Susan Walsh, File, Associated Press
In this Jan. 21, 2015 file photo, Senate Health, Education, Labor and Pensions Committee Chairman Sen. Lamar Alexander, R-Tenn. listens to testimony on Capitol Hill in Washington. It’s something most everyone on both sides of the aisle can agree on _ an update to the Bush-era No Child Left Behind education law is much needed and long overdue. This week, the Senate and House take up rewrites of the 2002 law, with lawmakers seeking to finally resolve a key question Congress has struggled with for many years

WASHINGTON — Congress is making another run at rewriting the Bush-era No Child Left Behind education law, even as the White House urges changes that the administration says would ensure that schools be held accountable when their students are seriously lagging their peers in other better-performing elementary and middle schools.

The Senate opened debate Tuesday on an update to the 2002 law, with the bill's main sponsor, Sen. Lamar Alexander, R-Tenn., calling it "the most effective path toward higher standards, better teaching and real accountability."

The annual reading and math tests outlined in No Child would continue to be a part of the law. But the so-called "Every Child Achieves Act" whittles away at the federal role in education policy and instead shifts to the states decisions about how to use the required reading and math assessments to measure school and teacher performance.

The measure also would expressly prohibit the federal government from requiring or encouraging any specific set of academic standards. That's a reference to the Common Core standards, which were drafted by the states with the support of the administration but have become a rallying point for those who want a reduced federal role in education.

As the Senate began its debate, the White House issued a statement strongly urging revisions to "strengthen school accountability to close troubling achievement and opportunity gaps, including by requiring interventions and supports in the lowest-performing five percent of schools, in other schools where subgroups of students are not achieving, and in high schools where too many students do not graduate."

It added: "Parents, families, and communities deserve to know that when children fall behind, their schools will take action to improve."

As the Obama administration pressed for stronger accountability provisions, Republicans are expected to use the floor debate to urge more flexibility for the states.

Alexander previewed the debate, saying it will be contentious at times and that "this isn't an issue-free piece of legislation."

The House this week is also taking up its own version of an education bill, sponsored by Rep. John Kline, a Minnesota Republican who chairs the House Education and the Workforce Committee. The legislation gives the states more control over accountability and includes a school choice provision that would allow public money to follow low-income children to different public schools — something Democrats don't support.

The House abruptly canceled a vote on the Kline bill in February when it became clear that it didn't have enough support from conservatives to pass. The White House has said Obama would veto it.

Seeking to close significant gaps in the achievement of poor and minority students and their more affluent peers, No Child Left Behind mandated annual testing in reading and math for students in grades three to eight and again in high school. Schools had to show student growth or face consequences. But critics complained the law was rigid, overly ambitious and punitive, and there was too much testing.

Anticipating that No Child's goal that all students should be able to read and do math at grade level by 2014 could not be met, the Obama administration has been granting states waivers around some of the law's more stringent requirements. In return, schools agreed to certain conditions, like using college- and career-ready standards such as Common Core. The administration has granted waivers to 42 states, Puerto Rico and the District of Columbia.