While I somehow managed to avoid the usual run of undergraduate psychological crises, I was once so anxious about approaching a professor about my health that I took his midterm with a temperature of over 100. In retrospect, this was not, perhaps, the most brilliant accomplishment of my undergraduate career; come to think of it, I had doubts at the time about the wisdom of my behavior. (What? Taking an exam while somewhat dizzy isn't a good idea? You don't say.) And so, in a very small way, I could sympathize with Ianqui's student. Many students have a difficult time admitting that they're running a fever on exam day, let alone that their life is imploding; who wants to deal with skeptical faculty when, for once, the sky really is falling? Moreover, I suspect some students are trying to convince themselves that they can handle everything--when, in reality, they're overwhelmed. Asking the instructor for a deferred exam or an extension on a paper would mean admitting that things are as bad as they seem. Even when you repeatedly remind students that there's assistance available if they ask for it, a substantial number don't quite believe you (or, perhaps, fear that you'll think less of them?). The results are as frustrating for the instructor as they are for the student; after all, who enjoys failing somebody who clearly ought to have done better?
