Muriel Bowser, David Catania and Carol Schwartz talk about their leadership styles, their worst traits and the biggest management challenge facing Washington's next mayor. (Gillian Brockell/The Washington Post)

Carla Ferris can name the moment that local elections in the District changed from background noise on the radio to something personal: the day she enrolled her daughter in school.

Before that, she said, “I really couldn’t have told you much, if anything, about politics in D.C.”

Now the 32-year-old mother of two and a newly minted PTA president at Powell Elementary School is streaming the mayoral debates online. She hosted her first political event, a backyard barbecue meet-and-greet with David A. Catania, the at-large D.C. Council member she thinks is best positioned to continue improving the city’s schools as the next mayor.

Public school enrollment has climbed 15 percent since the last election, four years ago — a boost generated in part by middle-class families who, rather than running to the suburbs after the first sonogram, are sticking around to give the public schools a try.

City officials say it is a vote of confidence that the District’s school reforms — including a hefty investment in preschool, a spike in charter schools and updated academic standards — are on the right path.

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While academic performance is improving, according to the results of a national math and reading test, the city’s public schools still have a long way to go. The District lags behind other major cities, and D.C. public schools have the nation’s largest achievement gap between white and black students and white and Hispanic students.

A central question for the District, and in the matchup for the city’s top job this year, is whether the wave of middle-class families will stay and have a lasting effect on the schools. The candidates have been working to appeal to these highly motivated voters, aiming to give them a vision for the future, particularly for the city’s middle and high schools.

The mayor of Washington has unusual control over public schools, but parents are split as to how hands-on and visionary they want their mayor to be. It’s a debate largely playing out between the two leading candidates.

Council member Muriel E. Bowser (Ward 4), the Democratic nominee, has centered her education platform on maintaining the status quo and keeping progress in the hands of Schools Chancellor Kaya Henderson. Independent candidate Catania has not committed to Henderson and, as chairman of the council’s education committee and the author of multiple education-related bills, has a more detailed vision and record.

Independent candidate Carol Schwartz, who is trailing in polls, has said she would keep Henderson in her post to foster stability.

In Petworth, a rapidly gentrifying area in Ward 4, the question is consuming many parents who bought homes and enrolled their children in public schools but say they nonetheless feel restless. They are continuously reevaluating their school choices, plotting next steps and contingency plans, and are always aware that some of the nation’s most respected school systems are just a few miles away, across the District’s borders.

“Literally all my conversations are: ‘Did you get into a good school, or are you going to Maryland?” said Wayan Vota, an international development expert and father of two. “The choice for middle-class families is very clear: You either have good public schools or you move.”

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Wayan and his wife, Amy Vota, moved to the neighborhood near Georgia Avenue NW in 2007, lured by an affordable house that was still a bike ride or jog away from work.

They got a dog and decorated the living room walls with old Soviet posters, a reminder of Wayan’s time in the Peace Corps in Moscow. Seven years later, their featured art collection includes many more crumpled pictures of flowers and rainbows and fish colored by their two daughters, who are now 5 and 4.

Outside their front door, there is a steady sound of drills and hammers as rowhouse after rowhouse undergoes renovation — and more families move in. Amy, a physician’s assistant, manages a “Petworth Parents” e-mail group that gets 10 subscription requests a month from new parents.

The renaissance is possible, as Wayan sees it, because of school reforms that former mayor Adrian M. Fenty and his schools chancellor, Michelle Rhee, put in motion in 2007. Those changes have yielded some elementary schools east of Rock Creek Park that middle-class families want to enroll in.

“We are now moving in a really positive direction with the schools,” Wayan said. That’s why he supports Bowser, who he thinks would keep the momentum going. “In education, the perfect result we could have is to stay the course.”

The Votas hosted the Ward 4 council member at their house a few times for potlucks with neighborhood parents. Wayan said he was impressed with her political acumen, particularly her ability to be responsive to concerns and to “thread the needle,” keeping the conversation positive as tensions flared between advocates for charter and traditional schools.

But Wayan said many of his neighbors are leaning the other way, eager for a more aggressive candidate on schools. He said one issue with what he called Bowser’s “bland” approach to campaigning causes him concern — what to do with middle schools. Enrollment in the city’s traditional public schools drops off by sixth grade, when families leave the city or seek out charter or private schools.

