Imagine this: You’re a gym teacher at a struggling high school. Because of the way teacher evaluations were implemented in your school, 40 percent of your rating is based on test scores in a subject you don’t teach and from students who aren’t yours. And the students do poorly. Even when your principal says you’re doing well, or exceptionally well, in classroom observations, state law says that an “ineffective” for student learning means you’re stamped with an overall “ineffective” rating.

City and union officials said they had thousands of teachers like this one in mind when they agreed to a new appeal process as part of their contract agreement. Beginning this year, the process makes it easy for an “ineffective” rating to be boosted if it’s based on test scores of subjects and students that the teacher does not teach—as long a supervisor gives the teacher higher marks.

The new process isn’t protection for the sake of protection, local officials say. “It’s an appeal to address a particular problem that exists as a result of a lack of assessments,” said UFT Special Representative Amy Arundell.

But the new appeal process will also benefit thousands of math, English and other core subject teachers who receive “ineffective” ratings based on their own students’ academic growth. And shifting the weight of some teacher evaluations away from student performance metrics could make it controversial with state officials, who must approve the evaluation proposal.

core tenet of the state’s evaluation law is flunking teachers whose students show no academic growth. That’s an idea Gov. Andrew Cuomo and State Education Commissioner John King have fiercely defended over the years.

“If we’re serious about supporting excellence in teaching, we can’t have an evaluation system that permits a teacher who scores a zero on student achievement to receive a positive rating,” King said in 2011 in response to a legal challenge from the state teachers union to modify the role of state tests in evaluations.

The use of standardized test scores in teacher evaluations has garnered plenty of criticism, but the scores are preferred by officials because they are seen as a tougher standard than principal observations. Last year, for instance, just 1 percent of teachers across the state received an overall “ineffective” rating, though 6 percent of a subgroup of teachers were rated “ineffective” based solely on standardized test scores.

Research into the reliability of any one measure for teacher evaluations is mixed, with new studies casting doubt on both observations and value-added measures.

The deal has provided more ammunition for the union’s critics, who say it’s another way to weaken teacher accountability.

“Removing objective measures of student achievement undermines the intent of teacher evaluations, which we know was Mike Mulgrew’s goal in the first place,” said StudentsFirstNY Jenny Sedlis said. “Any professional needs an honest assessment of what’s working and what’s not in order to develop and improve.”

The problem with that critique, teachers say, is that the city hasn’t offered an “honest assessment” for many types of educators, including 5,000 physical education and arts teachers, librarians, and others who teach foreign language, health and career education—even though they’re evaluated like the rest of their colleagues.

“I’m being measured largely on kids I don’t even teach this year,” said Tara Brancato, a high school music teacher in the Bronx who, along with the rest of the school’s art department, will be evaluated based on how all students in the school do on their English Regents exams.

The city and union plan to improve assessment options in non-tested subjects, but Arundell said a safeguard is needed until fewer schools use learning measures that don’t relate to the work of some teachers.

“There’s an acknowledgement that there is a lack of authenticity to a person’s rating if you’re going to evaluate both on students you do not teach and subjects you do not teach,” Arundell said.

Brancato and other teachers who could be affected said the change was a welcome step toward addressing what they say has been a neglected part of teacher evaluations.

“They really are taking into consideration all teachers in the system,” said Jason Zanitsch, a high school drama teacher at the High School for Public Service in Brooklyn. “It’s far from perfect, but it’s definitely a step forward.”

Still, there are assessments available to evaluate many of the core subject teachers who will also qualify for appeals. Partially to prevent an onslaught of new tests, many schools opted to rate all teachers using a “group” measure, which gives an entire school’s staff—including math and English teachers—the same rating for the piece of the evaluation based on student performance on state tests. Having a “group” measure factor in to your evaluation qualifies a teacher for the new appeal process.

City officials said they were unable to calculate the number teachers who are being rated on “group” measures this year. But they said they anticipated that only a small percentage would use the appeal process, because the combination of receiving the lowest rating for student learning and an “effective” or “highly effective” rating by a supervisor is rare.

For those who do end up with that combination, the odds of a negative rating being boosted are in a teacher’s favor. The appeal process includes the presumption of a higher rating, meaning the burden of proof needed to uphold the original “ineffective” rating would fall on the city.

A separate appeal process would also be set up for teachers rated “highly effective” on student learning measures, but who earn an overall “ineffective” because of a principal’s observation. In that case, the UFT can choose which cases to appeal to an arbitration panel of three teachers.

Now, the deal must get a final sign-off from Commissioner John King. The city is supposed to submit a draft of its proposal to King by Thursday. A spokesman for the State Education Department declined to comment on the plan.

Department of Education officials said they believe the city’s proposed plan complied with state evaluation laws and regulations. In a statement, a spokeswoman said the agreement “focuses on raising student achievement in ways we’ve never been able to do before.”

Want the latest in New York City education news? Follow Chalkbeat on Facebook or @ChalkbeatNY on Twitter.