"This," says Matthew Carpenter, "is my favorite exercise." I peer over his shoulder at his laptop screen to see the math problem the fifth grader is pondering. It's an inverse trigonometric function: cos-1(1) = ?
Carpenter, a serious-faced 10-year-old wearing a gray T-shirt and an impressive black digital watch, pauses for a second, fidgets, then clicks on "0 degrees." Presto: The computer tells him that he's correct. The software then generates another problem, followed by another, and yet another, until he's nailed 10 in a row in just a few minutes. All told, he's done an insane 642 inverse trig problems. "It took a while for me to get it," he admits sheepishly.
Carpenter, who attends Santa Rita Elementary, a public school in Los Altos, California, shouldn't be doing work anywhere near this advanced. In fact, when I visited his class this spring--in a sun-drenched room festooned with a papercraft X-wing fighter and student paintings of trees--the kids were supposed to be learning basic fractions, decimals, and percentages. As his teacher, Kami Thordarson, explains, students don't normally tackle inverse trig until high school, and sometimes not even then.