The budding scholars in Alexandria’s gifted ­classes are bright and curious enough to make any teacher beam, but these days they’re also an emblem of what the school system calls one of its greatest failures: a lack of diversity among the academic elite.

Most of the city’s students are black or Hispanic. Most in gifted programs are white.

This imbalance in classes tailored to gifted and talented students is echoed across the region and the nation, a source of embarrassment to many educators.

In theory, a racial enrollment gap in gifted programs should be easier for schools to close than a racial achievement gap. But in practice, experts say, there are many obstacles. Among them, they say, are testing and outreach methods that fail to ensure children from all backgrounds get an equal shot.

In Alexandria, where a bitter struggle to desegregate public schools ended a half-century ago, administrators have vowed over the next year to tackle the problem.

“It’s simply unacceptable,” said Gregory Hutchings, director of pre-K-12 initiatives for city schools. “These numbers tell us that we’re not serving all kids.”

At Cora Kelly Elementary School, Rosalyne Cameron teaches seven gifted fourth-graders, all of them engaged in the kind of high-level inquiry considered a hallmark of gifted education. Last month, Cameron launched a discussion about modern art by asking the class, “What is art?”

The philosophical volleying commenced.

“Anything can be art,” one said.

“No, it has to be beautiful,” another responded.

“It has to be beautiful and interesting,” a third said.

The debate continued, getting increasingly heated.

Four of Cameron’s students are white, two black and one Hispanic. In the city’s elementary and middle school gifted program, 61 percent are white, 17 percent black, 11 percent Hispanic and 6 percent Asian.

By contrast, 25 percent of Alexandria’s 12,000 students are non-Hispanic white. About 5 percent are Asian, 31 percent are Hispanic and 34 percent black.

Alexandria is debating how to diversify gifted classes without sacrificing rigor. That pursuit could raise questions such as how intelligence is measured and the function of a program catering to the academic elite. “It’s all on the table,” Hutchings said.

While educators across the country face the same problem, Alexandria is particularly sensitive to racial questions. In the 1950s, the city resisted early efforts to allow black students into public schools, firing employees who disagreed.

As the school system today redoubles efforts to boost minority achievement, officials see the “gifted gap” as a hurdle to that aspiration.

“In many ways, the district has been resegregated,” Superintendent Morton Sherman said.

To get into a gifted class in Alexandria, the first step is generally a parent or teacher referral. Sometimes candidates are identified through high state-test scores. Then, candidates are typically given tests that measure intellectual and academic aptitude.

In recent decades, local school agencies and state and federal governments have wrestled with how to define gifted students. Intelligence tests have been tweaked. The referral process in many districts has changed. But many gifted classes remain stacked with white and Asian students.

“It’s a national problem,” said Joyce VanTassel-Baska, an education professor at the College of William and Mary, “and in some districts it’s extremely hard to make progress.”

Hutchings, a product of Alexandria schools, remembers thinking that gifted classes were “off-limits.” As a black student, he said, he noticed that the classes “didn’t include any kids that looked like me.”

That was more than 20 years ago. Hutchings worries that not much has changed. He’s now crisscrossing the city, holding town-hall-style meetings about the gifted program and who might be eligible for it.

“There are parts of the city where parents have never considered that their kids might be gifted,” he said. “No one has ever told them. That needs to change.”

Among local school systems, Prince William County’s has taken perhaps the most aggressive policy on diversity in gifted classes. It mandates that the demographic composition of the gifted program reflect the overall racial and ethnic makeup of the school system. To do that, Prince William has amended its identification process to ensure that it finds gifted students from a variety of backgrounds.

The Fairfax County system and others in Northern Virginia have started an enrichment program that targets high-achieving minority students.

Fairfax’s “Young Scholars” program aims to find underrepresented minorities and get them into gifted classes. Some parents have voiced opposition to that initiative, claiming it shouldn’t restrict such services to a narrow population when thousands of students countywide might benefit from them. Still, Fairfax’s gifted program is overwhelmingly white and Asian.

Gifted programs vary from place to place. Some local schools provide “gifted centers,” others an hour of special instruction per day.

In nearly every local system, white students are disproportionately represented, even though most gifted programs explicitly target students with natural talents and aptitude, which are spread evenly across racial groups and social classes.

Experts say one factor that skews enrollment in gifted classes is intelligence testing.

Students living in poverty, particularly those whose parents are uneducated or speak English as a second language, are less likely to develop verbal skills measured by traditional intelligence tests. But that doesn’t mean they’re not gifted. Assessments that measure spatial and mathematical intelligence as well as curiosity and leadership abilities are more likely to identify a diverse crop of gifted students, experts say.

“We used to think that gifted meant students who could read and write at an early age. That’s changed,” said Carol Horn, director of gifted education in Fairfax. She said that Fairfax has learned that using a variety of assessments can help broaden the pool of gifted students.

Some experts say that the parental- and teacher-referral process leads to uneven representation. Many parents might not refer children for testing because they are not familiar with gifted programs. Without a teacher or parent referral, most students are not fully evaluated.

In Alexandria and elsewhere, officials have started a campaign to recast the referral process, encouraging more parents to recommend their children and training teachers to consider a wider range of criteria.

First-grade teacher Sheila Walsh said she looks for students who are not just academically advanced but able to make connections between their studies and the world around them. In such moments, the Alexandria teacher says to herself, “I can’t believe I’m having this conversation with this little person.”

She typically finds about two of those students a year. For those who are found, the payoff is clear.

“I used to get bored in my class. Everything moved so slow,” said Jawad Adams, 9, a black student in Cameron’s fourth- grade class at Cora Kelly Elementary. “Now things are up to speed.”