The word “drill” has come to define bad teaching. The piercing violence that “drilling” evokes just seems not to belong in sensitive pedagogy. Good teachers don’t fire off quiz questions and catechize kids about facts. They don’t plop students at computers to drill themselves on spelling or arithmetic. Drilling seems unimaginative and antisocial. It might even be harmful.

“In educational circles, sometimes the phrase ‘drill and kill’ is used, meaning that by drilling the student, you will kill his or her motivation to learn,” explains Daniel Willingham, a University of Virginia professor of psychology who has written extensively on learning and memory. “Drilling often conjures up images of late-19th-century schoolhouses, with students singsonging state capitals in unison without much comprehension of what they have ‘learned.’ ”

Oh, those schoolhouses — with the hickory sticks and the dunce caps. “Harrisburg! Salt Lake City! Montpelier! Tralalalala!” That does sound kind of fun — I mean, authoritarian. And drilling hardly has a better reputation outside academia. On message boards, students complain bitterly about Kumon, the extracurricular Japanese system of worksheet drills that many also admit has made them superb at math. Only unsportsmanlike parents hellbent on raising valedictorians, it seems, require their kids to do such rote work. At the same time, parents dismiss cutesy, flashy apps and Web sites that drill students using elaborate animation (like PopMath for arithmetic, iFlipr for custom flashcards, Cram for custom practice tests) as superficial edutainment, on par with children’s TV.

But while drilling might not look pretty — students doing drills don’t tend terrariums or don wigs to re-enact the Constitutional Convention — might it nonetheless be a useful way for some students to learn some things? By e-mail, E. D. Hirsch Jr., the distinguished literary critic and education reformer, told me that far from rejecting drilling, he considers “distributed practice,” the official term for drilling, essential. A distributed practice system, Hirsch explained, “is helpful in making the procedures second nature, which allows you to focus on the structural elements of the problem.”