State education officials unveiled recommendations for a new teacher evaluation system on Monday, providing some clarity but easing few concerns about the bitterly contested policy.

The State Education Department’s proposal appeased those who had called on the state to preserve a principal’s primary role in teacher observations and to create a system for districts to get around an unpopular deadline for implementing the new rating system. But it went against feedback the state received in other areas, proposing that standardized tests and other state-created measures factor even more heavily into a teacher’s rating.

The recommendations came less than two months after the legislature and Gov. Andrew Cuomo passed a law that changed several aspects of the evaluation process for teachers. Many questions about how teacher evaluations would work under the law remained unanswered while the department gathered feedback and designed its proposal.

A discussion about the proposed changes, presented for the first time at the state’s Board of Regents meeting in Albany, filled in some of those gaps. But it culminated with frustration from the Regents, who complained the law’s strict parameters kept them on the sidelines. They pointed to the law’s requirement of a “matrix” approach to rating teachers, in which state test scores seemed to count for more than half of an evaluation in some scenarios.

At one point, some members asked if they could symbolically vote to reject the law to compel the legislature and Cuomo to make changes before the legislative session ends in mid-June. The request was denied.

“Beyond the law, we have a moral and ethical responsibility to, as a board, do what is right for children and we should do what is right for teachers,” said Betty Rosa, one of three Regents who voted against evaluation changes in 2011.

The Regents won’t cast their votes on final recommendations until June 15, two days before the official end of the legislative session — a final stretch sure to be packed with negotiations over education issues. On Monday alone, a bill extending mayoral control by three years passed the Assembly education committee, as did a bill that would wipe out many aspects of the current evaluation law by eliminating the required independent evaluators, delaying implementation for a year, and eliminating the penalty of forfeiting state funding for districts that don’t comply.

The dissent is symbolic of a new power dynamic among the Regents, a number of whom won their positions promising to push back against education policies ushered in over the last five years under Chancellor Merryl Tisch and former Commissioner John King.

Tisch acknowledged the dissent in an interview after the meeting.

“People at that table do not want to implement the system as written in the law,” Tisch said. “To me that is very clear. Are they a majority on the board? I don’t know.”

The legislation represents the fourth time that lawmakers have changed the state’s evaluation system since an inaugural law in 2010 first established a four-category rating system. This year’s law is the most substantial overhaul yet.

One significant change is that the law creates the need for independent evaluators, who have to observe every teacher at least once a year. The requirement leaves districts to train and coordinate their visits, a logistical challenge that Chancellor Carmen Fariña has said will be costly.

Another change is the scoring methods for turning scores into final ratings. Under the system that’s currently in place, a teacher’s final rating is based on a 100-point scale, on which teachers can earn up to 40 points based on student performance and 60 points based on classroom observations. Teachers who earn between 91 and 100 points, for instance, receive a rating of highly effective, while those who earn less than 65 points are rated ineffective.

Instead of a 100-point scale, final ratings in the new system are strictly based on the combination of how well teachers do on two main components: student performance and observations. The “matrix” that combines the scores shows that the two measures more or less count equally, although there are some scenarios where one factors slightly more than the other.

How ratings on each of those components are scored became clearer on Monday with the release of the state’s recommendations.

On observations, 80 percent of a teacher’s rating would be come from the principal. The remaining 20 percent will come from the independent evaluators, though that would drop to 10 percent for districts that opt to use peer evaluators as well.

For student performance, teachers would be rated entirely on growth from state tests such as math, English, or science exams, Regents exams, or other standardized measures. That would fall to 80 percent if districts opt to add second, local assessments.

The state recommended “scoring ranges,” a technical process through which scores from different measures are turned into a rating for each component.

But it was the matrix that frustrated Regents the most, particularly two scenarios in which the combinations unfairly penalized teachers based on test scores. In one scenario, a teacher rated highly effective on his observations could end up with a final rating of developing, the second-lowest rating, if he is rated ineffective on student performance. In the other, a teacher rated developing would sink to ineffective overall if he received an ineffective on student performance.

“What are we going to do with those two cells?” said Tisch, admitting the Regents’ hands were tied and that changes to the matrix would require the legislature. “I don’t know how you get around those two cells.”

Here is the state education department’s full set of recommendations: