Think the debate about annual testing ended when House and Senate leaders introduced bills to rewrite the Elementary and Secondary Education Act that kept annual testing in place? Think again.

U.S. Sen. Jon Tester, D-Mont., introduced legislation Tuesday that would roll back the ESEA’s testing schedule, which right now calls for assessments in reading and math in grades 3 through 8 and once in high school. Under Tester’s bill, students would take such tests just once in elementary school, once in middle school, and once in high school. He could offer the legislation as an amendment when and if the Senate takes up a rewrite of the law—possibly even before Memorial Day.

Sound familiar? There’s a similar grade-span testing bill over on the House side of the Capitol, introduced by Reps. Krysten Sinema, D-Ariz., and Chris Gibson, R-N.Y. The full House didn’t get a chance to vote on that amendment when it debated—but ultimately hasn’t been voted on—a bill to rewrite the law, the current version of which is the No Child Left Behind Act.

That could change with Tester’s legislation over in the Senate, though, since it’s typically easier for rank-and-file lawmakers to offer changes during floor debate on a piece of legislation in the Senate than in the House.

The National Education Association, a 3-million-member union, is a big fan of the Tester bill.

“What is clear after years of too much testing is that the status quo isn’t working for students, especially those in high-poverty areas,” said Lily Eskelsen Garcia, the NEA president. “We must reduce the emphasis on standardized tests that have corrupted the quality of the education received by children.”

Of course, there are many, many folks that want to keep the tests in place, including civil rights groups, business leaders, and advocates for state chiefs—not to mention the Obama administration. So it’s unclear if Tester’s provision will gain sufficient support to become part of the bill.