[lordnacho]

I feel the same. How can it be that I went to a world famous institution providing 2-to-1 student-teacher ratios, but I still think the best explanations are these modern internet explanations? I guess the best explanations just bubble up in the modern environment.

> you're not supposed to learn everything in college, you're supposed to learn how to learn

But to learn how to learn, you gotta learn some things to a somewhat decent degree. I think at some point you need to have these linalg/divgradcurl things down, if only briefly. You might forget any particular topic, but if you've indexed it you should be able to pick it up again, particularly in the modern learning environment.

Just imagine coding without access to StackOverflow.

[sdenton4]

Interesting to think a bit about student/teacher ratios (STR).

The up-side is that with a low STR (2:1), the teacher can adapt to the particular strengths and weaknesses of the students, to get the best reinforcement. The /downside/ is that the students will typically also have fewer teachers overall, and are maybe stuck with a bad one. (This is the problem of bad grad school advisors in a nutshell...) In this world, teachers are very expensive, though, so we end up with students competing for access to good teachers, by paying super-high tuitions, dedicating their early childhood to olympic-level basketweaving, etc.

In the medium-STR regime (30:1 or 100:1), we get the worst case: There's no teacher adaptation to individual students, but teachers are still the bottleneck.

The internet has something to say about extremely high STR (1MM:1). In this regime, things flip and any teacher can teach every student: Teachers are no longer scarce, and so have to compete on giving the best instruction. Instruction quality increases as a result. And on the flip side, there's no student competition, which /maybe/ causes student quality to drop.

[mywittyname]

> which /maybe/ causes student quality to drop.

Not maybe. Absolutely. Even paid-for online courses have a relatively high drop out rate.

But that's okay. It's the price to pay to achieve the volume needed to pay for great instruction. I can take a music theory class from an instructor who would never waste their time teaching someone like me. Even though I may not get much more than entertainment value from it. I'm effectively subsidizing the students who do learn something concrete from the course.

There might be an argument to be made that pandering to an "edutainment" crowd might reduce the quality of instruction, but a good instructor should be able to find the right balance.

[MontyCarloHall]

The latter regime is less a function of the ratio itself and more a function of the total number of accessible teachers, and the ability to switch teachers at will to find the one most suited to your learning style. If a university had 100 teachers all teaching the same course in the low or medium STR regimes and students were able to easily swap between teachers at will, the effect would be the same.

[sdenton4]

The ratio is really what matters more than absolute numbers; it tells us where the bottleneck is (supply or demand).

If the STR is 2:1 and you've got 1000 teachers, it means you've got 2000 students. If only 5% of teachers are good (see: sturgeon's law), you've still got competition centered on the student side, as 2k students fight to get into the classes with the 50 good teachers.

[MontyCarloHall]

Ah, I get your point now. In my hypothetical example, you could still have those 2000 students enrolled with only the 50 good teachers. The overall STR would still be 2:1, but most of the teachers would have no students, so the effective STR would be 40:1.

The main thing distinguishing online education is the ability for students to all flock to the good teachers and completely abandon the crappy ones.

[hasmanean]

The flip is an emergent property of the 1 Million to 1 student teacher ratio.

[SavantIdiot]

> Just imagine coding without access to StackOverflow.

That was the beginning of my career in the PC industry!

C compilers for PCs were in their infancy, so all of the code I was writing was x86 assembly using MASM 6 on MS-DOS 5.2 (hello TSRs and config.sys).

I forget the company, but some tech house published a giant 500 page PC encyclopedia every year that listed all of the x86 CPU instructions, IO ports, interrupts, DOS interrupts, etc. The last issue I had was white with pink lines on it and weighed about 3 kilos! Then the internet showed up and that all went away.

Well, except the mentors. Mentors will always be a step-function way to learn new material.

[nimish]

Turns out that mathematics pedagogy is poor, in general. Especially for geometry and vector calculus, where it's either obsolete, busted systems or incredibly abstruse ones.

Skipping over div/grad/curl and Gibbs-Heaviside vector calculus by going straight to differential forms and Clifford algebras (geometric calc) would save a bunch of heartache and pointless effort.

Linear algebra is essential since the whole point of differentiation is to construct linear approximations of functions...among other things.

[pfortuny]

Honest question. 2-to-1 student-teacher ratio?? Where is that? Totally stunned.

[ectopod]

Oxford tutorials do this. They typically have one, two or three students.

[sideshowb]

Cambridge also

[lordnacho]

Oxford, and the place out in the marshes.

It's not that there aren't massive lectures, tutorials are in addition to those.

Not bad value actually, despite what I said earlier. You do get to ask about whatever your mental block is, and the tutor is gonna know. But studying is time consuming, an hour is not as much time as it seems. You probably learn the most on your own, which nowadays ought to mean on the internet.

[nimish]

Yeah, the idea was/is that you spend 5-10hrs studying for every hour in tutorial. You got what you put in.

[pfortuny]

Oh I thought it was accross the pond. I knew about Oxford etc. but for whatever reason I took it to be in the Colonies.

[lordnacho]

On that side I suspect some of the smaller liberal arts colleges are your best bet for small classes. But I'm no expert on the overseas possessions.

[mensetmanusman]

The answer is statistics: what is more likely, that the best explainer of a certain topic is within a group of people you have access to, or that person is somewhere else in the world?

This is very analogous to the problem industrial research groups face trying to answer a certain problem, e.g. ‘how do we ensure that our team is the most likely to solve a particular problem first?’

This is why start up acquisitions are so common even among the best funded tech companies.

[lordnacho]

Might also have something to do with the explanation size: this Poisson thing is one little thing. With the internet, it's perfectly acceptable to just do a blog post on one little thing.

Previously, if you were to write a textbook or teach a tutorial, you needed to teach a bunch of things.

So in the internet age there's a bunch of fine grained "best explanations" coming from a variety of authors that beats the best that one guy can do across a range of topics.

[lanstin]

You are assuming that the best explanation can be given without interaction. I don’t have to be a great explainer but only have enough social skills to do an iterative search thru explanations, using my learning friends face and questions as metric, and find a very good explanation for that person at that time. If but only if they missed some but of linear algebra, i can sketch it out. And while Many people learn well by listening and note taking, many others also learn well by doing. We have documents and so on at work but when I see a good PR then I know the message is understood.

Start ups are better than large companies not because the people are so much smarter, but because the structure enables for so much more rapid learning and search of the solution space.