A plan to make it more likely that higher- and lower-performing students on the Upper West Side go to middle school together is stoking divisions among some families there.

Officials in District 3 are pushing a plan to offer at least a quarter of seats at the district’s 16 middle schools to students whose state test scores suggest they are not proficient in reading and math. Ten percent of admissions offers would go to students scoring at the lowest level, and another 15 percent would go to students scoring just below the proficiency bar.

The change would have dramatic effects at some of the district’s schools, according to a city analysis, while other schools would see their student population change less.

Most likely to be shaken up by the proposal, if it goes into effect: The expectation in the district that high test scores — achieved most often by the district’s middle-class students — should guarantee families their top choice of middle schools.

“A lot of people are afraid of change,” said Maria Santa, whose daughter attends a district elementary school that few middle-class families choose. “I don’t think people are going to stand for this.”

Indeed, the proposal has drawn sharp criticism at some of the public meetings that the education department is holding to inform parents and drum up support. An NY1 report about one meeting, held at P.S. 199 during the school day Tuesday, featured parents who pushed back strongly against the proposal, saying their kids would be shut out of the most sought-after schools.

“You’re telling them, ‘You’re going to go to a school that’s not going to educate you in the same way you’ve been educated: Life sucks!’” one woman shouted.

But many of the district’s elected parent leaders are on board, as are other local parents. So, too, are principals in the district, who say the move could protect their schools after the city barred them from seeing how students ranked them on their applications.

That change, announced in June, was the city’s effort to eliminate strategic tricks that weren’t in middle school directories but were known by savvy parents and consultants that some families hire to guide them through the admissions process.

But in District 3, one of three Manhattan districts currently using “revealed rankings” in middle school admissions, principals said they actually used information about how much students wanted to go to their schools to engineer more diverse student populations.

“What first choice allowed us to do is fairly distinguish between [students], because anyone could list us first,” said Marlon Lowe, principal of Mott Hall II in Morningside Heights. “We would interview you, we would get to know your scholar and we would make a serious, thoughtful decision based on many variables.”

Mott Hall II’s admissions process resulted in a relatively diverse student population – but other schools in the district are segregated by race and achievement level.

About 87 percent of admissions offers at J.H.S. 54 Booker T. Washington, for example, went to students who earned top scores on state tests, and about 60 percent of students are white. At P.S. 149 Sojourner Truth, a pre-K through 8th grade school where more than 60 percent of students are black, just 6 percent of offers went to students who earned high test scores.

“We are not offering all students equity and access across all the district,” said District 3 Superintendent Ilene Altschul. “We need to do something.”

At one recent meeting, Altschul hastened to reassure parents who might worry that top-scoring students will have a tougher time getting into the most coveted schools. She admitted that fewer families would get their first pick under the plan — but she said the percentage of students who are admitted to one of their top three choices should remain about the same.

A simulation based on application data from 2017 suggests there could be significant changes, especially in schools that attract top-scoring students. At West End Secondary School, the number of students with the highest test scores would fall 19 percentage points, resulting in 66 percent of all students earning top test scores. But at P.S. 180, which has middle school grades, the simulation found that just one more high-performing student would be offered admissions under the new plan.

That’s a product of how families are ranking the schools, said Kristen Berger, a parent who has been leading the district’s diversity efforts as chair of the parent council’s middle school committee. Higher-scoring students just aren’t ranking schools where a majority of students have lower test scores, she said. It may also be harder to change the makeup of K-8 schools, Berger said, since many students chose to stay through middle school.

“The most crucial component to this is to give serious consideration to a wide range of schools,” Berger said. “It’s a big step, I definitely recognize it … but in the long run this is better for our children.”

Some members of the district’s elected parent council said that reality means the city needs to do more than just reserve seats for lower-scoring students.

“This is not remotely enough,” Daniel Katz, who sits on the council, said about the projected change at P.S. 180. “The number of impacted children at these schools is basically non-existent.”

Another council member, Genisha Metcalf, raised concerns that the proposal could steer more families away from schools that currently serve many low-performing students.

“If we want to see true diversity,” Metcalf said, “the plan needs to both include how do we get students into those highly sought-after schools, and, how do we ensure that the schools people are considering undesirable are not in an even worse spot.”

Education department officials have long made it clear that grassroots support is critical to pursuing any diversity efforts. (New Chancellor Richard Carranza has indicated he is more open to pushing for integration than his predecessor, Carmen Fariña, who said changes to schools’ demographics should happen “organically.”)

A previous plan to make District 3 middle schools more economically diverse died after parents and principals rallied against it. In 2016, Altschul proposed setting aside 30 percent of seats at each middle school for low-income students, but wasn’t able to build support for the change.

Now, Altschul has won over principals, but parents are airing concerns. At a recent public meeting, one father stood up to ask whether his son’s teachers will get extra help if more students with low test scores are admitted to his school.

He was echoing a concern that has come up repeatedly at selective schools, where parents worry that any changes to admissions could water down instruction. While research suggests that academic integration generally benefits all students, some research shows that when the gulf among students is too wide, neither high- nor lower-performing students are better off.

“That’s my biggest concern,” said the father, whose son attends the Computer School and who declined to be quoted by name. “With more challenging kids in the class, you’re putting on much more stress” on teachers.

Some middle-class families say they’re prepared to embrace the changes, even if their own children might face a tougher path to their first-choice middle school. Nicole Greevy, who has a child in third grade in District 3, acknowledged it may take time for the plan to have a noticeable impact in schools, but she called it a “terrific start.”

“I think diversity benefits everyone,” she said. “I did not have a classmate who was African American until I got to college and that was a failure on the part of my schools. I want my child to have a better experience than I did.”

If Altschul formally proposes the changes to the education department and it gets city approval, the changes would go into effect in the 2019-20 school year — the same time when the citywide middle school changes will be implemented. She said the change is needed to help boost performance for all students.

“This is the work we really need to do around closing the achievement gap,” she said. “Integrating students across all levels is really what’s essential. It really does strengthen learning for all students.”