At the beginning of the year, I identified a few students like this in my PreCalculus class. Today, I knew I had reached some of them when two of these students, independent of each other, asked me, "Why did log(-4) on my calculator give me an error message?" It was at the end of class and it was totally unsolicited. It's a question I had planned to ask my class that day, but we ran short on time. The bell had rung and these two students stayed after the bell to ask me their question. The fact that they had the curiosity to ask that question and not dart like Pavlov's dog at the sound of the passing bell means that I have won. It means that they, too, are now winning.