The District’s latest proposal to overhaul school boundaries has generated plenty of pushback, but it also includes at least one far-reaching idea that appears to have strong support: guaranteeing access to pre-kindergarten for students who live in-bounds for high-poverty schools.

Currently preschool enrollment is determined by lottery. No one is guaranteed a seat, and it’s not unusual for students to be shut out of the schools to which they apply. This spring, 12 percent of 3-year-olds and 23 percent of 4-year-olds who entered the first round of the city’s preschool lottery did not get in anywhere.

Under the new proposal, 3- and 4-year-olds who live in-boundary for a high-poverty Title I school — a category that includes most of the traditional public schools in the city — would have a right to attend pre-kindergarten at that school.

At recent community meetings on the boundary proposals, a few people expressed concern that the guaranteed access could end up trapping students in struggling neighborhood schools, limiting their access to better schools across town.

But many people spoke in favor of the proposal, calling it an important step toward ensuring that more of the city’s neediest children enroll in preschool. Proponents also said guaranteeing preschool access would encourage more families to give their neighborhood schools a try instead of starting out right away in a charter or out-of-boundary traditional school.

Dunbar High math teacher David Tansey has been trying to persuade Bloomingdale families to invest in their local elementary school, Langley. But it’s slow going when families have no control over whether their children will get into Langley for preschool.

“It’s a whole lot easier when they know they can go there,” Tansey said, speaking at a community meeting at Dunbar last week.

Scott Cartland, principal of Wheatley Education Campus in Trinidad, said at the same meeting that guaranteeing access could help bring in more students who most need preschool. “The issue we have is a lot of parents don’t apply in the lottery,” he said. “I think this is a great proposal.”

Under the new proposal, students would have to enter the lottery for preschool but only for technical and logistical reasons. Anyone who lives within a Title I school zone and fills out the lottery application form would be guaranteed a preschool seat.

In gentrifying neighborhoods like Bloomingdale, the policy could have the effect of pulling more middle-class families into local schools that they currently avoid.

“If the notion is, you want whoever’s living in the neighborhood to come together and create a community in that school — if that, over years, creates a more diverse school, that’s not a bad thing,” said Deputy Mayor for Education Abigail Smith, who is leading the effort to overhaul school boundaries and student-assignment policies.