Lessons I wish I had learned before teaching differential equations [pdf] (1997) • Hacker News Board

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

#61

Post by mnl » Mon, Nov 13, 2023, 1:01 PM UTC

contrarian1234 wrote: post #41

mnl wrote: post #22

Earlier quoted context omitted.

What's the problem with a good book, age? Baby Rudin's first edition is 70 and the latest one is from 1976. It's still widely used and will be for a while. Honestly your problem was that you didn't know any Classical Mechanics yet and you were assuming that the volume of recent developments made old books obsolete. Maybe in Biology, in Physics getting to recent developments would mean that you're familiar with Goldst…

You're conflating things. This issue isn't that Classical Mechanics has somehow evolved or changed. It's that people continue to find new and better ways to explain and illustrate concepts. At lest personally I don't know of any field or book where I've felt "Hmm, this is basically perfect and I can't imagine a better way to explain these concepts". Have you looked at for instance Khan Academy's Grant Sanderson (aka…

There are excellent textbooks on Classical Mechanics, probably because it's a crystal clear subject and you can give a detailed account of the essentials in a single volume without handwaving. Of course everything can be improved, but it also can be muddled. If it works think twice before fixing it. Kind of what happens with Rudin and introductory Real Analysis.

On the other hand, there's for instance Optics where you basically have to condense an encyclopaedia and there's always prettier pictures. Or Thermodynamics, Fluid Mechanics etc that can be taught in different ways depending on the curriculum.

There definitely should be pedagogical considerations in higher education, that's lacking because it's usually an afterthought. And it also should be very clear to people getting into higher education that at some later point pedagogy must end and you have to be capable of working your way through the material.

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

#62

Post by zozbot234 » Mon, Nov 13, 2023, 1:02 PM UTC

contrarian1234 wrote: post #57

JadeNB wrote: post #52

Earlier quoted context omitted.

> 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 main…

I don't think the line of thinking is directly "lets make this painful on purpose" but there is a sense of - everyone has to go through the same gauntlet and some people are just not cut out of math/physics/etc. It's just the way of the world. There is not direct desire to make the experience better/smoother/easier than it was your generation. I don't know how it is in the Math department, but in Physics there is alm…

> You're delighted at the students that have passed your IQ test. There is generally very little care given to the 70%+ of students that aren't making the cut.

That's because happy students are all alike, but every unhappy student is unhappy in their own way. It's just not feasible to care in depth about why any one of the 70%+ is not learning effectively. They're probably missing some prior topic that's effectively a prereq for the class, but that's something that should be addressed by the student themselves.

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

#63

Post by JadeNB » Mon, Nov 13, 2023, 1:06 PM UTC

contrarian1234 wrote: post #57

JadeNB wrote: post #52

Earlier quoted context omitted.

> 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 main…

I don't think the line of thinking is directly "lets make this painful on purpose" but there is a sense of - everyone has to go through the same gauntlet and some people are just not cut out of math/physics/etc. It's just the way of the world. There is not direct desire to make the experience better/smoother/easier than it was your generation. I don't know how it is in the Math department, but in Physics there is alm…

> What you should be "delighted" by is when you find a new way to explain something that resonates with most of the class

You are right, and I am! I don't think that's incompatible with also being delighted when someone shows interest or aptitude. In fact, the synergy is the best part, when someone shows interest or aptitude because they are willing to put in the work to follow the pathway that I have tried to open up for them.

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

#64

Post by HelloNurse » Mon, Nov 13, 2023, 1:09 PM UTC

monista wrote: post #37

f1shy wrote: post #19

Earlier quoted context omitted.

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”

And they were right imho. Having a clear notion of a subject is good for both physics and mathematics, but what's good for physics or engineering, is not enough for math, in math, you also need rigorous reasoning, or you'll fall into subtle mistakes.

Fundamentally, without sufficient rigor there can be no proofs; "maybe" and "someone says so" aren't good theoretical building blocks.

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

#65

Post by contrarian1234 » Mon, Nov 13, 2023, 1:09 PM UTC

mnl wrote: post #61

contrarian1234 wrote: post #41

Earlier quoted context omitted.

You're conflating things. This issue isn't that Classical Mechanics has somehow evolved or changed. It's that people continue to find new and better ways to explain and illustrate concepts. At lest personally I don't know of any field or book where I've felt "Hmm, this is basically perfect and I can't imagine a better way to explain these concepts". Have you looked at for instance Khan Academy's Grant Sanderson (aka…

There are excellent textbooks on Classical Mechanics, probably because it's a crystal clear subject and you can give a detailed account of the essentials in a single volume without handwaving. Of course everything can be improved, but it also can be muddled. If it works think twice before fixing it. Kind of what happens with Rudin and introductory Real Analysis. On the other hand, there's for instance Optics where yo…

I think you have the perspective of somehow who's succeeded in Physics. In your typical introductory physics class less than half the students will walk away with a very solid understanding of classical mechanics.

To my mind, if the textbook was actually excellent then that would be 80%+. We're nowhere near there. I think there is LOT of room for improvement

But sure.. Thermodynamics.. things could be worse :)

Sometimes things are just hard because they're complicated and you need to buckle down and learn your multiplication tables. But at least in my own life experience, the vast majority of the time things are a problem because their poorly explained - often by people that poorly understand it themselves.

