Ian McKeachie is a freckled 15-year-old who "drifted along" in elementary school. Not because he didn't love to learn or because it wasn't a good school, but because he mastered new concepts so quickly that the classroom work presented no challenge.

"My teachers would usually use me as a tutor for the other kids," he says, "so I was engaged in school, just not in a way that had me learning."

Ian had hit a sort of "class ceiling" – the limits advanced students often encounter in an education system that groups kids by age and gives teachers little training or time to cater to individual needs.

Then he found a school designed to shatter that ceiling.

His first two weeks in world history class there were devoted to learning how to analyze historical events and the ideas that served as their driving force. They looked at overarching themes in history, not just individual events. Ian had never done such in-depth academic analysis. Before that, he says, "I didn't really know how much faster I could move, how much more I could learn."

The Davidson Academy opened in Ian's hometown of Reno, Nev., in 2006, and Ian entered a year later. All the students are considered "profoundly gifted," at the highest end of the ability range. It's a public school, free to students. But it has a private-school feel because philanthropic funding keeps student-teacher ratios low.

He and his schoolmates are, by definition, exceptional. But how many more American students share their experience of idling in their classrooms, unaware of their potential, or bursting with frustration because only a fraction of their curiosity and capability is tapped?

If public education helps all students achieve basic skill levels, is that enough? Should it be up to parents and students to find ways to take learning to a higher level, or does society have something to gain if more schools make it part of their mission?

What holds the ceiling in place?

One of the joists in the "class ceiling" that many observers point to is No Child Left Behind (NCLB). The goals of the federal education law, in effect since 2002, include bringing all students up to math and reading "proficiency" – grade-level skills – and closing achievement gaps correlated with race, income, and other factors.

Laudable goals, most agree, but critics take issue with how the resulting testing system has dominated schooling and led to unintended consequences – like neglect of students who might otherwise zoom ahead.

"Because the accountability systems are so focused on the lowest-performing students, teachers see A's and B's and good standardized test scores and they say, 'OK, they're fine, we don't have to focus attention on them,' " says John Bridgeland, chief executive officer of Civic Enterprises, an education and policy think tank in Washington, D.C.

The teaching in many schools is prescriptive, even scripted. "We have squeezed out of the curriculum the kinds of things that really contribute to the next generation of highly creative, productive, inventive, entrepreneurial people," says Joseph Renzulli, director of the National Research Center on the Gifted and Talented at the University of Connecticut in Storrs. It happens most "oppressively" in schools that serve poor and minority children, he adds.

Nearly 80 percent of teachers surveyed in 2008 by the conservative Thomas B. Fordham Institute in Washington agreed that "getting underachieving students to reach proficiency has become so important that the needs of advanced students take a back seat."

Such criticisms might be legitimate, but they're anecdotal, says Pat O'Connell Johnson, who oversees gifted K-12 education issues for the US Department of Education.

"It's not like there was this golden era that NCLB has ruined. It's really been a sort of constant struggle in America to figure out how to pay attention to the students that are exceeding what the expectations are for most students," she says. "Academic excellence is something we feel ambivalent about. There's this idea that the kids will do well anyway."

There's no national policy requiring that gifted children be identified and served by school districts. There's no national definition of "gifted."

The only federal program to support gifted education, known as the Javits Act, used to supply about $7 million a year, mainly for research on how to better identify and serve poor and minority gifted students. But Congress eliminated it this year.

State policies are a patchwork. About one-quarter of states provide no funding for gifted education, and 13 states bar students from entering kindergarten early, according to the National Association for Gifted Children (NAGC) in Washington.

NAGC estimates the number of gifted students at about 3 million, or 6 percent of the US student population. What happens to them is largely left up to local school districts, and when budget screws tighten, gifted programs are among the first to go. "There are many schools doing well with these kids and there are many that are not, so it's just an accident of birth or ZIP Code," Ms. Johnson says. "That's the unfairness in it."

The ceiling keeps us all down?

It might seem that the country has bigger problems to worry about than smart kids who are bored silly. But student success is linked to the success of the national economy, says a bipartisan chorus of advocates for more attention to top students.

