(Bloomberg View) -- It doesn't take much to see that science, technology, engineering and math (STEM) jobs are essential to the U.S. economy. Look at the sky-high salaries paid in Silicon Valley or in quantitative finance, or listen to company after company say it's hard to hire enough qualified talent.

More well-trained STEM professionals from low-income backgrounds would also help address economic inequality, since math skills are so highly correlated with increased incomes. Those who can think quantitatively rise to the top not just in finance and technology, but also advertising and analytics.

To get some idea of the scope of the challenge, though, let’s look at two hypothetical girls who are both interested in math and science. This exercise will also illustrate why doing more to help low-income students excel at math can put a dent in income inequality.

One student goes to a good, suburban high school. She takes advanced-placement calculus classes. She enters math and science contests and goes to an expensive summer program where she learns advanced math that challenges her to think in a way that her high school classes never do. Her uncle, who is an engineer, recommends a book on cosmology that inspires her to do a research project in astrophysics. She gets to the state-level science fair, never mind that she doesn’t win.

The other student goes to an urban school that serves primarily low-income students. Her school doesn’t offer calculus. It doesn’t have a math team. A summer math program seems out of reach, with a sticker price of as much as $5,000, and no uncle recommends a book. Her path to college is simple: get good grades, which she does in every class. She works hard, memorizes how to do problems and does her homework.

Both of these girls are exceptional, but who do you think will have an easier time in college-level math? One enters college knowing how to creatively apply abstract reasoning; the other remembers some formulas.

On the National Assessment of Educational Progress exam, just 18 percent of low-income students scored at the “proficient” level in math in eighth grade, compared with 48 percent of those who don't qualify for subsidized lunches. But proficient isn’t nearly enough for a good STEM degree! Look at the “advanced” rating. Only 2 percent of low-income eighth-grade students achieve it compared with 13 percent of the rest. By 12th grade, the percentage of low-income students scoring at the advanced level is so low it isn’t even given. It rounds to zero.

Is this dramatic gap in math achievement between rich and poor students an inevitable effect of poverty? The evidence says it isn't. In many countries surveyed on the Programme for International Student Assessment, wealthy students did do better in math -- but plenty of poor students also achieved at advanced levels. In Japan and Finland, a low-income student was about a third as likely to score at an advanced level as a wealthy student.

In Canada, a low-income student was about a fourth as likely to do that well. Where was the U.S.? Eleventh out of 12 countries tabulated. In the U.S., a low-income student is barely one eighth as likely to score at an advanced level as a wealthy peer! What the international data tells us is that the gap in math ability between rich and poor kids in the U.S. is a result of structural problems in our K-12 education system. These built-in deficiencies hold back low-income kids with math potential, contributing to economic inequality.

QuickTake Income Inequality

One paradox of the American education system is that in spite of how few students from poor backgrounds excel at math, the U.S. is actually quite good at producing students who are exceptional in mathematics. For those students who attend math circles, find challenging problems online, can afford to attend high-level summer programs, and do independent research -- they become world-class scholars, and they do it because of the huge ecosystem of opportunity in the U.S. This country is very good at providing extracurricular programs to support these young mathematicians and scientists -- provided they come from well-to-do backgrounds.

But for students who aren’t plugged in and can't afford access to that ecosystem, there’s little or nothing to help them find that challenge.

Five years ago, I founded Bridge to Enter Advanced Mathematics (BEAM) through the Art of Problem Solving Foundation. We work to help underserved New York City students access the same programs for advanced math study as their more affluent peers. Our students have gone on to advanced summer programs and to great colleges on merit scholarships.

BEAM students are not the exception; there are highly capable students from low-income backgrounds all over the country whose potential goes untapped. We need to figure out how to make resources for advanced math study systematically available to every student in the country. Not only will that help the country get the STEM workforce it needs -- trained right here in the U.S. -- but it can help put a dent in the growing income divide between rich and poor.

I can think of no greater shame than this: There are kids out there who want more math, who want to excel, but who are denied it simply because of their economic status. They’re told to do their work, keep doing the same practice problems and they’ll be fine. Well, they won’t be fine, and neither will our society as a whole, unless we can find a way to give every student access to challenging mathematics.

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