Jean Fisher, right, walks her grand daughters Kaitlyn, 6, left, Madison, 3, third from left, and neighborhood children to school. (Astrid Riecken/For The Washington Post )

Mayor Vincent C. Gray’s proposals to overhaul the District’s school boundaries and the policies that decide how students are assigned to schools are bound in a book. It is hefty with maps and charts and — to the casual observer — inscrutable permutations of set-asides, choice sets and feeder patterns.

But buried within the details is a central question that has riveted parents: Is the District ready to give up on neighborhood schools in favor of expanded lottery admissions that could scatter the city’s children, seemingly at random?

City officials say the effort to retool how students are matched with schools aims to improve education by making sense of a complex system that leaves some schools nearly empty while others face serious overcrowding, some schools struggling while others thrive. But their proposals pit the rising philosophy of school choice, which aspires to untether the quality of a child’s education from his Zip code, against a long-standing American ideal: the school down the block that serves as the center of the neighborhood, the anchor for the community.

The suggestion of a dramatic overhaul has triggered a firestorm of protest, particularly in affluent upper Northwest Washington, where many families bought homes based on the promise of the right to attend good schools nearby. They fear that their emotional and economic investments in their neighborhood could be ripped out from under them, their property values could plummet, and the future of their children’s education could fall into limbo or be left to chance.

“I love that my kids can walk to school,” said Katherine Martin, PTA president at Janney Elementary in Northwest. Martin also is a real estate agent who predicts a run on Montgomery County homes — an exodus from the city — if families are forced to trade guaranteed access to schools for a lottery ticket. “You get to know all your neighbors and all the kids who surround your house. The community thrives on that.”

Areas that could be affected by proposed changes to D.C.'s elementary school zone boundary

“You buy a house in a neighborhood for a school within walking distance,” said Nicole Fisher, another Janney parent. “You don’t buy a house to trek miles up the road.”

City officials will settle on a plan after considering community feedback in coming months. But both candidates vying to replace Gray (D) as mayor received the proposals with skepticism last week, setting up the possibility that the proposals could be significantly altered or scrapped after Gray’s term ends.

Democratic nominee Muriel Bowser, a D.C. Council member representing Ward 4, said she is interested in some of the ideas Gray floated, including replacing students’ right to attend one neighborhood elementary school with lottery admissions to one of three or four nearby schools. But she said she would neither support replacing neighborhood high schools with a citywide lottery nor cutting families off from good schools that their children currently can attend, saying that “parents want predictability.”

Independent David A. Catania, an at-large council member, vowed not to adopt any of the proposals if he is elected, and to focus instead on strengthening schools across the city. Catania said he does not support reassigning anyone to a lower-quality school or introducing changes that would “shock that fragile confidence” parents are building in city education.

Though the plans have stoked concern, for most families in this historically segregated city of disparate education options, neighborhood schools are already a thing of the past. Just 25 percent of D.C. children attend their assigned neighborhood schools. The rest forgo their local option in favor of charter schools, out-of-boundary traditional schools or selective magnet high schools.

“How do you preserve predictability for people who feel they want that, and at the same time provide options?” Abigail Smith, the deputy mayor for education, asked a crowd of hundreds of anxious parents at Coolidge High last week. “We’re tackling this problem as a whole city, and different parts of the city are experiencing it in different ways.”

One of Gray’s proposals would maintain the system of neighborhood schools with a percentage of seats set aside for out-of-boundary students. Two others contemplate replacing neighborhood high schools with citywide lottery admissions and float the concept of smaller-scale lotteries for younger students.

Most D.C. parents say they share the age-old ideal of building community via a neighborhood school, but many do not see sending their children to neighborhood schools as realistic. One self-described low-income mother who lives in Ward 8 said she would prefer that her son did not have to wrestle with public transit each morning during his journey to an out-of-boundary traditional middle school across the Anacostia River.

“I want awesome schools in every neighborhood,” said the mother, who requested anonymity because she works for the school system. But her neighborhood schools aren’t awesome right now, she said, adding that in Ward 8, “the schools are just different.”

