What is a “clear understanding”?
Understanding comes in two flavors, it seems: clear and murky.
Murky understanding is when you can replicate some argument or answer, but in your heart you know you’re doing it by rote. In the worst case, if you stumble—get a word out of order, for example—you’re lost and have to start over.
Clear understanding is when you grasp the argument in its essentials and thus can deal comfortably with starting anywhere, unexpected variants, etc.
In early years I couldn’t always tell the difference. I would stop working, satisfied with a murky understanding. The problem is that a murky understanding, like sand in a sieve, can be carried a little ways, but it’s constantly draining away and when you need it, it’s gone. A clear understanding is like boxes stacked in an organized way in a storeroom: you can get what you need whenever you need it.
Getting people’s names seems related: most are satisfied with a murky understanding of a new acquaintance’s name, figuring that we’ll gradually learn it, and within ten minutes we have no idea of the name. But if one can tell the difference between a murky and a clear understanding, and makes sure s/he has a clear understanding of the name, then the name is permanently remembered. I got to understand this idea when I was working in admissions: it was important that I remember people’s names, and suddenly I could: I just opened my mind, somehow, to a clear understanding of the name.
One reason that teaching something makes you learn it well is that explaining the idea, and answering questions about it, promotes a clear understanding. Questions from students force you to come at the idea from all directions, so soon you know it in the round, as it were: rather than knowing only the initial view, from when you first approached the idea, you now can immediately recognize it from any approach, and you can even recognize it in unrelated contexts, like a familiar face in a crowd.
I’m working through the irregular preterites on this page, noting any verb in which I make an error so that I can work more on it later. By doing many of these in a row, and thinking about why they have the forms they take, I’m starting to get a clear understanding. I’m beginning to grasp the underlying patterns. Cool.