There's an "extraordinarily strong relationship between [students] knowing math and science and how fast the country grows," says Eric Hanushek, a senior fellow at the conservative-leaning Hoover Institution at Stanford University in California.

The United States ranks 31st out of 56 nations in the percentage of students with advanced math skills, says Mr. Hanushek. Just 6 percent of American 15-year-olds scored at the advanced level in math on the 2006 Program for International Student Assessment, run by the Organization for Economic Cooperation and Development. That compares with 28 percent in Taiwan and more than 20 percent in both Finland and Korea.

While improvement is needed at both the bottom and top of the spectrum, Hanushek and others say, the top may be more important because the US needs home-grown talent – creative innovators, particularly in the sciences – to keep up with global competitors.

Hanushek estimates that if the US improved its overall performance to match a country such as Germany, which is 15th for students scoring advanced, the US gross domestic product would increase by more than $40 trillion. (For perspective: That's at least four times the total US cost so far of the conflicts in Iraq, Afghanistan, and Pakistan, according to researchers at Brown University in Providence, R.I.)

Students who show a talent for math early in life are more likely to become inventors. Researchers at Vanderbilt University in Nashville, Tenn., identified 13-year-olds in the top 1 percent of quantitative ability, based on the math SAT. They tracked the students for at least 25 years. Nearly 9 percent earned one or more patents, compared with a rate of just 1 percent of the general population.

But educational opportunities also matter. The same research, the Study of Mathematically Precocious Youth, found that 13-year-olds in the top 3 percent of math ability who took the project's fast-paced math classes were twice as likely to go into math or science careers than a similar group that didn't take the classes.

Too often, advocates for advanced students say, they lose interest in science and math – or even drop out of school because there's nothing to keep the spark alive. It's potential, they argue, that the US can't afford to waste.

Of the approximately 1 million school dropouts every year, nearly 1 out of 10 earned mostly A's. The biggest reason those A-students cite for quitting is boredom, notes "The Silent Epidemic," a landmark report in 2006 by Civic Enterprises.

A 2007 report by the same public policy firm identifies 3.4 million "strivers" in K-12 classrooms. These students are below the median income level, but they're in the top 25 percent academically, as measured by standardized tests. They're caught in an "achievement trap," the report says, because the education system pays little attention to them and many fall behind higher-income peers in school and college.

With a looming skills gap for high-wage jobs, "you could make an argument that [these strivers] merit the greatest investment, because they're going to be the greatest producers, based on their early academic achievement," says Mr. Bridgeland, of Civic Enterprises.

Inner-city ceiling-busters

Jovan Mercado could have been a "striver" stuck under the ceiling. Instead, as a sixth-grader, he's already become an inventor.

Statistically speaking, Jovan falls into all kinds of categories that are underrepresented in gifted education programs. His first language is Spanish. His skin is not white. His family doesn't make a lot of money. And he lives in Hartford, Conn., where virtually all the students in the public schools share some of these disadvantages.

After kindergarten, he says, the school told his mother he was capable of sixth-grade work. She opted to skip him only to second grade. "She worried I would be bullied 'cause I was so tiny," says Jovan, whose sweet smile is as striking as his mohawk.

Jovan's fifth-grade teacher offered to help him work through an eighth-grade math book. And even more important, he recommended Jovan for a place in a relatively new public school in Hartford – The Dr. Joseph S. Renzulli Gifted and Talented Academy.

The school exudes a sense of order, but it's a place where students' enthusiasm bubbles as they hover over plants sprouting in a lab experiment or gather around an interactive whiteboard to roll virtual dice in a lesson on probability.

Such an atmosphere makes it more likely that students will stay engaged and go on to college, says Mr. Renzulli, cofounder of the academy. "They were so used to the disruptive nature of their [previous] schools ... [where] there was never any waiting their turn to speak," he says. "It was pushing and shoving.... Now [the kids have worked on] politeness, time management, self-control."

