The result of cramming kids isn’t as predictable as enthusiasts hope or critics fear. Illustration by Golden Cosmos Audio: Listen to this story. To hear more feature stories, download the Audm app for your iPhone.

We know we’ve come to a crossroads when German childhood is being held up as an idealized model for Americans. It was, after all, Teutonic styles of child rearing that were once viewed with disgust—as in “The Sound of Music,” for a long time the most popular of all American movies, with all those over-regimented Trapp kids rescued by wearing the bedroom drapes and singing scales. But Sara Zaske’s “Achtung Baby: An American Mom on the German Art of Raising Self-Reliant Children” (Picador) is perhaps an inevitable follow-up to “Bringing Up Bébé,” that best-selling book about parenting the way the French supposedly do it—basically, as though the kids were little grownups, presumably ready for adultery and erotic appetites. So why not move eastward through Europe, until we get the book on parenting the Moldavian way?

What’s wrong with such books is not that we can’t learn a lot from other people’s “parenting principles” but that, invariably, you get the problems along with the principles. French kids are often sensitive and unspoiled in ways that American kids aren’t; they are also often driven so crazy by the enervating 8:30 A.M.-to-4:30 P.M. school system and by a tradition of remote parenting that they rebel as bitterly as American adolescents do, only putting off the rebellion until they’re forty, when the sex and drugs really start to kick in. And you can wonder whether the German molding system leaves German kids molded quite so thoroughly as Zaske, an American long resident in Berlin, insists.

In her depiction, the new German style of child rearing remains, well, extremely German: here are the most highly organized forms of not being highly organized that have ever existed. Nowhere else, it seems, will you find such tightly controlled varieties of freedom, such militarized ordering of open-ended play, such centralized rules for creative anarchy. Kids aren’t merely encouraged not to be dependent on toys; there is a “toy-free” month when no one at the day-care center is allowed to play with them. Adolescents are not only indulged in their freewheeling impulses; whole parks are specifically set aside for their explorations. “In addition to park areas designed for them, adolescents can go into almost all places in Berlin, including dance clubs and bars,” Zaske writes. “There are some rules, including a curfew: teens under sixteen must be out of the clubs and restaurants by ten p.m., those under eighteen must leave by midnight.” (Could these fine-print rules be effectively enforced anywhere except in Germany?) German parents don’t merely not hover; they refuse to hover, on considered principle, and send the kids off to school and back, after having digested the odds of a child’s being snatched along the way and, sensibly enough, decided that it’s a safe bet they won’t be.

And here we arrive at the real ghost that haunts these books, the one that sends us to Paris or Berlin for help: the sense that American parents have gone radically wrong, making themselves and their kids miserable in the process, by hovering over them like helicopters instead of observing them from a watchtower, at a safe distance. The helicopter metaphor is an odd one, since helicopters can often only hover, helplessly, as in the Vietnam-era newsreels, as the action goes on below. The style of middle-class child rearing that the Germans and the French and the rest might help us escape from is really more handcuff than helicopter, with the parent and the child both, like the man and woman agents in a sixties spy movie, shackled to the same valise—in this case, the one that carries not the secret plans for a bomb but the college-admission papers. Until we get to that final destination, we’ll never be apart.

In “Off the Charts: The Hidden Lives and Lessons of American Child Prodigies” (Knopf), Ann Hulbert seems to be taking up the opposite end of the child-rearing stick; rather than ordinary kids with ordinary parents, these are the outliers, right here in America. Yet her book shares some themes with the Europhile ones. There’s the same agonizing question of American achievement: What can we learn, in a society dedicated to high-achieving children, from children who seem “naturally” off the charts in their achievements? How can we make our children less anxious while still making sure that they achieve? Are prodigies a race apart, or are they merely more persistent than other kids? (As Hulbert cautions, the paradox of the self-made prodigy is that persistence itself is an inborn gift, as odd as any other.) The arguments seem to echo ancient religious ones—mysterious innate grace does battle with hard-won grit, Catholics vs. Protestants in undersized clothing—which may be a giveaway that what’s at stake is ethical before it’s educational.

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Hulbert’s book is smart—as all her books have been, particularly the child-centric “Raising America”—and often sad. There seems nothing more melancholy than the fate of prodigies. The book takes us from William James Sidis and Norbert Wiener, Jewish prodigies at Harvard at the beginning of the twentieth century (Sidis was the subject of a profile by James Thurber, of all people, in these pages), to their seeming successors in Silicon Valley, the hero-nerds who have become as much an American typology as the enfants sauvages of France ever were. Along the way, we encounter the big names in prodigy-land, among them Philippa Schuyler, the African-American child genius of the nineteen-thirties and forties (and also the subject of a New Yorker profile, by Joseph Mitchell), and Bobby Fischer, the chess-playing son of Jewish Communists, who ended up a crazed anti-Semite. That many of these kids, despite being outliers, have already been much documented suggests that we use mental prodigies the way Renaissance people used physical prodigies (the boy-wolf, the fish-woman): that is, to prove a moral point. In the nineteenth century, John Stuart Mill’s breakdown was a cautionary tale about being stuffed with too much knowledge; Louisa May Alcott included an ex-prodigy of this kind in “Little Men” to show the danger. We watch movies about Bobby Fischer in part because his is a touching story and in part because we are secretly glad that our kids, though not prodigious, are at least not that.

Hulbert does the good work, throughout, of resisting morals or too neat generalizations; one suspects that the alliterative “Lessons” in her subtitle was a publisher’s creation. Some prodigies are pushed; some do the pushing from within. Sidis had a bleak life after Harvard: never quite finding his footing, he self-published speculative manuscripts on the second law of thermodynamics, the crank’s specialty, and obsessively collected street-car transfers. But Norbert Wiener, who spent his career at M.I.T., became one of the most significant scientists of his era, the founder of cybernetics and a pioneer in information theory. He suffered from depression, it’s true, but was no more miserable than many other tenured professors. Philippa Schuyler had a terribly unhappy adulthood; Hulbert produces a heartbreaking letter of indictment that, in her late twenties, she wrote to her pushy, well-meaning mother. Yet Shirley Temple, her show-biz counterpart in the thirties (she was, as Hulbert points out, the first white female ever to dance with a black man onscreen, albeit in a movie where she wears a Confederate cap), went on to have a successful life as a Republican politico and diplomat.