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Benito comments on Rationality Quotes April 2014 - LessWrong
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So you wanted to know not how to derive the solution but how to derive the derivation?
I wouldn't blame the teacher for not going there. There's not enough time in class to do something like that. Bringing the students to understand the presented math is hard enough. Describing the process of how this math was found, would take too long. Because especially for harder problems there were probably dozens of mathematicians who studied the problem for centuries in order to find those derivations that your teacher presents to you.
Derive the derivation? Huh? And you say that's different from 'understanding' it. No, I just didn't have the most basic of intuitive ideas as to why he suddenly made an iterated equation, and I didn't understand why it worked, at any level. It was all just abstract symbol manipulation with no content for me, and that's not learning.
Furthermore, he does have the time. We have nine hours a week. With a class size of four pupils.
He may actually not know. People who teach maths are often not terribly good at it. Why don't you post the equation and the thing he turned it into? One of us will probably be able to see what is going on.
In all fairness, at university, being lectured by people whose job was maths research and who were truly world class at it, I remember similar happenings. Although they have subtler ways of telling you to shut up. Figuring out what's going on between the steps of a proof is half the fun and it tends to make your head explode with joy when you finally get it.
I just gave a couple of terms of first year maths lectures, stuff that I thought I knew well, and the effort of going through and actually understanding everything I was talking about turned what was supposed to be two hours a week into two days a week, so I can quite see why busy people don't bother. And in the process I found a couple of mistakes in the course notes (that of course get passed down from year to year, not rewritten from scratch with every new lecturer).