One of few bright spots in the just-released National Assessment of Education Progress (NAEP) results was an increase in the number of students reaching "advanced" level in both math and reading at the 4th- and 8th-grades.

But the results masked large racial and economic disparities. While 30 percent of Asian students and 13 percent of white students scored advanced on the 8th-grade math test, for example, just 2 percent of blacks, 4 percent of Hispanics, and 3 percent of low-income students reached that level.

The highly selective Thomas Jefferson High School for Science and Technology in suburban Washington, D.C., known as TJ, offers a window into a significant source of the disparity, and suggests a solution to the problem.

A recent survey of TJ parents revealed that Asian-American students, who make up a disproportionate percentage of students admitted to elite public STEM schools like TJ, are spending their afternoons, weekends, and breaks learning math.

Most of them enroll in advanced math classes as early as possible in their school careers, even though by their parents' admission fewer than one third of them are highly gifted in math. But more importantly, their parents do not rely on school programming to prepare their children for TJ admissions or any other milestone on their way to top STEM careers.

Instead, they make sure that at every step of the way their children have access to high-quality extra-curricular math that prepares them for, clarifies, complements, and extends the instruction they're obtaining in their accelerated public school programs.

If we're really serious about increasing the number of low-income students and students from underrepresented groups who are learning math at the level required to contribute to our increasingly computational world, we should take a page from the playbook of those who are already successful: We should provide high-quality math enrichment for many more kids, as early in their educational lives as possible.

In focusing in recent years on raising the bottom of the learning curve, the nation has neglected those at the top, essentially ignoring the growing "excellence gap" between groups of high-performing students. But this is not the only reason that the gap has been growing.

Even when policymakers and administrators have made closing the excellence gap a priority, they have had little success because they have focused almost exclusively on expanding access to public school advanced programs. Unfortunately, increasing the number of students from underrepresented groups in advanced programs has not automatically led to increased achievement. That's because, as the families of the most successful students recognize, even the most advanced programs at the best public schools are insufficient to prepare students to achieve at the highest levels.

Nor are the families of successful students the only ones who know the secret to STEM success. Education experts have long been aware that extra-curricular math is essential for high-level math achievement.

Almost 20 years ago, a College Board task force found that "some of the most academically successful groups in our society have created a network of supplementary opportunities for their children that may best be described as a parallel educational system." The panel recommended that "a much more extensive set of supplementary education institutions and programs…for minority students should be deliberately designed to provide the breadth of supplementary opportunities available to many youngsters from more educationally advantaged and successful groups."

The reason we haven't implemented the suggested programs is because providing students from underrepresented groups with years of quality math enrichment takes time, money, faith in the ability of students to prevail against all odds, and a willingness to acknowledge the limits of our educational system—all of which are in short supply. It is far more politically expedient to heed repeated calls for quick-fix measures such as admission quotas for exam schools like TJ that alter the numbers while doing nothing to provide students with needed skills.

In addition to the above challenges, misguided beliefs about the causes of the excellence gap hinder our ability to reverse it.

Myth 1: The excellence gap is primarily a result of socioeconomic disparities.

At New York City's elite Stuyvesant High School, the school with the City's most competitive admissions process, 68 percent of students admitted to the Class of 2022 were Asian; and at TJ, 65 percent of students admitted to this fall's class were Asian. In both cases, most of these Asian students were the children of immigrants.

But the similarities end there. At TJ, 61 percent of families with two Asian immigrant parents have incomes over $200,000 per year and 76 percent have advanced degrees. In fact, only seven of the 485 students admitted to this fall's class were eligible for free or reduced lunch. At Stuyvesant, however, Asian students make up the overwhelming majority of the 45 percent of students who are eligible for free or reduced lunch. Yet, despite financial and other constraints, Stuyvesant's low-income Asian students obtain high-quality math enrichment, and it is perhaps even more critical to their success than it is to the success of TJ's upper-middle-class Asian students.

Myth 2: The excellence gap is primarily a result of cultural, or even innate, differences.

Asian immigrant parents have high expectations for their children's academic performance and believe hard work matters more than natural ability. They prioritize education, sacrificing time, money, and other goals in order to give their children the best chance at a better future. And they bring a competitive approach to education from their home countries.

