passed a bill in May directing a task force to study the issue and make recommendations for the 2013 legislative session, rather than giving the state Education Department authority to develop evaluations meeting the waiver’s requirements.

“I think this raises significant concern about federal overreach as well as executive overreach,” said Michael Petrilli, executive vice president at the Thomas B. Fordham Institute, a Washington-based think tank.

The five states approved for waivers Friday were among 26 states that submitted requests for flexibility in February. The Education Department announced waivers for eight of those states in May. Another 13 are still under review. Waivers for the first 11 were granted in February.

In Arkansas, schools will continue to be assessed annually on student performance in math and reading, but now also on achievement growth and high school graduation rates.

“We are not turning our back on accountability,” Tom Kimbrell, the state’s education commissioner, said in a statement. “With our new system of accountability, support and intervention, we will focus on specifics problems unique to each public school in Arkansas.”

Some concern has arisen over whether accountability for the performance of struggling students will be weakened through the waiver process. Rather than evaluating schools based on the performance of each group of students, some states have proposed combining multiple groups.

“The real fear with those super subgroups is we could return to a place where the performance of some groups of students masks the challenges that other groups of students are experiencing,” said Daria Hall, director of K-12 policy development for The Education Trust.

She said the plans for many of the first states granted waivers are vague in ensuring safeguards are in place in case any one group of students falls behind.

“That’s not going to say nothing is going to happen for these kids,” Hall said. “But I think it’s critically important that advocates and families keep states’ feet to the fire and make sure they are living up to their commitment to all schools and all students and not focusing only on those schools that are considered focus or priority.”