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Kourtney Mills鈥� name sat on a waiting list for five years before she moved her family into an apartment at Potomac Gardens, a sprawling, blond-brick public-housing complex less than two miles from the U.S. Capitol.

鈥淚 was lucky,鈥� she said, adding that others have waited longer.

Fifty years after President Lyndon B. Johnson declared a War on Poverty, the U.S. rental-assistance programs expanded through that initiative鈥攑ublic housing and rental vouchers鈥攈ave provided a measure of stability for participating families and their children.

But too many families who qualify for help won鈥檛 get it, housing-policy experts say, and children in assisted families still often live in areas of concentrated poverty, which can have negative effects on their education.

Students in such areas are more likely to attend schools packed with other poor children, where high rates of truancy and mobility can disrupt learning, and the resources needed to serve high-need populations are often lacking.

A half-century of efforts to ameliorate the environmental impacts of living in poor housing conditions鈥攂y providing rent subsidies, moving entire families from poor neighborhoods to better-off communities, or remaking neighborhoods altogether鈥攈as demonstrated limited results in improving educational outcomes for children.

鈥淓ven as school choice has increased, three-quarters of [poor] students still attend the neighborhood public school,鈥� said Richard D. Kahlenberg, a senior fellow at the Century Foundation, based in Washington. 鈥淪o to the extent that our housing is segregated by race and socioeconomic status, our schools are going to be segregated by race and socioeconomic status.

鈥淚t is possible to make high-poverty schools work,鈥� he said, 鈥渂ut it鈥檚 extremely difficult.鈥�

No Safety Net

Ms. Mills, now a full-time student in a medical-technician program, has lived in a two-bedroom apartment at Potomac Gardens for 3陆 years鈥攐ne of the longest periods of stability for the 37-year-old mother of four since she dropped out of high school in 9th grade. She had two children when she moved in, and she鈥檚 had two more since.

In prior years, she worked as a waitress, moving her children from one temporary housing situation to another, she said鈥攁 house that her relatives shared with a group of drug users, homeless shelters, rented rooms, and a one-bedroom apartment that she and her then two children shared with a friend. The $1,000-a-month rent there strained the two adults鈥� budgets.

Research shows situations like Ms. Mills鈥� aren鈥檛 uncommon.

鈥淲hen people think of the nation鈥檚 public-housing program, they think of a housing safety net,鈥� said Linda M. Couch, the senior vice president for policy at the National Low Income Housing Coalition, in Washington. 鈥淭hey think if you鈥檙e really down on your luck that you鈥檒l have a place to go so that you won鈥檛 be out on a street with your kids.

鈥淚n that sense, the programs have failed,鈥� she said. 鈥淭hey meet a very small portion of the country鈥檚 need. Simply because you are eligible for them does not mean that you have access to them.鈥�

Federal public-housing programs, administered by a patchwork of state and local agencies, typically target rental aid to those earning less than 50 percent of the area鈥檚 median income. An estimated 19.3 million families were eligible for the assistance in 2011, but only 4.6 million received it, according to a December 2013 report by the Joint Center for Housing Studies at Harvard University.

鈥楢 Silent Crisis鈥�

In what U.S. Secretary of Housing and Urban Development Shaun Donovan has called a 鈥渟ilent crisis,鈥� the country鈥檚 lowest-income renters have seen their real incomes fall steadily in recent years, while the cost of rent grew faster.

Households that receive rental assistance typically pay 30 percent of income in rent, with government subsidies paying the rest. Housing agencies consider rent costs unaffordable if they make up a larger share of income.

In 2011, nearly 51 percent of U.S. renters paid more than 30 percent of their income for housing, up from around 41 percent in 2001, the Harvard study found.

And the problem is more severe in cities like Washington, where neighborhoods once deemed undesirable are now home to young professionals who are driving up housing costs.

The Department of Housing and Urban Development, or HUD, sets the fair-market rent for a two-bedroom apartment in the city at $1,412, a rate that prices out minimum-wage workers.

President Johnson acknowledged the link between housing and education 50 years ago this month in an address to Congress detailing his anti-poverty plans.

