What's this have to do with lectures and my students' complaints? Well, far too often, lectures and recitation sessions are just like the conversations Steve and I had with Paul. When somebody else is presenting a detailed explanation of how they solve some problem, it's very easy to nod along and say "Yes, yes, of course, that's the thing to do." You leave the room perfectly convinced that you've understood everything, but when you try to apply what you think you know by explaining it to someone else, you find that you didn't really understand a thing.