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Lessons I wish I had learned before teaching differential equations [pdf] (1997)

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Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#11

“Why is it that no one has undertaken the task of cleaning the Augean stables of elementary differential equations? I will hazard an answer: for the same reason why we see so little change anywhere today, whether in society, in politics, or in science“ I see a lot of parallels with the Physics department and I think the reason is much more depressing. Both fields embrace a sort of masochism and active desire to keep…

Just out of curiosity, what was that classical mechanics textbook?

Goldstein?

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#12
post #6
post #5

Earlier quoted context omitted.

> I had a lot of hope for things like Khan Academy, but the issue is video is not text and it's hard to iterate and improve on When the entire video is generated by an AI, that dynamic changes. It's no issue to improve "the script", and have it seamlessly regenerated. We can't be that far away from this capability, and it could have a profound impact on available learning resources.

The problem isn't writing a better text, it's having departments willing to teach it, or to try alternate approaches at all.

The OP referenced the Khan Academy as an attempt to displace the ossified educational institutions we have. But it has its own limitations and challenges, some of which will soon be rendered moot by the coming wave of AI technologies, perhaps giving it the final push it needs to truly take hold.

Can imagine a world where it doesn't matter where or how you get your education, all that matters is that you can have your knowledge verified by an accredited _testing_ institution. This would open education up to a world of creative competition for students, and allow individuals to find a learning paradigm that best works for themselves.

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#13

Previous discussion from 2022... https://news.ycombinator.com/item?id=32530035

They talk (rightly) about mathematics replacing infinitely small but not 0 numbers with limits there. Infinitesimals were later reintroduced with rigor through https://mathworld.wolfram.com/NonstandardAnalysis.html

I have long thought such would be easier to work with on modern computers.

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#14
If when I started learning about calculus at 14/15 someone had explained why we were doing this it would have made it so much less confusing. Explaining in terms of speed/distance/acceleration seems to make complete sense now (one of several potential examples). However discussing a function and talking about splitting in into small (infinitesimal) strips of delta quantities and a list of equations / proofs made it completely dry and uninteresting. I don't think I had any ideas one what was going on until it was mentioned in physics several years later.

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#15
post #6
post #5

Earlier quoted context omitted.

> I had a lot of hope for things like Khan Academy, but the issue is video is not text and it's hard to iterate and improve on When the entire video is generated by an AI, that dynamic changes. It's no issue to improve "the script", and have it seamlessly regenerated. We can't be that far away from this capability, and it could have a profound impact on available learning resources.

The problem isn't writing a better text, it's having departments willing to teach it, or to try alternate approaches at all.

You have to have a pretty helpless attitude to blame someone else (teachers) on your inability to learn from a good textbook.

How are you ever going to learn anything truly novel in the world if you always delegate teaching to a teacher?

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#16
post #14

If when I started learning about calculus at 14/15 someone had explained why we were doing this it would have made it so much less confusing. Explaining in terms of speed/distance/acceleration seems to make complete sense now (one of several potential examples). However discussing a function and talking about splitting in into small (infinitesimal) strips of delta quantities and a list of equations / proofs made it c…

Physics doing the work of actually teaching math is a universal embarrassment to math departments. Or, well, it should be.

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#17
Nicely written. But isn't a corollary that we should stop exams in Maths (and Physics/etc/etc) degrees and just teach people who want to learn, how much they want to learn?

Exams are for people designing bridges and doing surgery. Basic science just learn and start doing some to see if it is for you.

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#19
post #16
post #14

If when I started learning about calculus at 14/15 someone had explained why we were doing this it would have made it so much less confusing. Explaining in terms of speed/distance/acceleration seems to make complete sense now (one of several potential examples). However discussing a function and talking about splitting in into small (infinitesimal) strips of delta quantities and a list of equations / proofs made it c…

Physics doing the work of actually teaching math is a universal embarrassment to math departments. Or, well, it should be.

I remember my first calculus exam at the University: I made a lot of explanations and justifications based of physics. Of course I did not pass. As I asked why? It was all correct, right? The prof. said “is perfect reasoning, but this is the math department, physics is one floor below”

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#20

“Why is it that no one has undertaken the task of cleaning the Augean stables of elementary differential equations? I will hazard an answer: for the same reason why we see so little change anywhere today, whether in society, in politics, or in science“ I see a lot of parallels with the Physics department and I think the reason is much more depressing. Both fields embrace a sort of masochism and active desire to keep…

> "Both fields embrace a sort of masochism and active desire to keep knowledge impenetrable b/c it acts as a mechanism to feed out the dummies. The system acts an an informal IQ test - that maintains the prestige of the departments. If you're pigheaded and clever enough to get through the masochistic torture is that their undergrad textbooks then you're probably pretty clever and so the prestige of the degrees is maintained."

So true, in many areas. I know a couple of young people that got destroyed by this kind of meat grinding machinery. Typically applies to every medical studies in France, where many kids (with parents that have the money to pay) are going to Spain, Romania or Belgium to study in a less oppressing environment and better teaching methods.

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