Oral exams

One of my grad students is about to defend his PhD thesis, which got me thinking about oral exams. Most undergraduate students never experience an oral exam, but they're the best and I think fairest way to assess a student's understanding.

Usually the examining committee has several members, who each ask the candidate a series of questions. The goal is to find out the limits of the student's understanding, and the strength of oral exams is the flexibility of the questions. So when the student easily answers one question, the examiner responds with a harder question on the same general topic. If this is answered well, the next question will be even harder. Any question the candidate can't answer defines one boundary of their knowledge. The examiner responds by changing topics, again starting with an easy question and moving to harder questions if the student's answers are good, until another boundary is reached.

So taking an oral exam is a scary experience. No matter how well or how badly you are doing, you'll still spend a substantial fraction of the time dealing with questions you find very challenging, and you probably will be unable to answer some questions. But knowing that this is supposed to happen to even the best students can save you from panicking when it happens to you.