SEATTLE — States, not the federal government, would choose how to sanction or help struggling schools under a proposed rewrite of the federal education law known as No Child Left Behind.

The proposal, released Tuesday, was written by the Republican chairman of the Senate Education Committee, Lamar Alexander of Tennessee, and the committee’s ranking Democrat, Patty Murray of Washington.

Their bipartisan agreement calls for a shift of power away from the U.S. Department of Education and back to states and school districts, allowing states to decide how much student test scores should be a factor when judging a school’s performance or a teacher’s effectiveness.

It also marks a potential end to the stalemate over how to rewrite the widely criticized No Child law, which was enacted in 2001 and expired in 2007. Since then, nearly every state has asked for waivers from the strictest consequences of the law, which required all students to be proficient in reading and math by 2014, a goal that many critics have long said was impossible.

“This bipartisan compromise is an important step toward fixing the broken No Child Left Behind law,” Murray said in a news release. “While there is still work to be done, this agreement is a strong step in the right direction.”

Murray said the proposal would fix what’s broken in the law but keep what has worked, including tracking the academic progress not just of whole schools and districts, but also of smaller groups of students based on race, income and disability.

Under the proposal, students would still be required to take standardized tests in reading and math each year in grades 3 through 8 and once in high school, as well as a science test three times between kindergarten and 12th grade. States would also be required to use students’ scores from those tests – as well as graduation rates – when evaluating schools, but states could choose how much weight to put on the scores and what other factors to use.

Murray and Alexander also are proposing a pilot program into what they called “innovative assessment systems,” but provided few details about what that might look like.

The bill would continue federal grants to help states and school districts improve low-performing schools, but school districts – not the Department of Education – would decide how to use that money to intervene. Under the current No Child law, schools deemed underperforming by Department of Education standards must set aside some of their federal money to offer students the opportunity to go to higher-performing schools, or to receive outside tutoring.

Also included in the Murray-Alexander proposal is language that would prohibit the government from mandating states or providing incentives to adopt any one set of learning standards, like the Department of Education did when it made adopting the Common Core learning standards a factor in its Race to the Top grant program.

Murray and Alexander have scheduled a discussion next Tuesday of their proposal in the Senate Education Committee.