Kindergarten students at Guilford Elementary school run during physical education class in February. (Evelyn Hockstein/For The Washington Post)

In the wealthy suburbs of Loudoun County, elected officials say they cannot afford to offer something that more than three-quarters of American schoolchildren get: full-day kindergarten.

Fewer than a third of the school system’s nearly 4,900 kindergartners attend full-day classes, qualifying for the longer classes because they come from ­low-income households, are English-language learners or are ­special-education students.

Superintendent Eric Williams is aiming higher. This year, he tripled the number of students in full-day kindergarten by adding classes at all schools that had room for it and by lobbying for an additional $2.5 million to hire more teachers and aides.

Williams is proposing the expansion of full-day classes for half of all students, regardless of family income. His proposal, which will cost tens of millions of dollars, is reigniting the debate over the benefit of full-day kindergarten and whether it is worth the hefty price tag.

The vast majority of kindergartners in Loudoun County attend half-day classes, with some elected officials resisting expanding the program because of cost, lack of space and skepticism about its benefits. Expanding the program would require the district, already squeezed for space, to build new classrooms.

“In essence, it will be an enormous challenge for us,” said Eric Hornberger (Ashburn), the chairman of the Loudoun County School Board, who said he would not support expanding full-day kindergarten if it meant cutting elsewhere or raising class sizes. “There hasn’t been up to this point the will to do it financially.”

At a School Board work session last week, Mike Martin, the director of elementary education in the county, put the cost of adding teachers and aides at schools where there is existing space at $1.4 million. And constructing 12 additional classrooms over four years could cost up to $36 million. Those estimates do not take into account what it would cost to hire teachers for those new classrooms. The county estimates it would be able to provide full-day kindergarten to about half of all 5-year-olds, starting in four years.

School board member Debbie Rose (Algonkian) said in a candidate forum said that she supported the expansion of the program so that all parents would have the option of enrolling their children in full-day classes. At last week’s work session, she expressed ambivalence about the superintendent’s proposal.

“It would seem that after $32 to $36 million, we would be getting up to only 50 percent of our students,” Rose said, adding, “I’m not even sure how I feel about it.”

Even as full-day kindergarten has emerged as an essential starting point for public education for some, Loudoun has faced difficulty in expanding its full-day program. In the past 15 years, the county’s school population has more than doubled, from around 32,000 to nearly 76,000 this year. It has constructed schools at a breakneck pace, doubling the number from 44 to 88. In that period, it was difficult for elected officials to contemplate expanding full-day kindergarten as the school district struggled to keep up with the growth.

Kindergarten students also must have their own in-classroom bathroom facilities and cannot use portable classrooms. Today, many schools use one classroom for a morning and afternoon class of half-day kindergarten.

But there is also skepticism from school board members who argue that the benefit of full-day kindergarten classes has not been proved for most students. Research has shown that full-day kindergarten has clear advantages for low-income students, English language learners and special education students. But the research is less clear for students who do not fall into those categories.

“It’s not necessarily conclusive . . . that adding full-day kindergarten for non-at-risk students is going to necessarily provide us with a proven benefit,” Rose said at the work session last week.

School officials countered that full-day kindergarten could provide a lot of intangibles that are difficult to measure and that is one of a number of factors that can make a difference in a child’s academic performance.

“It’s not a magic bullet. It’s not a forever vaccination. But it’s a really good start at preventing students from falling behind and intervening if they are behind,” Ambrose said at the meeting.

The county, once ranked as one of the wealthiest in the country because of its six-digit median household income, is the only one in the region that does not offer full-day kindergarten. This distinction has led to an annual debate over whether the school system should expand its program.

“We’re the richest county in the country. There’s just no excuse for us to be in the situation we’re in,” said Jessica Sandberg, a mother of five whose twin preschoolers will enter kindergarten next year.

Sandberg sent her older children to private school for kindergarten so they could benefit from full-day classes and then enrolled them in public school beginning in the first grade, an option that is out of reach financially for many families.

But there are signs that resistance to full-day kindergarten is waning. In a candidate forum organized by the Loudoun Education Alliance of Parents, several contenders for school board seats expressed support for universal full-day kindergarten.

This year, the school system allocated extra money for full-day kindergarten, nearly tripling the number of seats from 518 last year to about 1,500 this year. The expansion meant that every at-risk students got a seat, when hundreds had been squeezed out in the past, and that there were even seats left over that were given away to other students via lottery.