Richard Feynman relates an amusing story in his book, "Surely you’re Joking, Mr. Feynman" that describes some fellow students amazed by his "discovery" that the lowest point of a french curve has a tangent that is horizontal. None of them realized this was the definition of the lowest point! He then says:
I don’t know what’s the matter with people; they don’t learn by understanding; they learn by some other way—-by rote, or something. Their knowledge is so fragile.
Nothing is the matter with people, they have just been trained that rote memorization of facts and recipes is the easiest way to perform well in an academic setting. As an instructor my goal is to set up a classroom environment that encourages and rewards true understanding, while discouraging rote memorization. I want to harden fragile knowledge and make it robust.
I try to create in the course an atmosphere in which it is safe, even encouraged, to admit when you do not understand. I believe that admitting ignorance is the first step to gaining understanding. This can be difficult for many reasons: fear of ridicule, ego, even worry that it will affect a grade in the course. Modeling this behavior is an important, if humbling, step. Even after teaching several years of introductory physics, my students can still ask me questions that point to the limits of my understanding. Letting them know, by example, that it is all right to say, "I don’t know," and then demonstrating how to find the answer is an invaluable lesson for them.