In Lake Wobegon, Garrison Keillor’s mythical radio homeland on his program “A Prairie Home Companion,” Keillor tells us that “all the children are above average." I wish it were so. In the real world, schools must deal with a mix of students – above, below and on average.

Each student is a unique individual, often with a unique learning style. Many are stronger in some areas and weaker in others. The same student who is above average in math might perform well below average on writing assignments, and the outstanding science student might have a hard time mastering a foreign language.

But education at the K-12 level is too often ruled by averages. Teachers teach to the middle of the class, to the detriment of those on the top and the bottom. SAT tests designate 500 as the mean score so that 100 points either way constitutes a standard deviation. And students are often graded on a curve, with the midpoint being the average.

Because each child is different, schools need to be sufficiently nimble to ditch the averaging instinct when confronted by the qualitatively different. A one-size-fits-all education winds up fitting very few.

There’s no question that schools must do everything possible to help below-average students struggling to master course material and in danger of dropping out. To borrow a slogan, no child should be left behind.

Too often, efforts to customize education for the brightest students are denounced as elitist, as if recognizing that some students perform above average is somehow anti-democratic or hostile to students who perform at below-average levels. This is inaccurate.

But ditching the averaging instinct also means helping students who excel. Just as no child should be left behind, no child should be abandoned ahead.

Too often, efforts to customize education for the brightest students are denounced as elitist, as if recognizing that some students perform above average is somehow anti-democratic or hostile to students who perform at below-average levels. This is inaccurate.

When I was New York City schools chancellor more than a decade ago, I wrongly assumed that the brightest students – even when they came from low-income families – didn’t need a lot of attention. I thought they would succeed and get into good colleges with the help of scholarships on the strength of their intelligence and ambition. But in reality, these children need our help and attention too.

High performing, low-income students face above-average obstacles blocking their path to higher education, especially at elite college and universities. Many come from single-parent homes, some have parents who speak little or no English, and few have parents who attended college and can explain the college application process.

Many of these students attend schools where inadequate funding results in overcrowded classes and a lack of instructional materials, and where there are fewer Advanced Placement courses than at wealthier schools.

Most have high school counselors who are responsible for advising hundreds of students, and so are unable to give them much individual attention.

Worst, the common assumption is that schools should aim exclusively to get those at the bottom to graduate rather than help those at the top get into the best college they are capable of.

In a democracy, we need to do both.

Many students from poor families must hold afterschool jobs that prevent them from participating in extracurricular activities that college admissions officials value. They can’t afford the expensive SAT and ACT coaching that help affluent students substantially boost their scores.

These above-average challenges facing smart low-income students explain why so few of them make it into America’s most selective colleges – even though a report by the Jack Kent Cooke Foundation, where I am executive director, found that such students can perform as well as wealthy students.

Unfortunately, despite their proven abilities, the top low-income students are rarely admitted to America’s top colleges. A Cooke Foundation study released earlier this year found that at our nation’s most selective colleges, a mere 3 percent of students come from families with the lowest 25 percent of incomes. In contrast, 72 percent of students come from families with the highest 25 percent of incomes. This means that for every low-income student at the elite schools there are 24 wealthy students.

These startling and disturbing statistics show that high-achieving students from low-income families need special attention to break through the cash ceiling and reach their full potential. For them, averages just don’t work. If we fail to acknowledge the importance of individual differences, we could lose a generation of strivers.

Focusing on averages ensures that our nation will get only average results, and that students who could reach great heights of achievement never climb as high as their abilities can take them. To remain competitive requires more. For outstanding low-income students, we can and must do better than settling for average.

Harold O. Levy, is executive director of Jack Kent Cooke Foundation, which has awarded nearly $147 million in scholarships to more than 2,000 high-achieving, low-income students since 2000. He served as New York City schools chancellor in 2000-02.