Public concern about the impact of new immigration on America has reached a pitch not seen since the early 20th century. Americans have experienced an immigration surge unprecedented in their lifetimes. This is an unsurprising coincidence in light of the fact that our immigrant population of 37 million is, in absolute numbers, greater than it has been at any time in our history. It’s nearly as large a percentage, 12.5%, of the population as it was at its historic peak at 14.5% in 1890. Today, there are more immigrants from Mexico than there were foreign-born residents from all countries in 1970.

Most of the debate over immigration has focused on whom we admit and why, and why our border control is so ineffective. At least nine million immigrants are here illegally, according to the U.S. Census Bureau.

It is a mistake, though, to think that Americans are more worried about who has a green card than they are about immigrant assimilation, a less discussed matter. The idea that immigrants should, and can, become Americans has been a powerful one, a reflection of the fact that ours is a society based on values and laws, rather than a single faith and a common blood.

Lately, discussing immigrant assimilation has become less than acceptable in polite company out of a concern that assimilation imposes Anglo-Saxon Protestant culture on others. But the majority thinks that newcomers should learn English, which is endorsed by 87% of Americans in one Rasmussen survey, and become American citizens. This makes clear that, notwithstanding the affection for multiculturalism among elites, average Americans still believe in the melting pot.

But is the melting pot still working? A new Manhattan Institute report by an economist at Duke University Jacob Vigdor, “Measuring Immigrant Assimilation,” uses Census data to determine how similar immigrants from some 120 countries are to native-born Americans — in other words, how assimilated they are.

The report examines three broad categories: socio-economic, including employment and education; cultural, including English proficiency; and civic, including rates of naturalization and military service.

It turns out there is plenty of assimilation going on. Cubans and Vietnamese, for instance, are economically indistinguishable from natives. Germans are indistinguishable both culturally and economically. Some cities are doing better than others at assimilating newcomers. Houston, where Mexican and Central Americans predominate, has an assimilation index of just 19. New York, where no one group predominates, has a score of 31.

But the most striking finding is much less positive. The current overall assimilation level for all immigrant groups combined, measured on a scale of zero to 100, is, at 28, lower now than it was during the great immigration wave of the early 20th century, when it never went below 32. What’s more, the immigrant group that is by far the largest is also the least assimilated. On the zero-to-100 scale, Mexicans — 11 million emigrated to America between 1980 and 2006 — score only 13.

Although Mexican assimilation does occur, it’s extremely slow. Mexicans who arrived in 1995 started out with Index scores around five — and increased only to around 10 by 2005. In other words, our largest immigrant group arrived with little education and even less knowledge of English, and they have stayed that way for an extended period.

By contrast, Vietnamese started at similar low levels and in 10 years rose to an Index level of more than 40. Notable, too, is that Generation 1.5 — Mexicans who came to this country as children aged five or younger — are also remaining distinct, and in some worrisome ways: they are less likely than other immigrant groups to become citizens, and more likely to be in prison or be a teen mother.

But even groups that are doing much better than Mexicans in some areas, such as earnings, are assimilating slowly in others. Vietnamese, for instance, demonstrate that one can improve one’s economic situation without necessarily learning English. “Americanization” has always been about more than just economics.

Why, then, if the idea of assimilation remains popular, has the process slowed? Some, notably Samuel Huntington, have argued that the new immigration is different from the old in that the gap between some foreign cultures and our own has widened and is unlikely to be bridged. Perhaps so. We cannot, however, discount the possibility that immigrant assimilation is lagging because, unlike our predecessors, we have not made it a conscious national priority.

A hundred years ago, there was a pro-assimilation movement led by the nation’s cultural elite. Across the country, more than 400 settlement houses — from New York’s Henry Street to Chicago’s Hull House — were established. Their mission, taken up by the privileged of that era, included Americanization of newcomers. Indeed, the Pledge of Allegiance, first published in 1892, was written as a primer of America’s values just when immigration was hitting its peak.

Today, the pledge is regarded as chauvinistic, particularly by those who should be leading the assimilation effort. We can’t bemoan low levels of immigrant assimilation if 21st century America’s most fortunate lack the cultural self-confidence to promote it.

When I was a boy, my grandmother gave me a book about the history of immigrant Jews in America, of which she was one. Its title, however, mentioned neither Jews nor immigrants; it was, simply, “Americans All.” It was not just a description of immigrants, but spoke about the aspirations of both natives and newcomers alike — aspirations that remain worthwhile.

Mr. Husock is vice president for Policy Research at the Manhattan Institute.