The flashiest method is that of Irwin, a young hotshot brought in by the headmaster (who, as played by Clive Merrison, bears a startling resemblance, physical and temperamental, to Mr. Burns, the scheming nuclear power plant owner on "The Simpsons") to add a little sheen to a class of eight senior boys swotting away in preparation for the Oxford and Cambridge entrance exams. The idea is not so much well-roundedness as to make the boys seem the equal, in cleverness, glibness and false sophistication, of competing candidates from the elite private schools.

For Irwin, education is essentially a stunt in which the whole point is to distinguish oneself in interviews and exams. His favorite strategy is to attack received opinion, just on principle, and stand it on its head. "The wrong end of the stick is the right one," he tells the boys. "A question has a front door and a back door. Go in the back, or better still, the side." He suggests Stalin as an example: "Generally agreed to be a monster, and rightly. So dissent. Find something, anything, to say in his defense. History nowadays is not a matter of conviction. It's a performance."

Irwin is in part the playwright's not-so-hidden dig at revisionary historians like David Starkey and Niall Ferguson, who have made careers out of debunking some of Britain's most cherished beliefs. Mr. Ferguson has famously argued about World War I, for example, that Britain was as much to blame for starting the war as Germany, and that Britain need never have got involved.

Americans looking for an analogy closer to home need only think of the online magazine Slate and The New Republic in the heyday of Michael Kinsley's editorship, when a routine tactic was to take some familiar item of conventional wisdom — that Wal-Mart is bad, or that magazine fact-checking departments are good — and demonstrate that it's all wrong.

But as most successful students already know, the Irwinian method is practically foolproof and works on everyone except teachers like Hector, Irwin's antagonist at the school. A fat, shambling, bow-tie-wearing eccentric, Hector believes in learning for its own sake and in turning out truly well-rounded human beings, not the fashionable Ivy League sort. His pupils are required to learn by heart great swaths of Hardy, Auden and Larkin, but also the songs of Gracie Fields. A typically rollicking class might include a re-enactment of the cigarette-smoking scene from "Now, Voyager" or, for a French lesson, a skit taking place in a brothel: "Pour dix francs je peux vous montrer ma prodigieuse poitrine."

Hector takes a very dim view of the exam process, and doesn't seem to think it matters very much whether the boys go to Oxbridge or not. "I count exams, even for Oxford and Cambridge, as the enemy of education," he says at one point. "Which is not to say that I don't count education as the enemy of education, too."

Hector belongs, in short, to the great tradition of memorable, idealistic and life-altering schoolteachers, in the same company as Mr. Chips, Miss Jean Brodie and the Robin Williams character in "Dead Poets Society." That's both his appeal — especially in our age of results-oriented education — and his limitation. He's the teacher we all wish we had, including the Oxford-educated Mr. Bennett, who has said he wrote the play in part because no such figure had ever turned up in his classes at a Leeds grammar school not unlike the one in "The History Boys."

And then there is Mrs. Lintott, who stuffs her pupils so full of facts that they invariably excel at their A-levels — the equivalent of our Advanced Placement tests. She gets the fewest lines and the shortest shrift but is also the least fragile of the characters and the most contemporary figure at an institution that seems a little otherworldly, more 50's than 80's — the kind of school where the fumbling gropes of a closeted gay teacher are genially tolerated by the students, if not the administration, and where, amazingly, no one listens to rock music.

Irwin isn't an anachronism exactly; he's just so slick that these days he wouldn't be caught dead in a classroom. He'd work for IvyWise helping students enhance their portfolios and add contrarian, attention-getting touches to their personal essays: "Why Flunking Driver's Ed Was Good for Me."

Mrs. Lintott's position is a somewhat unfashionable one both in the play and in real life these days, where mere competence sometimes seems undervalued. She is not a particularly exciting teacher, we gather, just a highly effective one. Her great virtue is the way she suggests to the boys on the stage and the grownups in the audience that education has its limitations. If you don't get into one college, she reminds us, you will almost certainly get into another, and while education may be a necessary preparation for life, it is in no way a substitute for it.

In every high school there are students who are culturally and intellectually superior but socially aggrieved. These high school culturati have wit and sophisticated musical tastes but find that all prestige goes to jocks, cheerleaders and preps who possess the emotional depth of a cocker spaniel. The nerds continue to believe that the self-reflective life is the only life worth living (despite all evidence to the contrary) while the cool, good-looking, vapid people look down upon them with easy disdain on those rare occasions they are compelled to acknowledge their existence.

These sarcastic cultural types may grow up to be rich movie producers, but they will remember their adolescent opposites and become liberals. They may grow up to be rich lawyers but will decorate their homes with interesting fabrics from the oppressed Peruvian peasantry to differentiate themselves from their jock opposites.

In adulthood, the former high school nerds will savor the sort of scandals that befall their formerly athletic and currently corporate adolescent enemies — the Duke lacrosse scandal, the Enron scandal, the various problems that have plagued the frat boy Bush. In the lifelong struggle for moral superiority, problems that bedevil your adolescent opposites send pleasure-inducing dopamine surging through your brain.

Similarly, in every high school there are jocks, cheerleaders and regular kids who vaguely sense that their natural enemies are the brooding poets who go off to become English majors. These prom kings and queens may leave their adolescent godhood and go off to work as underpaid sales reps despite their coldly gracious spouses and effortlessly slender kids, but they will still remember their adolescent opposites and become conservatives. They will experience surges of orgiastic triumphalism when Sean Hannity eviscerates the scuffed-shoed intellectuals who have as much personal courage as a French chipmunk in retreat.