“You go to certain places, their houses would be painted,” he continued. “Others, they can’t afford that as much, so you don’t see it as often. It’s not a bad thing, it’s just a socioeconomic thing.”
Several United States senators reintroduced a bipartisan bill this year that would greatly increase funding for the tax-credit program and prohibit community members from vetoing projects.
“One of the biggest obstacles that has always existed and that remains in building affordable housing in higher-income, higher-opportunity neighborhoods is local opposition,” said Diane Yentel, the president and chief executive of the National Low Income Housing Coalition.
Although the Treasury Department administers low-income housing tax credits, each state is left to decide which projects are funded. Ever since Texas made changes to its selection process four years ago, projects have increasingly gone into neighborhoods that are whiter and more affluent, according to a study by the Texas Low Income Housing Information Service, the fair-housing group that Ms. Palay works for.
Whether that is what’s best for low-income families is at the center of a dispute between Houston and the Department of Housing and Urban Development, which is the government’s chief enforcer of fair-housing laws.
In January, in the waning days of the Obama presidency, the department sent a scathing letter to Houston, saying that the opposition to the Fountain View project was partly motivated by race. The department had found that 81 percent of tax-credit developments in Houston were in census tracts where eight in 10 people are minorities. HUD threatened to take the city to court if it did not approve the development.
Mr. Turner took exception to the department’s demands.
“I don’t think the right message to be sending to kids in low-income families is that the only way they can succeed is that they have to move into affluent communities to do that,” he said.
Instead, Mr. Turner has strongly advocated investing in black and Latino communities that lack resources, saying new housing could be one tool to help improve them.
“But this is the same thing we have been hearing for years, if not decades,” said Gustavo Velasquez, a former assistant HUD secretary who worked on the Houston investigation.
Mr. Velasquez described telling Mr. Turner in a meeting that Fountain View represented a balanced approach to developing affordable housing in both poor and affluent areas.
“This was the opportunity for the city to take that bold step and start reversing Houston’s legacy of segregation,” he said.
Research suggests that when children from low-income households grow up in affluent communities, they tend to get a better education and earn more money as adults. But a study published last year by two Stanford professors made a case for building tax-credit housing in high-poverty areas, finding that home values around the developments rose by about 6.5 percent and that segregation decreased modestly.
Ben Carson, the secretary of housing and urban development, declined to comment on the Houston project, but he has publicly stressed the importance of investing in low-income communities and questioned government-driven efforts to promote integration.
“The secretary strongly believes that all cities should provide the opportunity for their residents to have a diverse range of housing options,” Raphael Williams, a HUD spokesman, said in a statement.
He added that the department was still contemplating what to do about the Fountain View project. The city has asked HUD to withdraw its complaint, and the fate of the project hinges on whether the department complies or tries to force Houston to allow it to be built.
One Houston resident, Katrina Rhodes, wants the development to be built. As she sat in her second-floor apartment one afternoon, holding her 21-month-old daughter, Chassity, Ms. Rhodes had fresh worries about her 9-year-old daughter, Leeah.
Just a day earlier, Leeah, who walks more than a mile to and from school every day because school buses do not come out that way, was chased home by fourth graders in a dispute over someone being sprayed with Silly String, Ms. Rhodes said. Without any extracurricular activities at the school, Ms. Rhodes, 31, worries about what will keep her children busy.
She wants a neighborhood like the Galleria, where, she believes, the schools are better and they will have the best chance to succeed.
“If there was an opportunity for me to move over there, guess what: I would go,” she said.
Not everyone thinks it would be a good idea to move.
“No,” Erica Ashton, 38, said of whether she would move to the Galleria from her spartan, low-income apartment complex in a predominantly black part of northwest Houston. She was worried about the discrimination she might face.
Her brother-in-law, James Smith, wondered if integration could even work as he bounced his 15-month-old daughter, Jamie, on his lap. If black people moved into the Galleria, white people would flee, he said, adding that it would be more instinctive than intentional.
“Out there,” said Mr. Smith, 46, “they were taught: ‘This is us. If anything from the outside tries to come in, we shall stop it.’”