Bowser has campaigned on an “Alice Deal for All” slogan, calling for the city to improve all middle schools by providing the kinds of academic and extracurricular opportunities available at the most-sought-after middle school.

But most of the city’s middle schools have a small fraction of Alice Deal’s enrollment, far higher rates of poverty and more students performing below grade level, making it difficult to replicate the same offerings and success. Parents want to see more specific — and realistic — plans for improvements.

In Ward 4, the only stand-alone middle school, MacFarland, was closed in 2013 because of low enrollment. Parents are pushing to reopen it with a renovated campus and bolstered academic program.

Bowser said it was a difficult decision to shutter the school but also said it provides an opportunity for a fresh start. She worked to secure $7 million to draft plans for a new middle school in Ward 4, but there’s no firm opening date or budget allocation for the project.

Families in the neighborhood also want more urgency on a plan to redraw boundaries across the city for the first time in more than 40 years. Mayor Vincent C. Gray (D) adopted a comprehensive boundary overhaul plan in August, after a 10-month process. But Bowser said she would restart the boundary discussion as mayor, and Catania said he would pause the process for a year to explore its implications.

That stance appeals to residents in wealthier neighborhoods, particularly those who lost access to Deal or high-performing Woodrow Wilson High, because they want to remain in the attendance areas for those schools. But stalling the boundary change would mean more uncertainty for other families with young children who are interested in investing in their neighborhood schools but can’t be sure which schools will be theirs.

Wayan Vota summed up sentiment among his peers this way: “Make a decision. Just tell us what it is so we can plan.”

The Vota family’s experience with public schools so far exemplifies the unpredictability that’s common in many city neighborhoods, where the traditional schools are low-performing and families live by the enrollment lottery — applying each year for the charters or out-of-boundary schools that are getting the most buzz.

Soon after the Votas moved to Petworth, their neighborhood school closed because of low enrollment. A high-performing charter school, E.L. Haynes, moved into the building. They could almost see the school from their house, but they were No. 168 on the waiting list when they applied for preschool.

They enrolled their daughters in a different charter school, but that school’s lease expired this summer. Amid the uncertainty, the Votas decided to try Powell, their current neighborhood school, which offers a dual-language program.

A new principal was brought in to turn the school around in 2009. Enrollment increased from 219 to more than 400 last year, amid rising test scores. Henderson recently cited Powell as an example of a comeback she hopes to emulate elsewhere. A few months in, the Votas are optimistic.

Carla Ferris and Horacio Artiga likewise feel that Powell is moving in the right direction.

They live across the street from Oyster Elementary, a well-regarded school west of Rock Creek Park that Artiga attended as a child, but Oyster doesn’t have preschool for 3-year-olds. So they applied to Powell, a 15-minute drive away, where Ferris’s sister used to teach. Two years later, they liked it well enough to stay put instead of returning to their neighborhood school for kindergarten this fall.

Ferris, who owns a pet-sitting business, became active on the PTA and has been lobbying for funding to modernize and expand the aging brick building. The school had been promised funds for many years, but the project kept getting bumped down a long waiting list. The city updated one wing last year, but the rest of the building was untouched.

Parents invited council members to come see the peeling paint, broken plumbing and the modular classrooms set up in the back to accommodate rising enrollment.

Catania visited with parents in the library, listening and asking questions. “Before he left, he said, ‘I am going to make you one of my top priorities,’ ” Ferris recalled. She was surprised to hear such a firm commitment. “So often, you get told, ‘Oh, well, I will see what I can do.’ ”

By March, the school had been allocated nearly $20 million. Construction is scheduled to begin this fall.

Catania supporters say he does his homework and gets things done. His opponents see him as overly aggressive and unnecessarily disruptive.

Catania has visited about 150 of the 200-plus public schools in the District, by his count. And he has drafted multiple pieces of education legislation, including three measures to overhaul services on special education that were unanimously approved this month.

Parents mostly want to see results, she said. His record gives Ferris confidence that he can deliver on the reopening of MacFarland, which he says is a priority.

“You can’t reform D.C. schools without making some people mad,” she said. “It’s just such a huge task.”