WASHINGTON — House Republicans on Thursday pushed ahead with a plan to update the federal No Child Left Behind education law by shifting more control to states and school districts in determining whether children are learning.

A hearing on a pair of bills to have states develop their own systems to identify low-performing schools and turn them around came days after President Barack Obama freed 11 states from some of the George W. Bush-era law’s most stringent mandates. To get waivers, states had to submit plans and get the administration’s approval.

The administration says the waivers are a stopgap until Congress updates the law. Several other states are expected to apply for waivers by Tuesday during a second application round.

It’s widely agreed that No Child Left Behind needs to be updated, but there are varying views on how much of a federal role there should be in education policy.

House Education and the Workforce Committee Chairman John Kline, R-Minn., who wrote the Republican bills, said the president’s plan still ties schools to a failing law. He said his plan replaces a “one-size-fits-all federal accountability system” with one that directs each state to develop a system that takes into account the “unique needs of students and communities.” He said it also empowers states to develop their own teacher evaluation systems based on student learning.

Kline said his plan continues to use data broken down by demographic groups to help protect “vulnerable” student populations.

Passage appears unlikely in a gridlocked Congress.

Rep. George Miller of California, the House committee’s senior Democrat, has called Kline’s effort a partisan one and said Thursday the bills “have the very real potential to turn the clock back decades.” Miller and Sen. Tom Harkin, D-Iowa, who chairs the Senate Health, Education, Labor and Pensions Committee, have said any plan without bipartisan support would have a difficult time getting passed.

Harkin’s committee last year passed a bipartisan bill to update the law, but the administration expressed concerns with it, and it did not come up for a vote in the full Senate.

The law was designed primarily to help the nation’s poor and minority children. It was passed in 2002 with widespread bipartisan support and has been up for renewal since 2007. It requires annual testing, and districts were forced to keep a closer eye on how all student groups were performing, not just relying on collective averages.

Schools that didn’t meet requirements for two years or longer faced increasingly harsher consequences, including busing children to higher-performing schools, offering tutoring and replacing staff. Supporters of the law said a strong federal role was necessary because states and local districts had historically shown an inability to teach all students.

The law requires that all students perform at grade level in reading and math by 2014, which is a deadline schools are increasingly failing to meet.