Jim Zuber, a volunteer for Mount Vernon at Home, stops by to help Mary-Carroll Potter, 78, of Alexandria, hang a picture at her home. (Nikki Kahn/The Washington Post)

Mary-Carroll Potter, 78, raised four children in Hollin Hills, near Mount Vernon, but they are spread out across the world, from Portland, Ore., to Cape Town, South Africa.

Although she’s been invited to move closer to them, she prefers to remain in the neighborhood that has been her home for 50 years, even if it means continuing to live alone.

Thanks to a phenomenon that has swept through the Washington area at an astonishing rate in recent years, she’s been able to do so. Potter is a member of Mount Vernon at Home, a “senior village” that, for an annual fee of $700 per individual or $950 per couple, coordinates volunteers to provide older residents with services that help them live independently.

“I’ve had a man come in to help change the light in the ceiling, I had another man do some caulking and another man change a lot of pictures in the house,” Potter said. “It’s not a total substitute for your child, but it’s certainly a substitute for having a child who lives nearby.”

A generation or two ago, many Americans assumed that when they grew older and more frail, they would go to a nursing home or assisted-living facility. But aging looks different now, and along with embracing dating sites and Zumba classes, today’s older Americans — 88 percent of those 65 and up, according to a recent AARP study — prefer to stay in their residence for as long as possible.

They’re also more assertive about getting what they want, with increasing numbers embracing the grass-roots movement of senior villages.

“The attitudes are changing. People don’t want to just get old and sick and isolated, so I think they’re looking for alternatives to that,” said Debra Umberson, a professor of sociology at the University of Texas who studies aging and relationships. “The boomers want to stay independent — they want to stay more active and vibrant and connected . . . and that’s being reflected in their housing choices.”

The Washington area is leading the country in the surge of senior villages, going from about five in 2010 to 40 that are up and running or in development, according to Village to Village Network, a national umbrella organization.

Nationally, the number of villages registered with the network has increased from 50 in 2010 to 124 this year, with more in development. The first, in Boston, opened in 2002.

Senior villages are typically organized in neighborhoods to offer older residents a variety of volunteer services — including grocery delivery, lawn mowing and transportation — and to connect members with providers of paid services. Membership fees in the Washington area usually are several hundred dollars a year.

The village movement started mostly in urban areas but has increasingly spread to the suburbs and recently to rural places, said Natalie Galucia, Village to Village Network’s member-services coordinator. As the movement matures, villages have added more complex services, such as social work, discounts with local merchants, trips, cultural activities and, at one District village, a program in which volunteers accompany members to doctor’s appointments to take notes.

That village, Northwest Neighbors, started the service in December with 16 trained volunteers.

“It has helped our members especially when they’re facing critical illness . . . and members who have poor recall,” said Marianna Blagburn, the village’s executive director.

Ally Feldman, 92, a retired professor, said he appreciated the note-taker going to a recent appointment with his arthritis doctor.

“Her being with me was very helpful in that she took notes and she understood things that I didn’t understand,” he said. “You see, I’m old.”

The Washington area may be particularly receptive to villages because it is a more transient place than many metropolitan areas, with close relatives often living far away, said Barbara Sullivan, Mount Vernon at Home’s executive director. “We have a lot of members who raised their children here and the children have moved away.”

But the concept also works particularly well here because the area attracts so many career government and nonprofit workers, said Andy Mollison, vice president of the Washington Area Villages Exchange and founder and former president of Palisades Village in the District.

“Washington has always been a hotbed of volunteer activity,” he said. “People who’ve been running things all their lives, whether it’s PTAs or local food drives.”

Ed Missiaen, 72, is both a Capitol Hill Village member and volunteer. For him, the camaraderie of the village — which opened in 2007 and is the oldest in the area — echoes his stint as a Peace Corps volunteer in the 1960s.

“It’s the idea of working together, trying to make things maybe a little bit better, which in a way was what we were trying to promote when we were in the Peace Corps.”

For him, as for many, membership is also a form of insurance. With grown sons living on the West Coast, Missiaen said he and his wife joined not because they need the help so much now, but because “maybe one day I’m going to need these services.”

Village members like to say, “If you’ve seen one village, you’ve seen one village.” Each develops differently in response to members’ needs. While urban villages tend to serve denser, more “vertical” geographical areas, suburban villages are typically more sprawling.

Mount Vernon at Home, a five-year-old village of 190 members whose average age is 82, is spread out over 14 square miles.

“Transportation is 80 percent of what we do,” Sullivan said.

“Our county can’t provide it. We don’t have walkable communities, so most of our services involve driving people to medical appointments, grocery stores and social events.” The village also offers technology classes and has added care management to its services, helping people find close-by rehabilitation centers and figure out which ones accept their insurance.

In March, Lake Barcroft Village in Fairfax County plans to start a service that will help people with financial and medical planning.

In many cases, the social component has over time become as important as the services provided, said Katie McDonough, executive director of Capitol Hill Village, which, like a growing number of villages, offers social memberships that don’t involve services. The village includes literature clubs, opera clubs, and cancer and caregiver support groups.

“In the last couple of years, this has really taken off as a whole part of the organization that the founders didn’t envision,” McDonough said.

Silver Spring Village, which opened in October, offers such activities as architectural tours, lectures and performances as well as a weekly happy hour.

At the same time, some villages have taken a more active role in medical care. Capitol Hill Village has a care coordinator who matches trained volunteers with people with special needs, and this month, Foggy Bottom West End Village, which opened in October, plans to start a quick-response team, training and aligning specific volunteers with members who are identified as needing more attention.

“As baby boomers, we’ve worked with aging parents and some of the things you know from your own experience,” said Susan Haight, president of Foggy Bottom West End Village.

Some municipalities have encouraged villages as a complement to their own aging services.

Fairfax has a designated liaison to assist people who want to start one and to help connect villages in the area. Libraries in Montgomery County offer a guide to starting a village, and the county is hiring a villages coordinator.

The village model has been more successful in more prosperous areas, which tend to have a larger number of people with time to volunteer or money to pay for membership. Many villages offer reduced or sliding-scale rates for lower-income members.

The District’s Office on Aging recently awarded two $15,000 grants to organizations in wards 7 and 8 looking to help start villages in low-income areas.

Liesbeth Boxman, a freelance licensed city guide in her 60s, said that membership in Foggy Bottom West End Village has brought perks far beyond the services it provides.

A native of the Netherlands with no relatives living close by, she has lived in the District for 40 years but had not really known her neighbors, she said.

Since the village started last year, she said, “you already can sense the difference — people are walking down the street and they’re looking at each other to see if they know each other. . . . Whoever came up with this brilliant idea, I owe a lot to.”