Democratic Nominee for DC Mayor Councilmember Muriel Bowser. (Melina Mara/The Washington Post)

It was a subtle change, striking out a two-word phrase. But when Muriel Bowser, the District’s Democratic nominee for mayor, made that alteration to her stated position on a proposed overhaul of the city’s public school boundaries, it highlighted the issue’s deep political implications.

For many parents — especially those who have bought homes based on the promise of guaranteed access to a good school nearby — “choice sets” is a poisonous term, shorthand for replacing the certainty and community of a neighborhood school with the uncertainty of a lottery.

Last week, Bowser listed choice sets as the first of many “very good ideas” she saw in a controversial boundary reorganization that Mayor Vincent C. Gray (D) has proposed.

Four days later, “choice sets” was gone from Bowser’s revamped public statement.

“Let me be clear about my position: I will only support neighborhood school assignment,” she said in her second statement, on Sunday. “This means that students must have by right, as opposed to lottery, an assignment to a school at the elementary, middle and high school levels in their area.”

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

In an interview Monday, Bowser (Ward 4) said her initial statement was misunderstood.

Choice sets are of intense interest to parents seeking clues about where the candidate stands in a debate about the future of city schools.

Gray’s proposals would redraw school attendance zones for the first time in 40 years to fix boundaries that have grown unworkable after decades of school closures and demographic shifts. But they also could fundamentally change how students are assigned to schools, and that has set off a citywide discussion about whether the District is ready to give up neighborhood schools in favor of lottery admissions that could scatter the city’s children.

Though Gray plans to announce a final plan in September, it would not become effective until 2015, after his term ends, ultimately leaving decisions about how to proceed in the hands of whoever is elected mayor in November.

With her initial support of “choice sets,” Bowser had signaled to many voters that she was open to forgoing traditional neighborhood schools in favor of admissions via lottery at the elementary school level. That position triggered immediate backlash.

Under Gray’s proposal, choice sets would replace a student’s right to attend one elementary school with lottery admissions to one of several schools located close to one another, including at least one school with a specialty program such as Montessori or dual-language instruction.

On Monday, Bowser said she does not support — and never did support — the central element of choice sets, replacing traditional elementary school assignments with small-scale lotteries.

She said she was instead interested in the other element of choice sets, which would provide specialty programs at schools in every part of the city and would give parents more ability to choose those programs.

“What I meant was access to specialty programs across the city that would augment a by-right assignment, not replace it,” Bowser said, adding that she does not favor any of Gray’s school boundary and assignment proposals.

It’s not clear how parents would exercise such an added layer of choice for specialty schools. “We have to rely on our experts to show us how it would work,” Bowser said.

A spokesman for Bowser’s opponent in the mayoral race, D.C. Council member David A. Catania (I-At Large) — who has vowed not to adopt any of Gray’s school-boundary proposals — accused Bowser of flip-flopping after seeing voter reaction to her first statement.

“Her position is clear as mud,” said Ben Young, Catania’s campaign manager. “The ramifications of these proposals on parents’ decision-making, on even things like the real estate market, are enormous, and it doesn’t inspire confidence when the city’s leaders don’t have a real substantive understanding of the proposals.”

Bowser campaign manager Bo Shuff objected to that characterization, saying that while Bowser’s original statement on the school proposals was “unclear,” her position on by-right neighborhood schools has never changed. “The commitment to neighborhood schools is absolute,” Shuff said.