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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)

#41

Post by contrarian1234 »

mnl wrote: post #22
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…

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 3Blue1Brown) Math videos? it's really apparent there is a LOT of room for improvement in pedagogy.

As the linked PDF illustrates, most people are teaching along a set formula and sequence of concepts. Good teachers will try to tweak and iterate on these formulas and evolve a better curriculum that sinks in better for students.

Naturally as time goes on, if each author has to start from scratch, then it becomes harder and harder to beat "the best book on BLAH" from the last 100 years. (Though I refuse to believe it's a monumental task to write a better textbook than Rudin)

If you have open copy-left books, then in theory people could start with a Rudin, fork it, tweak it and improve it. 70 years of improvement could yield some amazing forks!

"Often newer editions actually worsen textbooks"

That's typically because they select a random new author to in-effect update their copyright date.. and the new author is rarely of the same caliber as the first

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

#42

Post by zozbot234 »

zzbn00 wrote: post #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.

Exams are ultimately for the students' collective benefit; they ensure that lecturers are teaching effectively, with good learning outcomes. If you're someone who "just wants to learn" and don't care for the rigor of a full Math/Physics curriculum, that's one thing. But if you do care, exams are great.

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

#44

Post by throwaway98797 »

SaintRomuald wrote: post #33
siftrics wrote: post #15

Earlier quoted context omitted.

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?

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…

no one is there to give you anything

they are there to give you a chance

maybe it is impossible for you to do this, but it’s clearly not impossible for others

that challenge is valuable information

maybe a different area is a better pursuit for you

or maybe a better way to view learning

good luck

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

#45

Post by distcs »

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?

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 fuzzy feeling of having learned something cool but in reality that warm fuzzy feeling was not good enough for solving actual exercises that come in textbooks or really deeply understand the material.

I've given up on these online learning media. Back to textbooks. The difference is like night and day.

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

#46

Post by pif »

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.

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

#47

Post by andyferris »

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…

Hmm - I do wonder if for very particular things in physics their heyday has come and gone? Were there more ridiculously talented inviduals deeply steeped in classical mechanics and discussing amongst themselves in the past? I feel modern physicists move onto high-energy phyics or low-energy physics research pretty early in their careers...

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

#48

Post by zozbot234 »

eigenket wrote: post #40
ajkjk wrote: post #32

Earlier quoted context omitted.

Yeah it's not rigorous. The tragedy is that the organizations responsible for teaching math, like how to do it and how to understand things mathematically, for other purposes , would rather waste their time on rigor. No problem with there being a rigorous math department. For mathematicians. But, quite literally, no one else cares. Mathematicians and everyone else are at crossed purposes, and the mathematicians are w…

I quite strongly disagree with this. Mathematicians aren't rigourous just for the hell of it. We have examples where a lack of rigour caused a bunch of people to waste a bunch of time working of stuff that ultimately didn't work at all. For example the Italian school of algebraic geometry caused the waste of legitimately decades of work by many people because the foundations weren't right: https://en.wikipedia.org/wi…

On the other hand, if you want full and complete rigor that means formalizing things in a computer-based proof checker. Now, that can often reveal ways to refactor the argument into a cleaner, more elegant, more intuitive proof, which is why full formalizations are often regarded as publishable work - but the other side of it is that dotting all the i's and crossing all the t's does take a whole lot of effort since some published proofs are not nearly as clear as they're supposed to be.

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

#49

Post by baz00 »

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…

I don't think it's that at all. The real cause is just some entirely institutionalised academics wrote the textbooks and everyone else is copying it rote as if it's the way of doing everything because that's all they know.

You need people from outside the echo chamber. I found The Open University to be a considerably better education provider on that basis than the red brick I attended quite frankly. The material and tuition is far far far better.

Incidentally your point in Khan Academy is spot on. That's basically OU but the material is miles better and it actually leads to a qualification.

Example free course: https://www.open.edu/openlearn/science-maths-technology/intr...

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

#50

Post by contrarian1234 »

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 didn't mean to say videos are better - just as far as I can tell that's where the most creative new teaching techniques are on display. I'd definitely prefer they were in the written word. Especially if they were an open collaborative effort. Books are great for flipping back and forth with. You have an "ah-ha" moment and skip back several pages and reread something you misunderstood on a first read-through. It's somehow clunky and takes you out of the flow when you do it in a video.

Critically, you can read/listen to something and come away with the false impression you understand it. Sitting down and doing problem is .. not always fun.. but can be critical for the concepts to sink in. I think this is the main point of what you're saying

I could see in the future it being something like watching a video and then doing a programming exercise

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