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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)

#141

Post by mnl »

sheepshear wrote: post #106
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…

Your response does a pretty good job demonstrating the internal challenges universities face. The interest in making a change was motivated by unmet needs, and it's not going away until those needs are met. The only way to deal with people who won't meaningfully engage in the problem solving process is to go around them.

A textbook should be provided for reference. Copying its contents on a blackboard isn't teaching. You still have to design your course. There's goals to meet, you have to evaluate where your students come from and your job is getting them there.

Besides pedagogy, in college you have to respect your students as studying adults and give them a proper bibliography, emphasizing references for independent study if they don't like your lecture notes, nor your approach, nor whatever.

I understand what a university is, I also understand and am qualified in secondary education and it would be incredibly depressing turning colleges into extended high schools because of business models. That would be exploiting students, I never agree with that.

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

#142

Post by kriops »

meroes wrote: post #139

How math relates to the physical world is not at all clear. Like yes 2 apples clearly makes sense, but non physical quantities like 10^241 of anything start to break down the relationship. It’s not the abstraction that gets me usually, it’s the lack of an explicit relationship between math and physics. I’m sorry but personally I am not satisfied by what I learned in my math and math/science classes on this. It starte…

Can you elaborate on why you describe 10^241 as non-physical? Just because it's too large to describe anything physical?

Anyhow, Aristotle had another take on the problem of universals, and taking his view that every concept abstract or otherwise can only exist as part of our physical world (I'm not a philosopher, and there are variations on both themes that different people subscribe to), then your supposition would be nonsense in itself. Stated as a question: What is your reasoning for preferring a Plato-like model of the world vs. a Aristotle-like one?

(If it needs to be said: This is not a gotcha or anything - your opinion intrigued me, and I'm curious as to your reasoning)

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

#143

Post by da39a3ee »

threatofrain wrote: post #72
distcs wrote: post #45

Earlier quoted context omitted.

> Have you looked at for instance Khan Academy's Grant Sanderson (aka 3Blue1Brown) Math videos? I have. I went through Khan Academy, Brilliant and 3Blue1Brown. After spending more than 100s of hours I started getting the feeling that these are all good for elementary level math. But for any serious math (think real analysis, complex analysis, group theory and beyond), all these platforms did was leave me with a warm…

Note that 3B1B often warns you that his videos bring perspective for a book/class that you're doing or are already done with. And Khan Academy's focus is for K-12. If you want anything past Analysis 1 I think you'll find that universities guard their content.

> If you want anything past Analysis 1 I think you'll find that universities guard their content.

Not so; there's an absolutely vast amount of freely available undergraduate mathematics resources available at all levels. Honestly, so much that it makes it confusing to choose and not get distracted by the options -- perhaps AI-mediated distillation could be helpful in the future.

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

#144

Post by kjkjadksj »

zopa wrote: post #104
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…

Curricula are hard to change for the same reason widely-used apis are hard to change: it’s the downstream dependencies. There’s a shared understanding of what “took undergrad differential equations” means, and breaking from that has a cost. If you teach differently, your students will be at a disadvantage because they won’t know the things futre courses, tests and employers expect them to know. Maybe that will be out…

Otoh biology classes don’t suffer from this as much. Textbooks are routinely updated to reflect new understandings. Professors seem to have a lot of choice with what they cover, often highlighting their own subfield where they can speak more to it. Physics classes in comparison felt like a factory. You’d also pay twice as high a lab fee as any biology or chemistry lab to play with 40 year old brass weights and frictionless cars.

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

#145

Post by da39a3ee »

distcs wrote: post #45
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…

> Have you looked at for instance Khan Academy's Grant Sanderson (aka 3Blue1Brown) Math videos? I have. I went through Khan Academy, Brilliant and 3Blue1Brown. After spending more than 100s of hours I started getting the feeling that these are all good for elementary level math. But for any serious math (think real analysis, complex analysis, group theory and beyond), all these platforms did was leave me with a warm…

I think you're just parroting things you've heard other people say. 3b1b's videos are universally agreed to be excellent, and it's baffling that you think it is a choice between watching them and using textbook and doing the exercises. Anyone with the intellectual capacity to study that sort of material is not going to have a hard time comprehending that they are intended to be complementary, as Grant Sanderson makes very clear at numerous points.

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

#146

Post by whatever1 »

Just like solving analytically integrals, (O,P)DEs require tremendous skill of pattern matching. You need to know all of the available tricks, and pick the one that seems to fit. You test it and it just works.

No wonder there is super-high barrier of entry. And that is why us mortals are just using numerical methods instead.

