As I journey around the country talking with educators working hard on “closing the achievement gap,” I have come to realize that the top tier of achievement is not the main priority in most schools. Indeed, for most educators, their work is focused at the other end of the achievement spectrum: bringing the bottom kids up.

Improving the knowledge and skills of our lowest performing students is hugely important, and I will never suggest otherwise. Far too many children — disproportionate numbers of low-income students and students of color among them, but many white students as well — have such low reading and mathematics skills that they will be forever locked out of decent jobs and full participation in our democracy if we don’t do something different, and do it fast.

We will, however, never close the achievement gaps that many are so committed to closing if we focus only on bringing the bottom students up. Simple mathematics makes that clear. If we are going to get these gaps behind us, once and for all, we have to bring our middle-achieving, low-income students and students of color higher, and move our higher-end students higher still.

But too often, top performing black, Latino and less advantaged students do not get the attention they need in their schools. In our new report, “Falling Out of the Lead: Following High Achievers Through High School and Beyond,” we show how these students fare on the high school outcomes colleges care about and find significant problems. Although high-achieving black and Latino students have similar access to rigorous courses as their high-achieving, white peers, they receive lower grades, pass fewer of their AP exams, and score lower on the SAT/ACT. These students are then less likely to enroll in selective colleges and universities, or even to attend college at all.

The progress on course access is good news. But unless schools also focus on instructional quality and student supports, students won’t be adequately prepared to realize their potential after high school. According to high-achieving students profiled in the report, the quality of high school courses really varies — something too few schools, districts, and state departments of education are adequately addressing.

Falling Out of the Lead” is the third installment in our Shattering Expectations series, which focuses on gaps at the high-end of the achievement spectrum. If full racial equality is our goal, getting and keeping more black, Latino, and American Indian students into the highest reaches of achievement — the top 25 percent or top 10 percent — is especially important.