These factors undoubtedly contribute to their children's academic success. But cultural norms do not automatically lead to learning. Whatever the bright children of Asian immigrant parents are doing to master challenging math topics at younger and younger ages, other bright children can do as well.

Every diverse urban and suburban school district in this country would benefit from an intensive STEM enrichment program that targets capable students from underrepresented groups and begins as early as possible. Such programs should also embrace features of successful extra-curricular academies that serve low-income Asian students, including outreach to parents and an emphasis on fostering an environment where it's not only OK to be good at math but where students are admired for their genuine interest, aptitude, and perseverance. Sadly, very few such programs exist, and most of them are underfunded.

One is Boston's well-financed Steppingstone Academy, which provides summer, after-school, and weekend enrichment to low-income students, beginning in 5th- or 6th-grade. It has been phenomenally successful in increasing opportunities for students, 90 percent of whom gain admission to their schools of choice, including competitive public magnet schools.

Another promising program is New York City's BEAM (Bridge to Enter Advanced Mathematics) program, which identifies 6th grade students from low-income neighborhoods and provides intensive math instruction, relying heavily on curriculum from Art of Problem Solving (AoPS). Thanks to a Jack Kent Cooke Foundation grant, BEAM recently expanded to Los Angeles.

In a pilot program intended to test the benefits of reaching students at younger ages, an AoPS academy recently partnered with the foundation that supports the STEM magnet at Montgomery Blair High School (Blair Magnet) located across the river from TJ in Montgomery County, Maryland. The program, the Magnet Pipeline Project, aims to provide three years of after-school or weekend math enrichment to select students, beginning in 3rd grade, with the goal of increasing the number of underrepresented students admitted to the middle-school program that feeds into the Blair Magnet. The foundation has raised about $20,000 toward the cost of the program, largely from Blair Magnet alumni.

For its part, TJ provides summer STEM courses, mentorships, and test-prep for underrepresented 7th- and 8th-graders through a program launched with Cooke Foundation funding. And a company run by a TJ alum provides free test-prep for 8th-graders applying to the school. But these programs have had limited effect because they aren't reaching students early enough with the kind of math enrichment that makes a real difference.

We're going to need a lot more leadership and significantly more funding to ensure that programs like these succeed, and to spread the most successful ones to other school districts. We'll need the support of Silicon Valley entrepreneurs who know very well what it takes to achieve at the highest levels and who constantly complain of the lack of diversity in their applicant pool.

We'll also need buy-in from other STEM industry leaders who consider themselves stewards of their communities and likewise suffer from a lack of available talent. Closing the excellence gap should be the highest philanthropic priority of all who value what is most precious about this country, the unlimited opportunities it provides to those willing to put in the hard work.

Thirty-five years ago, A Nation at Risk linked the end of America's industrial dominance to a scarcity of workers with sufficient technological training and blamed both on our educational system, which it recognized as the institution responsible for ensuring that all children fulfill their potential. The report's warning is no less compelling today.

[Read More: The Audacious Ambiton of  'A Nation at Risk']

It is both a moral and political imperative that every student be able to reach his or her potential. In an era when Americans compete for jobs against, as well as work alongside, the graduates of educational systems from around the world, it is no longer enough that our strongest students graduate from college; they must enter the workforce with the skills necessary to succeed in a global economy.

Now that technology is available to do much of the easy work, our best graduates must be prepared for the complex work of building, training, and working with existing technologies, inventing new ones, and mastering any number of unknown and unpredictable challenges. Eliminating excellence gaps is therefore nothing less than "an issue of equity and social justice, community development, economic advancement, and national security."

Instead of viewing the excellence gap as a symbol of systemic failure, we should follow the lead of parents of the most successful students and aim to provide students from underrepresented groups with the most powerful extra-curricular interventions money can buy—even as we redouble our efforts to ensure that schools provide advanced course work for talented students of every background.

Hilde Kahn is the parent of three Thomas Jefferson High School for Science and Technology graduates and served for nine years on the board of the school's private foundation.