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

#147

Post by da39a3ee »

starcraft2wol wrote: post #93
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…

> people continue to find new and better ways to explain and illustrate concepts I strongly disagree. All the best math and CS books I have are old. New books about old topics tend to be less informed about the context and core ideas that led to their development.

Then you are objectively wrong. Look at Grant Sanderson's explanation of introductory Linear Algebra. Very obviously it adds something good to complement the best paper textbooks on the subject.

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

#148

Post by cyberax »

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…

> Have you looked at for instance Khan Academy's Grant Sanderson (aka 3Blue1Brown) Math videos? it's really apparent there is a LOT of room for improvement in pedagogy.

There is a study showing that you actually understand material better, if you use the most primitive methods: chalkboard and a lecture. Because you are forced to visualize the material yourself, instead of being presented with a ready-made animation.

It probably makes sense to use visual aids for students that just can't grasp the concept, but I believe this will only help in elementary math.

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

#149

Post by distcs »

mindcrime wrote: post #129
distcs wrote: post #45

Earlier quoted context omitted.

> Have you looked at for instance Khan Academy's Grant Sanderson (aka 3Blue1Brown) Math videos? I have. I went through Khan Academy, Brilliant and 3Blue1Brown. After spending more than 100s of hours I started getting the feeling that these are all good for elementary level math. But for any serious math (think real analysis, complex analysis, group theory and beyond), all these platforms did was leave me with a warm…

I've given up on these online learning media. Back to textbooks. The difference is like night and day. Are there people who think this is an "either/or" choice, as opposed to a "use both" thing?? I ask, because it's pretty well established that learning is enhanced by use of multiple media types and it seems self-evident to me that books and videos are complementary.

> it seems self-evident to me that books and videos are complementary

Can't speak for others but for me it is more about efficient utilization of time rather than complementing multiple learning methods.

I've found that time spent in learning math from videos have poor return of investment. That time is better spent re-reading a chapter or that thing that I couldn't fully understand the first time and doing more exercises.

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

#150

Post by SaintRomuald »

angra_mainyu wrote: post #100
SaintRomuald wrote: post #33

Earlier quoted context omitted.

I shouldn't need to read a 500page textbook to understand a class that a teacher has been 'teaching' for 20 years. He's there to give me an understanding of the subject. I have at least 5 classes each semester which are very technical and difficult, it's impossible for me to read a textbook on each while also reading a 20-30 page lab instruction each night, all written in a technical language which I barely understan…

The entitlement in your comment is staggering... Why such a desire to be spoonfed, whining about having to put in the work?

Am I not supposed to expect a quality lecture from a university professor? I have had such a bad experience with certain lecturers, I'm certain what they were saying wasn't incorrect but the way they were speaking made it impossible to follow. It wasn't just me who thought so. I admit I've had learning difficulties my whole life but I believe it is actually impossible to learn all the material from the classes with all the details from books. You can pick a field or two which interest you the most and delve deep into the details. An extremely fundamental topic at my uni is called "introduction to circuit analysis". It was taught by a professor who was so bad at teaching it there was no point in coming to his lectures. You would learn more from watching youtube videos. Everyone was aware of the state of that class. Even our lab professors would mock his teaching style. Now if every class was like this we would be lost. I'll give a recent example of another lecturer who I also consider bad, but fortunately he is teaching an easy subject. First class a kid asks 'what's the difference between a router and a switch'. The professor answers 'a switch works on layer 2 and a router works on layer 3'. In my opinion this is a non answer. Yeah he said the truth but it didn't mean anything. If that student didn't know the difference between a switch and a router then surely he doesn't know about the ISO OSI model. Before you think he probably didn't have time to answer more specifically to make sure he understands. This guy notoriously keeps digressing from the subject. As that classes subject is one I am familiar with I knew the way he taught it was impossible to make sense of because he never answered in a concrete way, everything felt so drawn out and lacking a focal point, it's hard to describe. It took him four hours to go over the ISO OSI model and honestly while I wasn't paying attention to every single word he said. With all the digressions and constant comments about stuff you just couldn't follow his train of thought. On the contrary electromagnetism class was absolutely amazing. It's still a difficult subject, at least for me because I've always been pretty bad at physics but the lad who taught it was brilliant. He made sure we all understood, he started with very basic concepts that everyone knew, just to be certain everyone is on the same page. His presentations were concise, easy to follow with links to read up/watch stuff that you didn't fully get or wanted to learn more about. They had plenty of visualizations with gifs of stuff. It's a pleasure going to his classes. So I think that I should expect the lectures to give me an understanding of a subject. If I had to read a book for every class there wouldn't be enough time in a day for me to catch up.
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