Muriel Bowser made her most forceful foray into the District’s education debates last week when the Democratic nominee for mayor and Ward 4 council member maneuvered to include seed money in next year’s budget for what she said would be one of four new or entirely remodeled middle schools if she is elected in November.

David A. Catania (I-At Large), the council’s education chairman who is running against Bowser, immediately blasted the proposal, saying she would begin building schools without a plan for how the new projects might affect existing schools. Those that could be affected, he said, include dozens that have been promised a share of the $1.6 billion the city plans to spend on school modernization in coming years.

The tense exchange offered a preview of debates between Bowser and Catania, and it highlighted a power that the city’s next mayor will wield: the authority to decide which schools are replaced or rebuilt — and therefore to influence to some extent which areas of the city become more attractive to families.

Bowser and Catania said in interviews Friday that they want to make the city’s plans for new schools more reliable and predictable. The District’s six-year renovation blueprint has shifted repeatedly in recent years, and Bowser and Catania voted for the latest version, passed Wednesday by the council.

Bowser said the city’s capital improvement plans for schools have been “a moving target.” She said that if she’s elected mayor, she will seek a “thoughtful process” for planning school renovation projects. Parents should be able to have confidence in at least the first two or three years of the city’s multiyear plan for school renovations, she said.

Catania said he would make a priority of fulfilling all of the currently promised school reconstructions through 2020.

“The presumption is in favor of the projects that are presently funded,” he said.

“But what’s important is that we be consistent. There has to be a rhythm to which schools are built, and we have to make sure the dollars are being fairly and equitably distributed,” Catania said. “We have invested significantly in high schools, but the increase in enrollment has been in elementary schools, so we really haven’t thought that through.”

Under former mayor Adrian M. Fenty (D) and now Mayor Vincent C. Gray (D), the city’s school-building plan has not always matched demand. More than $600 million has been spent rebuilding neighborhood high schools in recent years, but most remain under-enrolled. At the same time, free preschool has driven up enrollment in elementary schools, which in many parts of the city still have buildings that are outdated and increasingly crowded.

Promised renovations of schools from Northeast to Southeast Washington have been delayed repeatedly since 2007.

Modernizations at Roosevelt and Coolidge high schools were delayed a year for each school, drawing protest from parents as the city spent hundreds of millions of dollars elsewhere. A planned renovation at Capitol Hill’s Watkins Elementary was going to be pushed back for the third time in four years, and Orr Elementary’s renovation was delayed for eight years, until Catania’s Education Committee restored funding for both schools this spring.

The already fluid school construction plan could face further pressures from a realignment of school boundaries and feeder patterns. The city is debating Gray’s proposal for the first major overhaul of school boundaries in 40 years.

Bowser and Catania have said they oppose the plans. But similar to the idea Bowser outlined Friday, one of the boundary proposals calls for four new middle schools, projects for which no construction money has been allocated. Bowser’s move matched campaign promises she made in the run-up to the April primary, when she vowed to focus on middle schools, which remain a problem citywide.

As part of the council’s budget negotiations last week, Bowser successfully inserted $7 million for planning one new stand-alone middle school in Ward 4.

Catania said that Bowser could not fund a new middle school without taking money away from several others, because every dollar is already accounted for.

Bowser said she would identify money in future budgets to pay for construction and could do so without compromising existing promises to build other schools.

She said her effort to secure funds for a new Ward 4 school was no different from Catania’s move to insert $8 million into the budget to plan a new Ward 7 middle school.

“It’s exactly the same,” Bowser said.

Neither building has funds allocated for construction yet.

Catania disputed Bowser’s characterization, saying that the Ward 7 school has been a subject of discussion at hearings since last fall.

Valerie Jablow, who is the parent of a third-grader at Watkins Elementary and a seventh-grader at Stuart-Hobson Middle, is among parents who have repeatedly been frustrated by the city’s shifting promises on school modernization. Capital improvement plans for schools change so frequently that they are “meaningless” to parents, Jablow said.

“Basically, every year they start anew, and this is a huge, huge problem,” she said.