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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)

#101

Post by Workaccount2 »

ajkjk wrote: post #16
thorin wrote: 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.

Many math teahcers (and likely mathematicians) could not care less about the real world applications of math. My college calculus teacher had no interest in physics or science. She liked math in the same way someone would like doing a crossword or Sudoku. A puzzle game with a well defined rule set and the challenge of finding answers.

I cannot overstate how destructive this is, because it basically presents math as this arbitrary logic game rather than as a fundamental language of the universe.

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

#102

Post by jlokier »

pif wrote: post #78
michaelcampbell wrote: post #68

Earlier quoted context omitted.

> > 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.

???

For what it's worth, I was a researcher at CERN with colleagues from multiple countries, where I turned down an offer to do a PhD in particle physics :-)

(A foolish career decision in retrospect.)

I think they are saying that if you were clever enough to do physics at that level, you wouldn't understand the problem being discussed. So when you said you don't understand, you gave a live demonstration.

When you emphasised your physics credentials as if to say the above didn't make sense even to a physics-smart and well-credentialed person, that pattern-matched even more strongly with the idea that those who go far through higher education institutes don't relate to the problem so don't tend to work on improvements.

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

#103

Post by BobaFloutist »

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…

Why should pedagogy ever end? That's like saying at some point in health care medicine must end and you're responsible for your own treatment. What are the professors for, doing research and abusing their grad students?

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

#104

Post by zopa »

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 outweighed by the objectively superior education you’ll have provided with your bold new approach, and maybe not.

Not that we should give up and resign ourselves to outmoded received pedagogy, but these are hard breaking changes and we should set our expectations accordingly.

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

#105

Post by BobaFloutist »

hoseja wrote: post #85
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…

The problem is that the pedagogy, as in, the best most effective way to teach people things, should improve massively in 70 years. Whether it actually does, that is another question.

The problem is, like many social sciences, people refuse to apply the scientific method to pedagogy and would rather lean on vibe-based "theories".

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

#106

Post by sheepshear »

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…

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.

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

#107

Post by quacked »

acjohnson55 wrote: post #96
quacked wrote: post #53

Nearly every educator I've ever learned from has unconsciously insisted that learning material remain sterile, and never become as funny and opinionated as this essay. For most students, "learning" is outrageously boring until you get out of college (or into graduate school) and suddenly learn through essays and memoirs that what was presented to you for 12-16 years in a bone-dry format as established gospel truth wa…

> Nearly every educator I've ever learned from has unconsciously insisted that learning material remain sterile, and never become as funny and opinionated as this essay. As a former teacher, I think the reason for this is the educational system as we know exists to (attempt to) have reproduceable learning outcomes, at scale. We try to transmit the hard-won knowledge of centuries of geniuses into the minds of adolesce…

I couldn't agree more with you. I personally will attempt to circumvent "boring, mildly effective education" by homeschooling my children (who are at present still too young to even speak in words), but homeschooling is an ugly compromise to a stupid problem. A true comprehensive education would take place everywhere in society.

Have you ever read Ivan Ilich? I find his style almost too iconoclastic for even my contrarian tastes, and I can't stand his sentence structure. But he makes some very coherent points about exactly what you're talking about. John Gatto is a former teacher who writes in a somewhat less brazen style but keeps a lot of the same opinions. It was actually on HackerNews where I first read "the seven-lesson schoolteacher".

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

#108

Post by Chabsff »

starcraft2wol wrote: post #94
marcosdumay wrote: post #90

Earlier quoted context omitted.

I'd say that the Fourier Transformation doesn't belong in the calculus program at all. It should be taught in linear algebra, where it does not only make sense, but is a non-trivial example of application that the textbooks have so little of.

You need analysis to make sense of infinite series, indefinite integrals, exponential functions, etc.

At the end of the day, analytical Fourier analysis doesn't get nearly as much practical use as numerical approaches, and you don't really need THAT much background to make sense of DFTs.

I know that, for myself, revisiting Fourier Analysis after going through DFTs in my numerical analysis classes made a lot more sense, and I kinda wish I had started with that angle in the first place.

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

#110

Post by dooglius »

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…

One argument TFA makes is that a lot of the material is not ever subsequently used.
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