鈥淲hat does this poverty mean to those who endure it? It means a daily struggle to secure the necessities for even a meager existence,鈥� he said. 鈥淚t means that the abundance, the comforts, the opportunities they see all around them are beyond their grasp. Worst of all, it means hopelessness for the young.鈥�

Although public-housing initiatives were designed to lift children out of poverty, many families who use them still live in largely poor neighborhoods, and many of their children attend high-poverty schools as a consequence.

Poor children are also more highly mobile, frequently changing schools or skipping class when new living situations suddenly move them farther away.

Even when Ms. Mills lived in homeless shelters, she said, she made it a priority to wake up early and ride public buses with her two school-age children as far as she needed so that their school didn鈥檛 change, even if their living situation did.

But many parents in similar situations don鈥檛鈥攐r can鈥檛鈥攎ake that sacrifice, educators say.

Changing Approaches

The 352-unit Potomac Gardens, constructed a year after President Johnson declared a war on poverty, takes up an entire city block in the Capitol Hill neighborhood.

It has a reputation for crime and violence鈥擬s. Mills remembers once walking her children past a pool of blood on the sidewalk outside her building. In the early 1990s, the city erected an eight-foot, prison-grade iron fence around the property to keep out drug dealers and other criminals.

Large-scale multifamily public-housing projects like Potomac Gardens have fallen out of favor in the last 50 years as federal and local housing agencies moved to a scatter-site approach aimed at distributing low-income residents throughout mixed-income neighborhoods.

As an alternative to large public housing developments, HUD crafted rules in 1974 for tenant-based Section 8 housing vouchers, which subsidize privately owned, market-rate units for qualifying tenants. (See program glossary to the right.) Today, about 2.3 million households use the assistance, now known as housing-choice vouchers.

But voucher users are still often clustered in areas with great poverty, housing advocates say.

A study published in November 2012 by the Washington-based Poverty and Race Research Action Council found that children in the nation鈥檚 subsidized-housing programs live near schools with greater numbers of poor students. Researchers separately tracked a pool of participants in each of the major federal housing programs and found their children attended schools where a median of between 67.1 percent and 82.1 percent of students, depending on the housing program, were poor enough to qualify for free or reduced-price lunches. In those schools, between 19 percent and 31 percent of students scored at or above grade level on state-mandated standardized mathematics tests, the study found.

Those figures compare with a median subsidized lunch rate of 45.9 percent for all schools in the study and a median of 53 percent of students scoring at or above grade level on state math exams.

Researchers studying schools in Montgomery County, Md., an inner-ring suburb of Washington, found that children who live in subsidized housing in low-poverty neighborhoods and who attend low-poverty schools academically outperform their peers who live in areas with greater concentrations of poverty, even if those higher-poverty schools receive higher levels of funding.

Some education policy advocates see offering a choice of school alternatives鈥攃harters, magnets, and public schools outside a student鈥檚 designated attendance area鈥攁s a promising way to encourage economic integration within cities.

Ms. Mills reviewed standardized-test scores for schools in the District of Columbia, compared policies on school uniforms and discipline practices, and explored special academic programs before deciding to send her 16-year-old daughter, Janell, to Duke Ellington School of the Arts in the Georgetown neighborhood. There, Janell puts in long hours working on costumes and providing technical assistance for school productions.

Ms. Mills鈥� 8-year-old son Nathan attends Chamberlain Elementary School, a charter school with after-school learning programs and social support for students.

Ms. Mills is determined to help her children go to college, even though she knows little about admissions or financial aid. When her children tell her of careers that interest them, she researches them on the Bureau of Labor Statistics website to see the average pay for workers in that field.

鈥淚 tell them they鈥檝e got to be allergic to Cs,鈥� Ms. Mills said of her school-age children. She also has two younger children: 20-month-old Emily and 11-month-old Blake.

Researchers who explore the intersection of education and housing say low-income mothers like Ms. Mills are typically less likely to choose alternatives to their assigned neighbor

hood public schools than their higher-income peers. It can be complicated and time-consuming to locate a charter, magnet, or out-of-boundary school, and issues like transportation make it harder.

Moving to Opportunity

Nationally, various federal and local demonstration projects have had mixed success in producing academic benefits for students by relocating low-income families to low-poverty neighborhoods and schools.

