↑ comment by richard_reitz ·
2015-01-02T17:45:23.427Z · LW(p) · GW(p)
There's two problems here. First, we have duplication of labor in that we have something like 1% of the population doing essentially the same task, even though it's fairly straightforward to reproduce and distribute en masse after it's been done once. This encompasses things like lesson plans, lectures, and producing supplementary materials (e.g. a sheet of practice problems).
This leads into the second problem, which is a resulting quality issue: if you have a large population of diverse talent doing the same task, you expect it to form some sort of a bell curve. As noted above, we can take any lecture, tape it, and broadcast in en masse fairly easily. When we choose a system where each student is subjected to their instructor's particular lecture, a relatively small portion of them get an excellent lecture, a very large portion get an average lecture (rather than an excellent lecture), and a relatively small portion get an execrable lecture (rather than an excellent lecture). If you're really ambitious, you could even get the top, say, ten lecturers together and have them collaborate to make a super-lecture, and then get feedback on that particular unit, so they can improve the superlecture into a super-duperlecture.
(IMO, this is still a suboptimal way to do things. Try that process on textbooks (which are much easier to write collaboratively), and instead of getting feedback on hour-long chunks, get feedback on section-sized chunks (which, depending on the subject, can something like one-tenth the size). A good textbook is also cheaper to write, cheaper to distribute, more updateable, and better didactic material to begin with.)
It's worth noting that there's still a few wrinkles. Most importantly, there's really no such thing as a "best" lecture, lesson plan, problem set, or textbook; the "goodness" quality depends, not just on the lecture's content, but the intended audience. Think of this as a callibration issue. For instance:
Last I checked, MIT uses Sadava as their introductory biology textbook. If you dig around the reviews, you will find endorsements of another introductory biology book by Campbell that claim it's "SO much easier to understand. It's better organized, more clearly written". When I found myself needing to relearn introductory biology (this time with Anki so I actually retain the knowledge), I tried Campbell, since that's what my high school used, but gave up not halfway through the first chapter, frustrated by the difficulty I had understanding, the poor organization, and unclear writing; I find Sadava, however, to be much easier to understand, better organized, and more clearly written. Is the quoted reviewer lying, perhaps paid off by Big Textbooks? Perhaps, but a much better explanation is that Sadava is more technical; it's much closer to the "definition-theorem-proof" feel of a math text. This makes it a fantastic text if you're most students at MIT (or a typical LWer), but much less so if you're in the other 99% of the population. This also solves the callibration problem: write two (or more) supertextbooks.
(This also neatly explains why MIT sometimse seems like the only school that uses good textbooks and why SICP only has 3.5 stars on Amazon.)
A second wrinkle is individual attention, which I tend to be dismissive of (if the textbook is good enough, you shouldn't need any individual attention! And it's not like the current education system, with its one-way lectures, is very good at giving very much individual attention), but if we're optimizing education, there probably is more individual attention given to every student. However, because of reasons, I suspect that most of it should come from students in the same class, not staff. Also, it belongs after the reading.
A third wrinkle is a narrowing of perspectives. In any particular domain, there's usually several approaches to solving problems, often coming from different ways of looking at it. In the current system, if you wind up on a team and come across a seemingly intractable problem, there's a good chance that someone else has happened across a nonstandard approach that makes the problem very easy. If we standardize everything, we lose this. This is somewhat mitigated by the solution to the callibration problem, wherein people are going to be reading different texts with the different approaches because they're different people, but we still kind of expect most mathematicians to learn their analysis from super!Rudin, meaning that they all lack some trick that Pugh mentions. The best solution I have is to have students learn in the highly standardized manner first, and once they have a firm grasp on that, expose them to nonstandard methods (according to my Memory text, this is an effective manner for increasing tranfer-of-learning).
