Teachers and principals whose job performance is rated low because of aberrations in the state's controversial evaluation system now have expanded rights of appeal under regulations approved Wednesday by a divided Board of Regents.

Educators whose job ratings inexplicably bounce from "highly effective" one year to "ineffective" the next year, for example, could appeal to the state Education Department. A decision on whether to grant those educators alternative ratings based on a secondary set of measures would be referred to a panel of department staffers.

Teacher unions, while heartened by moves to modify the controversial ratings system, remained hostile Wednesday to the overall approach of linking evaluations to student test achievement.

Another critic of the system, Roger Tilles of Great Neck, who represents Long Island on the Regents board, predicted that incumbent state legislators could face upsets in the 2016 elections unless they reverse course on the issue.

"I think we need to get to the legislators to save them from themselves," Tilles said.

The Regents, in a 10-6 vote, gave final approval to the regulations that spell out details of the revamped evaluations law pushed through the legislature in April by Gov. Andrew M. Cuomo.

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That law increases the weight given to student scores on state tests in rating teachers' and principals' effectiveness to as much as half of their entire evaluation. Local school districts have the option of holding that weight to about one-quarter of overall evaluations, if they approve the use of a second battery of tests.

Wednesday's decision was a near-repeat of the Regents' action in June, when they gave tentative approval to a similar set of regulations in an 11-6 vote. The second vote confirms the official status of the new rules.

Tilles, who opposes the evaluation system in principle, joined the majority in voting "yes." Like others who voted in the affirmative, he said that opposing the regulations might result in the loss of federal and state financial assistance to schools that would hurt students.

Tilles also noted that parents across the state had pulled students out of state tests in massive numbers during the spring, and predicted that the opt-out movement could turn more political during the next state elections in 2016.

Parent leaders of the opt-out movement contend that evaluations tied to test scores put too much pressure on students and teachers alike.

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The second Regents vote, like the first, was preceded by extended debate, in which some Regents invoked "moral law" in explaining their reason for voting against the regulations. Legally, the Regents are bound to approve regulations putting into effect laws enacted by the legislature and signed by the governor.

"There's a higher law," said Regent Betty Rosa, an educator from the Bronx. "I'm willing to violate the letter of the law."