Dana Miller, who sends her 4-year-old to Garrison Elementary in Logan Circle, said she believes in the neighborhood school and wants it to succeed. She just does not see a path forward from Garrison, which feeds into Cardozo Education Campus, a middle-high school with one of the lowest graduation rates in the city.

So Miller is jumping ship — she gained a lottery spot at Mundo Verde, a sought-after bilingual charter school with plans to offer students instruction through 12th grade. She sees the irony, and she wonders whether the city could strengthen neighborhood schools by limiting other options, forcing parents to help create the change they want.

“D.C. has created so many escape hatches — you don’t have to invest,” Miller said. “Maybe they’ve got to close those hatches.”

School districts across the nation have grappled with student-assignment policies for decades, since the early days of desegregation when children in many cities were bused across town to diversify schools. Issues of race and class and equity continue to loom large in Washington and elsewhere.

Now, the nation is experiencing a new spasm of debate about the virtues of neighborhood schools, driven by the twin forces of urban gentrification and the rise of school choice, said Jeffrey M. Vincent, deputy director of the Center for Cities and Schools at the University of California at Berkeley.

Cities including San Francisco, Baltimore and New Orleans have partially or entirely done away with neighborhood schools in favor of citywide choice policies, which, advocates say, put parents more in control of their children’s education. In Nashville — where busing long ago helped to integrate schools — a recent push for a return to walkable local schools led to a backlash from those who saw “neighborhood schools” as code for resegregation.

“We, as a country, are grappling with this tension right now, and if we have communities or cities that are segregated, we are always going to have this problem,” Vincent said. “It’s not a school problem, it’s a housing-integration problem.”

In the District, many parents identify another problem: The city, they say, has failed to strengthen its schools uniformly. A move toward lottery admissions would shuffle children from one corner of the city to another but would not help more schools improve, they say.

“We ought to be able to work together to make sure that every neighborhood in the city has a quality school, not just fight each other for what’s left over,” said Jeff Gumbinner, the father of two students at Murch Elementary in Northwest and one of many parents calling for a halt to Gray’s effort and a push to improve low-performing schools.

That view is not confined to families at affluent, high-performing schools who could be seen as defending their turf. In recent years, families have fought plans to close their struggling neighborhood schools, citing the schools’ central role in building community. Last week, parents from Roosevelt High — which has low enrollment, poor test scores and high truancy — said they, too, would not want to give it up in favor of lottery admissions to other schools.

“The citywide lottery thing is crazy,” said Triena Rogers, a Roosevelt graduate and the parent of a Roosevelt junior.

Advocates of school choice, whose philosophies have driven education policy in many urban areas including the District, say families need more options because it is unrealistic to expect long-struggling neighborhood schools to improve.

“We’ve tried for 50 years to turn around low-performing schools, and the history of it shows it seldom works,” said Andy Smarick, a longtime choice advocate who said the idea of neighborhood schools is quaint. “It’s unfair to low-income families, I think, to promise them that we can make a great neighborhood school.”

D.C. father Randall Chandler also is skeptical. He would love to send his children to a school within walking distance of his home in Northeast. But he watched the city close his son’s elementary school years ago, and then he watched the city shutter dozens of other schools across the city, most of them in African American neighborhoods.

He does not believe the city is willing to seriously invest in schools in majority-black parts of town, so his daughter now treks to Hardy Middle School near Georgetown.

“If you feel like your outcome is predetermined by the city not fully backing the schools in your area, then you want to send your kids to where they’re really backing the schools,” said Chandler, who opposes citywide lotteries because of their random nature but wants a significant proportion of each school’s seats to be set aside for out-of-boundary students.

Across the Anacostia in Southeast, city firefighter Johnie Griffin expects to send his children to their neighborhood schools, and to help those schools improve as an involved parent. But he favors a citywide lottery.

“If a child from Northwest goes to Southeast, the parents will care about the overall school system, not just their own part of it,” Griffin said. “It would hold everyone accountable.”