A cafeteria worker serves lunch at Glen Forest Elementary School in Falls Church, Va. The share of students receiving free and reduced-price meals in Fairfax County’s public schools has risen from 19 percent in 2005 to 28 percent this year. (Jahi Chikwendiu/The Washington Post)

The District and dozens of other city centers across the country are becoming younger, more affluent and better educated while poverty rates in inner suburbs are rising, according to a study from the University of Virginia’s Weldon Cooper Center for Public Service.

The study is based on an analysis of demographic changes in 66 cities between 1990 and 2012. It follows research that has shown a rise in suburban poverty, including a recent Brookings Institution study that found that more Americans are living in poverty in the suburbs than in rural or urban areas.

This sweeping demographic shift has clear implications for public schools in the Washington area and nationwide. Student populations are changing in traditionally high-performing suburban school systems, and superintendents and school board members are wrestling with how to adequately serve the rising number of poor children who come to class with far more needs than their affluent peers.

“This is the new reality in America,” said Joshua P. Starr, the newly departed superintendent of the Montgomery County school system, which, despite its reputation as a tony suburb of the nation’s capital, has more low-income students than the District of Columbia. The amount eligible for free and reduced-price meals, a rough proxy for poverty, has risen from 29 percent to 35 percent just since 2009.

“I think that a lot of nonurban areas are unprepared, in many ways, to address the needs that a lot of folks have,” said Starr, who was criticized for failing to articulate a coherent vision for closing achievement gaps and who resigned in February after it became clear that he did not have majority support on Montgomery’s school board. “There are municipalities that are going to have to work harder to meet the needs of a different population of kids and families than were there before.”

For decades, most metropolitan areas formed a doughnut pattern: poor inner-city cores surrounded by relatively affluent suburbs. But that has changed as revitalized urban areas have attracted young, educated people and rising rents have pushed low-income city families into the suburbs.

The new University of Virginia study shows how the “old doughnut” has been replaced in most cities by a “new doughnut” — wealthier city centers surrounded by a ring of lower-income suburbs, which are, in turn, surrounded by another, farther-out ring of wealthier suburbs and exurbs.

The size of each ring varies, but the pattern is remarkably consistent in metropolitan areas across the country with only a handful of exceptions, said Luke Juday, the study’s author. He singled out Charlotte and Houston as the two cities that most clearly demonstrate the change.

Wanda Bamberg, superintendent of Aldine Independent School District in the suburbs north of Houston, said that since the 1980s, the rate of children eligible for free or reduced-price lunch has climbed from around 50 percent to more than 80 percent.

In the past several years, there has been an influx of unaccompanied minors from Mexico and Central America into Aldine, and poverty is so prevalent that Aldine recently began offering free meals to all of its students. At the same time, resources are tight. Per-pupil spending in Texas, as in much of the nation, has not recovered from recession-era cuts.

“Every year, the numbers of children who come to us with special learning needs — those numbers increase,” Bamberg said. “These challenges are going to continue to increase.”

In some parts of the country — such as Long Island’s Nassau County, home to 56 school districts — suburban school systems are geographically tiny. Some have seen a wave of needier children while the property tax base has evaporated.

“The commercial tax base that can take the burden off of homeowners is often pretty meager, and the burden falls on people who already are struggling just to stay in their homes,” said Lawrence Levy of the National Center for Suburban Studies at Hofstra University.

In the Washington area, by contrast, large countywide school systems mean that affluent families help foot the bill to educate the rising number of needy students. Sometimes that dynamic creates tensions for school system leaders.

In Fairfax County public schools, for example, the share of students receiving free and reduced-price meals has risen from 19 percent in 2005 to 28 percent this year.

The demographic changes appear most starkly in lower grades. In 2013-2014, more than one-third of the county’s kindergartners qualified for free or reduced meals.

In October 2012, the county’s total of homeless students was among the top recorded: More than 1,336 were enrolled in the district by the second month of the school year — nearly 400 percent more than the school system’s homeless population in 1996.

Schools with high populations of poor children qualify for additional staffing, which decreases class sizes. But schools with more-affluent populations don’t get those extra teachers, and ballooning class sizes there have caused frustration for some parents.

“We know we have got to address those overly large class sizes,” said Fairfax School Board member Jane K. Strauss (Dranesville), who represents a relatively affluent part of the county, including McLean.

Starr, the former Montgomery superintendent, said that in suburbs with vocal and politically active, affluent families, the decision-making can be influenced by the “loudest voices calling for starting schools later or for gifted-and-talented programs or art and music.”

But there are competing needs from students whose parents do not or cannot attend school board meetings, he said. That creates a difficult decision-making process for local government leaders who do not yet reflect the county’s changing demographics.

“You look at who is typically in control [and] who have been around the longest and have the most political power,” said Starr. “Will that political decision-making reflect the new reality?”