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by JackFr 1154 days ago
Professor I had for Real Analysis (the second time I took it) was probably the best math professor I've ever had. He had the most extensive mental catalog of the wrong ways people could understand and the failure modes of students. When you would ask a question he was able to help, not just because he understood the material, but because he knew why you didn't.

In my evaluation of him I mentioned this, but added that he was probably wasted on 3rd and 4th year math majors, and should be teaching more intro classes where the quality of instruction was markedly worse.
2 comments
CogitoCogito 1154 days ago
> He had the most extensive mental catalog of the wrong ways people could understand and the failure modes of students.

Back when I used to teach math classes as a grad student, I realized that a teacher has to actively work to keep that "mental catalog" for students. The problem is that longer you are in the math world, the clearer the subject becomes. The result is that to you the teacher it really just becomes braindead obvious what's going on. As time goes on, you have to fight this "problem" more and more to keep touch with the issues your students are having.

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seanw444 1154 days ago
I think that applies to many topics. Maybe math more than others due to the complexity of it all, but it seems commonplace that as you become more of an expert on a topic, the more detached from "newbyism" you become. It's harder to put yourself in the shoes of a beginner to see what they're seeing and know what they're missing.
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phkahler 1154 days ago
>> When you would ask a question he was able to help, not just because he understood the material, but because he knew why you didn't.

When my high schooler come to me with math problems, the first thing I do is look at the failures and figure out what higher level step or concept is missing in the brain. Then I explain that, sometimes more than once with different approaches. Once the higher level thing clicks, I can just sit back and mostly watch.

Sometimes I'm not sure how a concept clicked, but something did and the right answers start coming out.

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