James Piereson is the president of the William E. Simon Foundation, a private grantmaking foundation that supports some charter schools. Naomi Schaefer Riley is the author of “The Faculty Lounges: And Other Reasons Why You Won’t Get the College Education You Paid For.”

If you want to address income inequality, fix higher education. That seems to be the current thinking in Washington, where President Obama has urged college administrators to better serve low-income students.

Some colleges have been following that guidance. The University of Chicago has been praised for its new campaign to recruit low-income students — a strategy that reduces the financial paperwork in the admissions process, and guarantees low- and middle-income students summer employment while no longer expecting them to work during the academic year. And in April, Janet Napolitano, president of the University of California system, sent letters to 5,000 high-achieving, low-income California high school students encouraging them to apply, noting that the UC schools cover tuition and fees for students whose families make less than $80,000 annually.

Even college ranking systems are doing more to take price and student debt loads into account. Last month, the New York Times ranked colleges that have taken steps to enroll an economically diverse student body. At the top of the list were Vassar, Grinnell and the University of North Carolina at Chapel Hill. By next fall, the White House is expected to introduce a ranking system that measures campuses’ tuition and financial aid programs.

The fact that relatively few students from low-income backgrounds attend college is responsible in large part for the lack of upward mobility in the United States today, reporter David Leonhardt wrote upon the release of the New York Times’ rankings. With their oodles of endowment money, colleges may seem like a fat target.

But they aren’t the real problem; K-12 education is.

Getting more poor kids to college is not a new idea. The effort began in earnest as far back as the 1960s, when the federal government set up scholarship programs to help low-income students attend college. It’s been about a decade since Yale, Harvard, Princeton and Stanford replaced “early decision” admissions with “early action” programs that allow prospective students to apply early but don’t require them to commit. This change can be helpful for less-privileged students who want to compare financial aid offers before promising one school that they’ll attend. A number of the Ivies have also eliminated loans from financial aid packages, and some promise to keep tuition at zero for low-income students. Yale, for example, offers a free ride to students whose families earn $65,000 a year or less.

But so far, nothing seems to have had a significant impact. According to research published last year by Caroline Hoxby of Stanford and Christopher Avery of Harvard: “The vast majority of low-income high achievers do not apply to any selective college. This is despite the fact that selective institutions typically cost them less, owing to generous financial aid, than the two-year and nonselective four-year institutions to which they actually apply.” Indeed, right after Harvard implemented a policy in 2004 that no student whose family income was less than $40,000 would pay a cent to attend, the university gained 20 additional low-income students in a class of 1,600. That income ceiling has since been raised to $65,000 .

Of the 70,000 or so low-income students whose grades and test scores make them eligible to get into the top 10 percent of colleges, only about 20,000 apply, according to Richard H. Sander of the UCLA School of Law. Hoxby and Avery suggest that this is because qualified low-income students typically don’t come into contact with college counselors or other adults who have attended elite institutions. It’s an interesting observation, but it leads to the obvious question: Why are there so few high-achieving students in low-income schools? And why are there so few teachers who have gone to selective colleges working at our most impoverished schools?

Under the current system, teachers have more school choice than students do. Rather than sending the most qualified and experienced teachers to educate the kids who need them the most, we do the reverse. As The Washington Post’s Jay Mathews has noted, a 2002 study found that more than a quarter of New York City public school teachers had degrees from the least selective institutions (ranking 1 on a scale of 1 to 5).

Teach for America, which draws many applicants from top-tier universities, is the exception here. For the 2014-15 school year, it had 50,000 applicants and accepted about 5,300 of them. It’s a safe bet that the majority of the other 45,000 did not find their way into inner-city classrooms anyway. These are smart young people who are willing to go into poorer schools and work with kids who are years behind where they should be. But without the structure and prestige of Teach for America, they are probably less willing to become part of a system that is rife with mediocrity.

All you have to do is look at a high-performing charter school or private school in a poor neighborhood to realize that there is nothing about low-income kids that makes them incapable of doing well in school. A critical mass of these students do well, and in addition they come into contact with well-qualified guidance counselors and other adults who have gone to elite schools. KIPP, a network of charter schools in 20 states and the District, has created pipelines with Georgetown, Brown and Duke, among others; the universities don’t guarantee admission but are actively recruiting KIPP students. Last year, the University of Pennsylvania accepted 14 low-income students from the KIPP charter network alone, according to a KIPP spokesman.

Which brings us to the real hole in the debate over income inequality in this country: the problems plaguing our K-12 education system. Fifty years ago, it was possible for a child to grow up in a home where neither parent had a college degree, and still attend a decent public school, go to college and become a professional. Seventy-five years ago, it was possible to grow up in a home where no one spoke English and still attend a decent public school, go to college and join the middle (if not upper) class. Despite the quotas that were in place, making it difficult for racial and ethnic minorities to attend the most elite schools, state colleges were well within reach and provided a rigorous education for working-class kids. A high school graduate knew how to read, write and perform basic math. Any college professor will tell you that’s not always the case anymore.

Today, for most low-income kids, college is merely a fantasy. If you finish high school, you are probably unprepared to attend a good four-year university, even if you could get in. And if you do, you will probably need multiple remedial courses. About half of students entering the California State University system do, for instance.

According to 2011 research by Sean Reardon of Stanford University: “The achievement gap between children from high- and low-income families is roughly 30 to 40 percent larger among children born in 2001 than among those born twenty-five years earlier. In fact, it appears that the income achievement gap has been growing for at least fifty years.” One of the factors Reardon points to is greater residential segregation by income, noting that such divisions are “closely linked to school-attendance patterns.”

There are many problems whose blame lies squarely with our universities, including the dumbing down of academic standards and an overemphasis on political correctness, leading to a less free-thinking society. Between the ever-rising price tag of tuition — and the fact that most low-income students don’t realize they won’t pay that sticker price — and the ever-expanding number of silly essay questions, students can be easily intimidated into not reaching high enough.

But colleges are not ultimately responsible for keeping poor students from moving up the income ladder in this country. For all the publicity that policies like the University of Chicago’s receive, they are hardly making a dent in the real problem. The shameful state of our primary and secondary schools cannot be fixed with a few changes in the college admissions process. By then, it’s too late.

Twitter: @naomisriley

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