Starting in 1994, the federal Moving to Opportunity for Fair Housing demonstration program offered 4,600 randomly selected low-income families with children living in five cities鈥擝altimore, Boston, Chicago, Los Angeles, and New York鈥攈ousing counseling and special vouchers to relocate to census tracts where fewer than 10 percent of households earned less than the federal poverty measure. In a 10-year study, researchers compared various outcomes for those families with outcomes for a control group of families that were given traditional Section 8 housing vouchers.

Studies of the program鈥檚 impact found few statistically significant effects on participating children鈥檚 educational outcomes. Many children remained in their original schools, and those who did transfer often moved into schools that weren鈥檛 much more economically integrated, researchers concluded.

And a study by researchers from the Harvard School of Medicine, published this month in the Journal of the American Medical Association, concluded that the mobility experiment may even have had negative mental-health effects for boys who participated. Compared with boys in the control group, the boys whose families relocated to low-poverty areas were diagnosed with depression and conduct disorders at higher rates. Girls in the relocated group had lower rates of those conditions than girls in the control group.

Researchers suggested that boys may have lacked the social skills to cope after moving to a new, significantly different neighborhood. They also speculated that adults in the new neighborhoods saw the boys as threatening, while they saw the low-income girls as people in need of help and support.

Even when they are given a chance for change, some low-income families say the benefits of maintaining social and supportive relationships in their existing neighborhoods outweigh the benefits of relocating, said Lisa A. Sturtevant, the executive director of the Washington-based Center for Housing Policy.

鈥淭here鈥檚 this question of investing in low-income communities versus giving families an opportunity to move out of them,鈥� she said. 鈥淚 think the answer is that we need to do both.鈥�

Changing Neighborhoods

More recent efforts to transform neighborhoods themselves by replacing older housing projects with mixed-use developments have sparked tense policy debates. On the one side, developers and civic leaders have said such projects promote diversity and lift values of surrounding properties. On the other side, neighborhood activists say such efforts dislocate residents from rare housing units and disrupt the culture of established neighborhoods.

Those overhaul efforts have taken various forms, starting with special grants for urban renewal when HUD was created in 1965. But, with limited budgets for capital improvements and maintenance, many of the country鈥檚 existing traditional public-housing units were in need of repair by the 1980s.

A 1992 report by the National Commission on Severely Distressed Public Housing concluded that 86,000 of the nation鈥檚 1.3 million public-housing units could be considered 鈥渟everely distressed,鈥� referring to the physical deterioration of buildings, high rates of serious crime, and an array of poor social outcomes for residents, such as high dropout and unemployment rates.

The $6 billion HOPE VI, or Housing Opportunities for People Everywhere program, which started in 1993, sought to take advantage of the momentum created by young professionals moving into neighborhoods once considered unappealing. The federal program provided block grants for local authorities to work with private developers to tear down 鈥渟everely distressed鈥� public-housing projects and replace them with dense, mixed-income developments that are pedestrian-friendly and accessible to public transit. The program led to the demolition of 100,000 severely distressed units, HUD said.

Critics of the program said public-housing residents displaced by the new construction rarely returned to their old neighborhoods, in part because developers weren鈥檛 required to create a new low-income unit for every one they demolished.

Secretary Donovan acknowledged that criticism in a July 2009 speech at the National Press Club.

鈥淎s we build on HOPE VI, the next generation of housing policy must not penalize an extremely low-income family for the housing market they live in,鈥� Mr. Donovan said.

The Obama administration has a replacement for HOPE VI, the Choice Neighborhoods program, which awarded its first grants in 2010. The program dovetails with other Obama administration interagency efforts鈥攕uch as Promise Neighborhoods and Promise Zones鈥攁nd it encourages community involvement in planning and collaborative measures to improve schools alongside housing in affected neighborhoods. The cooperative approach was inspired in part by the Harlem Children鈥檚 Zone, a community based 鈥渃radle to career鈥� program for poor children in New York City.

The agency鈥檚 budget also includes funds to maintain existing public housing facilities.

鈥淚f a century of housing policy has taught us anything, it鈥檚 that if there isn鈥檛 equal access to safe, affordable housing, there isn鈥檛 equal opportunity,鈥� Mr. Donovan said.