Carmen Farina at P.S. 59 in Staten Island on Sept. 9, 2015. View Full Caption DNAinfo/Nicholas Rizzi

MANHATTAN — Schools Chancellor Carmen Fariña has been dragging her feet at integrating the city’s highly segregated school system, advocates say — instead saying that diversity can be achieved by having rich schools and poor schools be pen pals.

“You don’t need to have diversity within one building," Fariña told parents at an Oct. 14 town hall held at the Clinton School for Writers & Artists near Union Square. "But you need to look for diversity in many different places, in many different ways."

Fariña said schools interested in diversity should follow the “sister schools” model, in which affluent schools team up with low-income ones, sharing resources from wealthy PTAs, encouraging students to become pen pals and letting students visit one another.

"We adopt schools from China, Korea or wherever. Why not in our own neighborhoods?" Fariña told the room full of parents, in reply to a question about diversity in the city's specialized high schools.

"This is what we should be doing with the city," she said about resource-sharing between schools. "It also means the kids are pen pals. They visit each other on different occasions and they understand that they live in different neighborhoods, but they’re basically the same kind of kids."

Fariña reiterated her sister school stance as recently as Wednesday night at a town hall on the Upper West Side, saying, "Diversity for its own sake…is not going to be what takes us where we need to go."

She hailed the Upper West Side’s P.S. 87 — an elementary school where the PTA raises more than $1 million a year — and said it shares 5 to 10 percent of its fundraising bounty with a South Bronx school where students are pen pals and who visit each other on occasion.

Parents at P.S. 87 said Fariña was mistaken. They had a book fair to get new books for Mott Haven's P.S. 277, and with other Upper West Side parents helped raise about $3,000 through Operation Backpack for South Bronx schools and $8,000 through Donors Choose for South Bronx teachers.

But they have no other financial partnership, and did not know of any initiative that included pen pals and inter-school student visits, parents said.

Advocates have been outraged that Fariña, who was tapped nearly two years ago to take the helm of the 1.1 million-student system by the income-inequality-focused Mayor Bill de Blasio, has provided little in the way of policy to address the issue of school segregation despite a growing call by parents, students and school leaders.

Black and Hispanic students make up 90 percent or more of the student population at more than half of the city's 1,600 public schools, according to DNAinfo New York's analysis of 2013-14 data from the Department of Education. Meanwhile, half of the city's white students are concentrated in just 7 percent of the schools, and half of the city's Asian students are concentrated in just 6 percent of schools, DNAinfo found.

When several schools requested last year to introduce diversity-based enrollment policies as a way to foster diverse student bodies, including Carroll Gardens’ Brooklyn New School and Fort Greene’s Academy of Arts & Letters, Fariña and her team never responded, according to school administrators.

Principal Anna Allanbrook from Brooklyn New School told DNAinfo this week that they have heard nothing back from the DOE on their request.

Parent leader Ayanna Behin from the Academy of Arts & Letters also said her school received no response.

The DOE declined to discuss the status of the schools' requests.

"We are continuing to look at the proposals principals have brought to the table, and we share their commitment to seeing that the city’s schools reflect its diversity,” DOE spokesman Harry Hartfield said.

Advocates say more needs to be done.

“Legally, we know that separate and unequal schools do cause disparate impact,” said Mott Haven teacher Sarah Camiscoli, founder of IntegrateNYC4Me, which focuses on ways to break down walls of segregation in city schools through school-to-school exchange programs.

The students in her program say that the site visits only highlight the gap between the schools.

“My [exchange] partner from the Bronx ... kept his head down and avoided eye contact in the hallways," Caitlin, a student from an elite high school in Manhattan's District 2, said of her experience with a student who visited her school.

Some change may be on the horizon. At a Tuesday night meeting of the Panel for Educational Policy, the board voted to delete a footnote in policy that limits race from being used in admissions.

Fariña agreed to consider the change, Chalkbeat reported.

After a 45-day public comment period on the change, the panel will make a final vote, DOE officials said.

With additional reporting by Emily Frost.