Ahem...so I guess that a few of you (Kevin, HardDaysNight) knew it was a trick question and answered correctly, from the rare offensive skier's point of view. (Way to get out of the box, guys!)
For everyone else who assumed that if you don't turn, you'll just gain speed, at least until you reach terminal velocity, reread HardDaysNight's post. Note that I said nothing about which direction you were going in. If you assumed that you'd be going downhill, or at least didn't even question that, consider that you just might be in the old "conventional wisdom" box that could confine you to defensive skiing until you allow yourself to believe that direction and line are a choice, not a necessity. Uphill is just as possible as downhill.
Indeed, my two favorite words in skiing are "GO" and "uphill." Sounds odd, perhaps--after all, we call it "downhill skiing," don't we? But really, I get little joy out of going downhill. To me, going uphill is far more fun, and I go downhill only to gain the speed that allows me to glide further uphill. I know, sounds even odder now, doesn't it? But as I've noted before, it's like swinging on a swing when we were kids. What were you trying to do then? If you're like most of us, you were trying to go UP, not down. You'd go up until you stalled, feeling that sensational light, floating, weightlessness, and then the swing would dive back down. You'd "pump" it to try go even higher the next time--higher, higher, higher! The thrill was in the effortlessness and glide at the top, and the "down" part was important only to get the speed to go higher.
Offensive skiing--skiing the slow line fast--is like that, including the gliding, the effortlessness, the weightlessness and floating, and the exhilaration of flying. In some situations like halfpipes and natural gulleys, the analogy seems obvious. On flat runs, you may have to turn back up the mountain to go uphill, but the idea is the same. You may not always actually make it so far through a turn that you're going uphill, as friction, skidding, and so on fight against your speed even when you try to minimize them. But the goal is identical, and the outcome is just as sensuous!
FatOldMan--you have definitely "got it"! And your students are fortunate.