Thinking for yourself
As I recall, he was going to teach us about solubility and pH calculations. He stepped to the front of the class and said something like, "Well, I forgot my notes today, so let's see if I can re-derive everything I was going to present here instead of taking time to go back to my office to get them." Then he spent the rest of the class working through the material from (close to) first principles. By the end of the class, I understood how to do those calculations, and I remembered that for a long time, even though I never took another chemistry course after my freshman year.
More importantly, though, I understood that one can and often should work through things for oneself. For one reason, it was possible.
For another, better reason, one was arguably more able to understand a limited set of first principles in a field and then work from that understanding to solve a problem than to remember all the specialized formulas and procedures to solve any of a large set of types of problems. Besides, remembering all those formulas and procedures wouldn't help much when faced with a new problem, but remembering first principles would.
For a final reason, it would help one continue to learn in whatever situation one faced in one's career.
I was reminded of that yesterday when I read Brad DeLong's reposting of Joan Robinson's "Open letter from a Keynesian to a Marxist," as given in Mike Beggs' piece on the Jacobin blog.
I'm not here today to persuade anyone to become a Keynesian or a Marxist; I'm writing because Robinson sounds like she has the same approach as Dr. Salzberg, when she writes,
The thing I am going to say that will make you too numb or too hot (according to temperament) to understand the rest of my letter is this: I understand Marx far and away better than you do. ...
When I say I understand Marx better than you, I don’t mean to say that I know the text better than you do. If you start throwing quotations at me you will have me baffled in no time. In fact, I refuse to play before you begin.
What I mean is that I have Marx in my bones and you have him in your mouth.
Read her letter, and see what you think. Does she make sense to you about her way of knowing? She does to me, as did Dr. Salzberg.
By the way, I have no good reason to believe that Dr. Salzberg really forgot his notes that day; I fully surmise it was a pedagogical ruse to teach us exactly that message, and it worked. If he did really forget, I hope he forgot other years, too.
I noted one other paragraph in her letter: "But I want you to think about me dialectically. The first principle of the dialectic is that the meaning of a proposition depends on what it denies. Thus the very same proposition has two opposite meanings according to whether you come at it from above or from below. I know roughly from what angle you come to Keynes, and I quite see your point of view. Just use a little dialectic, and try to see mine." I think we'd be well served to think about that when we face some of the contentious issues of our time. She didn't ask him to adopt her views; she simply asked him to try to understand them, if for no other reason that it would help him understand his views, in some ways the antithesis of hers, better.