Once you truly understand something inside and out - and look back on it - it all generally looks relatively simple. But it takes a special talent to be able to go back and reexplain it from the naiive perspective

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

#66

Post by quacked » Mon, Nov 13, 2023, 1:09 PM UTC

contrarian1234 wrote: post #57

JadeNB wrote: post #52

Earlier quoted context omitted.

> 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 main…

I don't think the line of thinking is directly "lets make this painful on purpose" but there is a sense of - everyone has to go through the same gauntlet and some people are just not cut out of math/physics/etc. It's just the way of the world. There is not direct desire to make the experience better/smoother/easier than it was your generation. I don't know how it is in the Math department, but in Physics there is alm…

I don't know why you're catching downvotes, I think you're completely right. In my engineering curriculum in some cases the teachers were openly hostile to students that had a hard time understanding the material.

Professors of undergraduates don't seem to think from the undergraduate perspective. Most undergrads have only ever known school, and are just following directions while fumbling their way to their first interview. From that perspective it doesn't make any sense why some classes have to be immensely difficult and high-stakes, and others can be a little easier. From the graduated perspective, you can see "the big well-intentioned lie"--in truth, no field can be condensed into 16 weeks, even if you're studying it and nothing else 14 hours per day. The more difficult a class is, the closer it is to the truth that the class itself is a carefully structured playground, and the real field is more dizzyingly wide and complex than any student can imagine. However, I don't see why this lesson has to be so painful to students.

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

#67

Post by JadeNB » Mon, Nov 13, 2023, 1:13 PM UTC

quacked wrote: post #66

contrarian1234 wrote: post #57

Earlier quoted context omitted.

I don't think the line of thinking is directly "lets make this painful on purpose" but there is a sense of - everyone has to go through the same gauntlet and some people are just not cut out of math/physics/etc. It's just the way of the world. There is not direct desire to make the experience better/smoother/easier than it was your generation. I don't know how it is in the Math department, but in Physics there is alm…

I don't know why you're catching downvotes, I think you're completely right. In my engineering curriculum in some cases the teachers were openly hostile to students that had a hard time understanding the material. Professors of undergraduates don't seem to think from the undergraduate perspective. Most undergrads have only ever known school, and are just following directions while fumbling their way to their first in…

> In my engineering curriculum in some cases the teachers were openly hostile to students that had a hard time understanding the material.

While there's no excuse for it, I think faculty see so much apathy on such a regular basis that sometimes it's easy to mistake sincere struggle for a lack of desire to engage. For precisely that reason, I try very hard to recognize and reward my students who are willing to take the time to work with me, whatever their existing comfort or proficiency level with the subject is, but I know that there are times (probably many more than I'd like to imagine) when I don't rise to that ideal.

> Professors of undergraduates don't seem to think from the undergraduate perspective. … However, I don't see why this … has to be so painful to students.

I think you might underestimate how painful it is to faculty, too! Most of us are in this for the love of our subject, and many are even in it for the love of teaching, and it's painful to have something that's so beautiful and beloved for us be the cause of suffering in others.

Anyway—while I completely agree that it would be better if the learning experience could be the joy it should be, and free of the pain that it often carries, I do wonder if some of this might be intrinsic. There are certain topics that are just difficult, and on their first encounter with which most learners will find themselves lost and confused. But those topics have to be, or are believed to have to be, understood to be successful in the field, so that loss and confusion will have to be felt some time. Isn't it better if that's in the classroom rather than on the job?

> The more difficult a class is, the closer it is to the truth that the class itself is a carefully structured playground, and the real field is more dizzyingly wide and complex than any student can imagine.

This is a beautiful description. I know as a teacher that I try to communicate this to my students, but also that I surely fail much more often than I succeed.

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

#68

Post by michaelcampbell » Mon, Nov 13, 2023, 1:14 PM UTC

pif wrote: post #46

contrarian1234 wrote: post #3

“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 I have a PhD in particle physics, and I've been a researcher at CERN with colleagues from multiple countries. And I cannot understand what you are saying there.

> > 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.

> I have a PhD in particle physics, and I've been a researcher at CERN with colleagues from multiple countries. And I cannot understand what you are saying there.

Hrm.

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

#69

Post by mnl » Mon, Nov 13, 2023, 1:18 PM UTC

contrarian1234 wrote: post #65

mnl wrote: post #61

Earlier quoted context omitted.

There are excellent textbooks on Classical Mechanics, probably because it's a crystal clear subject and you can give a detailed account of the essentials in a single volume without handwaving. Of course everything can be improved, but it also can be muddled. If it works think twice before fixing it. Kind of what happens with Rudin and introductory Real Analysis. On the other hand, there's for instance Optics where yo…

I think you have the perspective of somehow who's succeeded in Physics. In your typical introductory physics class less than half the students will walk away with a very solid understanding of classical mechanics. To my mind, if the textbook was actually excellent then that would be 80%+. We're nowhere near there. I think there is LOT of room for improvement But sure.. Thermodynamics.. things could be worse :) Someti…

I almost wrote above that, to my knowledge and IMVHO, no one has succeeded at writing a book on Thermodynamics yet. I self-censored because that would be too flippant, wouldn't it? Lmao

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

#70

Post by tux1968 » Mon, Nov 13, 2023, 1:19 PM UTC

gumby wrote: post #30

tux1968 wrote: 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.

Then you could simply read the script — no need for the video at all.

For those who prefer to read the script, of course. For those who benefit from a much more multimedia presentation, the generated video and associated generated items, will be preferable.