An overhaul of federal education law moving through Congress — the biggest legislative change in 14 years — holds the prospect of a major shift in New York State’s contentious debate over the linkage of student test scores to teachers’ job evaluations.

The bill, dubbed the “Every Student Succeeds Act,” would ban federal officials from requiring states and school districts to rate the job performance of teachers and principals, though states could continue doing that on their own. It also bars federal authorities from specifying that student “growth” scores on Common Core tests be used in job ratings.

The Senate is expected to consider the measure this week. It sprinted through the U.S. House of Representatives, approved last week in an overwhelming 359-64 vote.

The revamped law essentially replaces the “No Child Left Behind” act, passed in 2001 during President George W. Bush’s administration.

Its provisions would remove a pillar of justification often used by state education officials in explaining teacher-evaluation methodology: No longer could they cite the federal government as mandating that teacher job ratings be tied to students’ test scores.

At the same time, the change would give Gov. Andrew M. Cuomo, Education Commissioner MaryEllen Elia and the state Board of Regents leeway to modify “reforms” that gave birth to a hard-charging activist movement driven by parents and teacher unions — with Long Island as its epicenter — that resulted in the nation’s largest-ever boycott of state tests last spring.

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Cuomo also will have input from a panel of his creation: The 15-member Common Core Task Force, asked to conduct a sweeping review of the academic standards, curriculum and exams, is due to report its recommendations this month. Cuomo has said he plans to consider its work in setting his 2016 legislative agenda.

Sen. Lamar Alexander (R-Tenn.), chairman of the Senate Education Committee, said the federal legislation has the effect of “restoring to states, communities and teachers the responsibility for improving student achievement.”

The vote in Congress represents a referendum of sorts on the work of U.S. Education Secretary Arne Duncan, who has wielded more power than any other federal education official in the nation’s history.

Over the past five years, Duncan has used a combination of financial incentives and regulatory waivers to push the use of teacher performance ratings based partly on student test scores. A total of 43 states, including New York, adopted such evaluations in exchange for waivers from other federal rules.

Duncan steps down at the end of this month. President Barack Obama recently praised the outgoing schools chief for doing “more to bring our educational system, sometimes kicking and screaming, into the 21st century than anyone else.”

His approach, however, has brought unprecedented revolt from parents and educators, with critics contending that teacher evaluations based on formulaic test results are statistically unreliable and educationally unsound.

Those opponents pointed to the House’s bipartisan vote as vindication.

“It’s a major victory,” said Bob Schaeffer, a leading national advocate for limits on standardized testing. “It eliminates the secretary’s power to grant waivers, which is where the requirement to assess teachers according to their students’ test scores is based.”

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Schaeffer, who grew up in Miller Place, is public education director for FairTest, a Boston-based group that advocates against what it regards as misuse of standardized tests.

The amended law, in some ways, resembles No Child Left Behind.

Students would continue taking standardized state tests in reading and math annually in grades three to eight and at least once in high school. The lowest-performing 5 percent of public schools in each state would continue to be subject to extra scrutiny.

But other sections of the legislation shift authority away from Washington: For example, states would gain broad discretion in setting rules for how school districts evaluate their employees and in dealing with failing schools.

In New York, parent leaders of the anti-testing movement observed that Washington’s retreat from issues of teacher accountability would leave Albany with sole responsibility.

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They want the state authorities — Cuomo, in particular — to cut the ties between testing and evaluations. They contend the current system puts too much emotional stress on students and teachers alike.

“Passing the buck will most likely end after this, as far as the evaluation system goes,” said Jeanette Deutermann, a North Bellmore parent and former teacher who heads the Long Island Opt-Out organization.

In April, parents across New York pulled more than 200,000 students in grades three to eight out of state tests in English language arts and math. About 70,000 of those pupils were in Suffolk and Nassau counties.

Newsday reported last month that the state’s political and educational leaders appear to be nearing agreement on a plan that would temporarily cut the linkage between test scores and teachers’ job ratings, possibly through a two-year moratorium.

Another option said to be under discussion would dramatically reduce the weight given test scores in such ratings. Proponents of this approach note that Massachusetts, which has the highest student scores in the nation, leaves to local districts the decision on how much weight to give test scores.

New York’s current law — pushed by Cuomo in April — allows districts to base up to about half of teachers’ annual evaluations on “growth scores” generated by a complex numerical formula. Supporters, including many business leaders, consider that a big improvement from a previous law that, until 2010, barred districts from considering test scores as part of evaluations.

Cuomo administration officials declined last week to speculate on what the governor might do, saying that he is awaiting recommendations from his Common Core Task Force.

Jim Malatras, the governor’s director of state operations, noted that dozens of other states are reviewing their approach to Common Core testing and related issues.

“We’re not alone in this,” Malatras said in a phone interview.

Meanwhile, nearly 90 percent of districts statewide are sitting on the sidelines, waiting to see what happens next.

On the Island, for example, 120 out of 124 public school districts obtained a time-extension waiver from the State Education Department. The waiver allows them to delay putting the state’s latest evaluation law into effect until at least the 2016-17 school year.

Such districts operate under an earlier version of the law, which stipulates that no more than 40 percent of teachers’ ratings be based on “growth” scores.

Only four local districts — Harborfields, Longwood, Lynbrook and Tuckahoe — have obtained state approval of plans putting the new evaluation law into effect.

Longwood’s superintendent, Michael Lonergan, said his district was able to take early action due to cooperation from its 800-member teacher union. The superintendent added that his district has intensified its teacher training, particularly in math, in order to prepare for the next round of state testing in April.

“We’ve been together in this for four years,” Lonergan said.