Narrowing achievement gaps is not always a sign of improvement in school districts. It can also signal trouble. (istockphoto)

Never have I found the uselessness of our fascination with achievement gaps better illustrated than in two lists from an admirable paper by Stanford University researchers, which that university’s Center for Education Policy Analysis published in April.

The Geography of Racial/Ethnic Test Score Gaps” was written by Sean F. Reardon, Demetra Kalogrides and Ken Shores. It identifies the 20 U.S. school districts with the smallest white-black and white-Hispanic achievement gaps in 2009 to 2012, based on standardized reading and math tests in elementary and middle schools.

The study has gotten a lot of attention. It reveals what creates gaps and the surprising places they occur. Americans assume that big achievement gaps are bad and little ones are good. Which school district, I wondered, had the smallest gaps?

I have been resisting reading glasses, so when I first looked at the lists I thought I had missed something. I squinted. I gasped. The national champion of achievement gaps, scoring pretty close to zero in the difference between whites and those two minorities on that scale, was Detroit.

Detroit is our nation’s worst school district, or close to it. Yet it tops this list because its white students are as poor and disadvantaged as its black and Hispanic students. It wins first prize in a weird contest that, I think, should be discontinued.

There are several ways that narrowing achievement gaps can signal trouble, not improvement. Low-income student scores can drop while high-income student scores drop even more. Low-income scores may stay put as high-income scores decline. Low-income scores could improve while high-income scores don’t.

We should instead be looking at how each group is doing, celebrating gains and addressing declines without comparing groups with different issues. I applaud programs that raise achievement for low-income and minority students, but also note that our best-performing students have sometimes not made the same progress. There shouldn’t be a ceiling on achievement.

One source of our obsession with academic differences can be found in this year’s political campaigns. The income gap in America has become a huge issue. Our resentment of company executives making 200 times as much as their average workers is distorting our view of education. Making money and learning about the world are different enterprises with different consequences.

I understand the distaste for billionaires who own several homes, boats and offshore bank accounts and who avoid paying taxes. But can anyone learn too much? Wisdom tends to enrich everyone who comes in contact with it, particularly in a free society. Mega-mansions in McLean don’t help the rest of us nearly as much.

The Stanford study provides the first comparable measures of ethnic achievement gaps in every U.S. school district, Reardon said. He said the academic disparities are larger “in places where white and minority students’ families differ more in socioeconomic conditions, . . . in more segregated places, . . . and in more affluent places.” He said wide gaps in affluent yet integrated communities like Shaker Heights, Ohio, may stem from “competition for educational success” being “particularly strong in such places.”

The paper says “one consistent predictor of achievement gaps is the differential rate of exposure between whites and minorities to poor classmates,” but it found “little or no association between achievement gaps” and available measures of school quality.

Reardon told me that studying gaps is useful despite my objections because “educational success is at least partly what sociologists call a ‘positional good’ — meaning that one’s educational success has value partly because of where one ranks relative to others.”

He’s right that many people feel that way, but it seems wrong. The happiest people I know enjoy growing intellectually and don’t see any point in resenting what elevated intelligences like Stephen Hawking, Oprah Winfrey and Malcolm Gladwell have achieved.

We should be working to raise everyone’s level. The gaps don’t matter, particularly if you are going to school in Detroit.