A highlight of Jovan's first year at Renzulli was the "Invention Convention" competition. His invention was "a prosthetic arm that could extend," he says. About a month before, during the school's "take apart day," students brought in old appliances and dismantled them. "I found a part of a fan that could rotate – I wanted the hand to rotate like this," he demonstrates as if turning a doorknob. Jovan's mom supplied a curtain rod. He dug out his sister's old arm brace and his dad's "big can of screws," and went on to win the local contest and compete statewide.

"What I like about this school is that there are many opportunities. You can make friends better," he says. "Bullying is not a problem."

Can we raise the ceiling and the floor?

Most American teachers are expected to reach students who are at wildly different points along the skills continuum. Their goal is to "differentiate" instruction to address individual students' needs. But it's not easy. Many teachers just don't have sufficient training or support.

"It puts teachers in the situation of being miracle workers," says Tom Loveless, a former teacher and senior fellow at the Brookings Institution in Washington.

Sixty-one percent of teachers say they can differentiate instruction a great deal. But among math teachers, only 46 percent say that, according to the 2010 MetLife Survey of the American Teacher. In schools where fewer students go on to college, teachers are even less confident that they have this skill.

In some schools, technology is being deployed to give students more individualized tasks at whatever level challenges them.

But the majority of teachers know little about strategies to meet gifted students' needs. Only five states insist that all teachers have training in gifted education before they begin their jobs, notes a 2009 report by the NAGC. In 36 states, no such training is required of general education teachers at any point in their careers.

Students should be grouped by ability, some parents and educators say. But how that's done can be controversial. "Tracking" became a subject of hot debate in the 1980s, with critics saying that students who start off at a disadvantage, particularly minority and low-income kids, often get stuck in low-level classes and are not being prepared for higher education or skilled jobs.

Now, in some circles, even talking about ability grouping can be taboo. But supporters say the pendulum has swung too far.

"We have no problem having [varsity sports teams] and lavishing attention on those kids.... But we don't do that for math ... literature ... science," says Mr. Loveless, author of "The Tracking Wars."

In an early 1990s analysis of hundreds of studies of ability grouping, researcher James Kulik found that high-IQ students in accelerated groups outperform nonaccelerated students of the same age and IQ by the equivalent of a full year of academic gain on achievement tests.

There is research on both sides of the debate, however, and detracking advocates say that's the better approach. What's needed, they say, is a high bar for all students – with teachers getting the support they need to engage both the strugglers and the high-achievers.

Rockville Centre, N.Y., began detracking its schools in 1989, ending a fourth-grade gifted program and offering the enriched curriculum to all fourth-graders. Eventually, all ninth- and 10th-graders were being taught what used to be the honors curriculum. Teachers offered support classes for students who needed extra help. Achievement gaps have narrowed, and test scores have increased, even among students who were already the highest achievers.

"The curriculum for the best kids becomes the best curriculum for all," the town's South Side High School principal, Carol Burris, asserted at a debate on detracking in Washington this year.

Can giftedness be taught?

In Project Bright Idea in North Carolina, teachers at low-income schools are trained to teach all K-2 students with curriculum and methods usually reserved for the top fraction of students.

"We try to change teachers' dispositions, to really get them to look at individual children, to look at their learning styles," says Margaret Gayle, director of the American Association for Gifted Children at Duke University in Durham, N.C. "Instead of trying to sort them by what they don't know, [teachers begin to] find out what they do know and what their interests are."

Teachers set up a variety of "performance tasks" so students can show what they're learning. They sometimes use ability grouping, but in a fluid way, with groups constantly shifting. The results show that, in a way, "giftedness" can be taught – or at least shifted from latent to blatant.

Overall, the students improved on a range of test scores. But more important, an independent evaluation of Project Bright Idea found that, on average across three years of the study, 20 percent of the K-2 students taught with these techniques were identified as gifted – compared with only 10 percent of a control group. In other words, the number of kids who show up on the radar screen as gifted actually doubles because of the way they're taught in the early grades.

"There's just a lot we don't know," Ms. Gayle says, "about what we can expect if we really tried to nurture each child as if we believed they have a lot of unusual ability that can be developed."