Many District residents viewed Mayor Adrian M. Fenty’s defeat four years ago as a referendum on his schools chancellor, Michelle A. Rhee, and her disruptive style.

On Wednesday, some saw the victory of D.C. Council member Muriel E. Bowser (D-Ward 4) in the mayor’s race partly as a vote of confidence in Rhee’s successor, Kaya Henderson, whom Bowser has vowed to keep.

“We have seen some improvements, and people want to continue that,” said Stephanie Maltz, an education advocate in Ward 2 who campaigned for Bowser. In a school system that has been rocked by change over the years, “people want stability,” she said.

Bowser will take the helm of the city — and the city’s schools — at an opportune time, when revenue and enrollment are growing and overall academic performance is ticking upward.

But prospects for thousands of D.C. children remain bleak. Many struggle with basic literacy and math abilities and drop out of school. The achievement gap is growing in some areas as more children of educated families enroll in the city’s schools. And while families are being offered higher-quality options by the rising number of charter schools, pressing questions have emerged about how to coordinate facilities and programs.

The city’s mayor has an unusually high degree of control over the schools and influence on how to tackle the challenges.

In addition to naming the chancellor, the mayor nominates members of the Public Charter School Board. Outgoing Mayor Vincent C. Gray (D) also named a deputy mayor for education, Abigail Smith, a position Bowser can keep or discard.

No local school board oversees the school system’s budget and operations. Instead, a State Board of Education mainly sets policies about graduation requirements and academic standards.

During her campaign, Bowser put much of her focus on improving middle schools citywide. She offered a “Deal for All” approach, offering to increase the kinds of programs and resources featured at Alice Deal, the city’s most sought-after middle school, which is in Ward 3.

Parents are eager for this kind of investment in middle grades.

“It would be great to have more Deals in other wards,” said Richard Nugent, a former parent at Deal Middle School.

But he said that creating schools that mirror Deal will be difficult because of vast disparities in financial resources and the academic foundations that children bring to middle school, and because of differences in parental involvement.

D.C. Council member Muriel E. Bowser (D-Ward 4) won big Tuesday to become the next mayor of Washington, D.C., defeating independent candidates David A. Catania and Carol Schwartz in a hard-fought contest. (NBC Washington)

“It’s not going to be done in the next two or four years,” he said. “But it’s important to make a start.”

A point of confusion for parents is the city’s new school-boundaries plan, which took effect at the start of the school year in August. Gray instituted new attendance zones across the District and a host of related student-assignment policies that D.C. Public Schools has begun to implement.

Bowser opposed the move early on. And at a news conference Wednesday, she said there is nothing related to the boundaries “that can’t be undone or tweaked” after she takes office.

Her stance will be welcome to parents unhappy with the changes. But Beth Bacon, a parent of two on Capitol Hill, said undoing the changes would be “rash.”

“This was a very long process, and a lot of people participated,” Bacon said.

When Bowser becomes mayor in January, her main opponent in the general election, D.C. Council member David A. Catania (I-At Large), will step down after 17 years on the council, including a productive run as chairman of the education committee.

“It’s a big loss,” said Judith Sandalow, executive director of the Children’s Law Center, who worked with Catania to develop a trio of special-education measures. Sandalow said Catania made a difference for children “with different learning styles and from all backgrounds.”

Mike DeBonis contributed to this report.