I've been reading Errol Morris' 5-part essay on not knowing what we don't know. The technical term is the Dunning-Kruger effect: our own stupidity hides our ability to know we're stupid. The classic example they site is of bank robber McArthur Wheeler, who thought that putting lemon juice on his face would make his face invisible from video cameras...
We say that one mark of an intelligent person is that they know what they don't know, but how is this possible?
Perhaps the smartest thing Donald Rumsfeld said was "There are known unknowns. That is to say, there are things we now know we don’t know. But there are also unknown unknowns. These are the things we do not know we don’t know."
Morris decides: "Using the expressions “known unknowns” and “unknown unknowns” is just a fancy — even pretentious — way of talking about questions and answers. A “known unknown” is a known question with an unknown answer. I can ask the question: what is the melting point of beryllium? I may not know the answer, but I can look it up. I can do some research. It may even be a question which no one knows the answer to. With an “unknown unknown,” I don’t even know what questions to ask, let alone how to answer those questions."
How can students recognize the differences between known unknowns and unknown unknowns?