Replies from: gedymin, adamzerner
↑ comment by gedymin ·
2015-01-02T18:04:49.135Z · LW(p) · GW(p)
A good writeup. But you downplay the role of individual attention. No textbook is going to have all the answers to questions someone might formulate after reading the material. They also won't provide help to students who get stuck doing exercises. In books, it's either nothing or all (the complete solution).
The current system does not do a lot of personalized teaching because the average university has a tightly limited amount of resources per student. The very rich universities (such as Oxford) can afford to give a training personalized to a much larger extent, via tutors.
Replies from: richard_reitz
↑ comment by richard_reitz ·
2015-01-03T04:41:01.635Z · LW(p) · GW(p)
Yeah. I've taught myself several courses just from textbooks, with much more success than in traditional setups that come with individual attention. I am probably unusual in this regard and should probably typical-mind-fallacy less.
However, I will nitpick a bit. While most textbooks won't quite have every answer to every question a student could formulate whilst reading it (although the good ones come very close), answers to these questions are typically 30 seconds away, either on Wikipedia or Google. Point about the importance of having people to talk to still stands.
Also, some textbooks (e.g. the AoPS books) have hints for when a student gets stuck on a problem. Point about the importance of having people to help students when they get stuck still stands, although I believe the people best-suited to do this are their classmates; by happy coincidence, these people don't cost educational organizations anything.
I'm tinkering with a system in which a professor, instead of lecturing, has it as their job to give each of 20 graduate students an hour a week of one-on-one attention (you know, the useful type of individual attention), which the graduate student is expected to prepare for extensively. Similarly, each graduate student is tasked with giving undergraduates 1 hour/week of individual attention. This maintains a professor:student ratio of 200:1 (so MIT needs a grand total of... 57 professors), doesn't overly burden the mentors, and gives the students much more quality individual attention than I sense they're currently getting. (Also, I believe that 1 hour of a grad student's time is going to be more helpful to a student than 1 hour of a professor's time. Graduate students haven't become so well-trained in their field they're no longer able to simulate a non-understanding undergrad in their head (an inability Dr. Mazur claims is shared among lecturers) and I expect there's benefit from shrinking the age/culture gap. Also, no need to worry about appearing to be the class idiot in front of the person assigning your grade and potentially not giving you the benefit of the doubt on account of being the class idiot.) (Also, it has not escaped my attention that this falls apart at schools that are small or don't have graduate students. And there's other problems. Just an idea I've had floating around that may be enough in the right direction to effect a positive change.)
↑ comment by adamzerner ·
2015-01-02T18:36:57.796Z · LW(p) · GW(p)
As for your point about quality I sense that it'd be inefficient to just take the lectures at the top of the bell curve and distribute them. I sense that it'd be more efficient to pool resources and "have them collaborate to make a super-lecture, and then get feedback on that particular unit, so they can improve the superlecture into a super-duperlecture".
Could you elaborate a bit on this?
Note: I agree with you about the wrinkles and I think they need to be accounted for. This may be oversimplified, but I think of it as a spectrum of how much you pool resources. The wrinkles explain why it isn't best to simply pool all resources. However, I think we both agree that right now we're hardly pooling resources at all and that we should be way more towards the side of pooling. I sense that talking about the wrinkles may be distracting from the core point of "why do you receive gains from pooling", but if you disagree please do what you think is best.
Replies from: richard_reitz
↑ comment by richard_reitz ·
2015-01-03T04:26:01.711Z · LW(p) · GW(p)
The argument goes "paying 20k camera-people for one year can replace 2M full-time equivalent jobs next year, which can either go into something more useful without changing anything else (1). Of course, once you're going to do that, you'd do well to look into seeing what elements of anything else could be changed to make it even more awesome."
If we optimize properly, I believe we wind up open-sourcing textbooks, somewhat like Linux. We have a core textbook, which has recieved enough feedback to make sure that everything is explained well enough that students generally don't come away with misconceptions, but because they're open source, every time you need to write for a particular audience, you have something to work from. LaTeX also supports comments, which makes it easy to include nonconventional perspectives for interested students (i.e. the ones who really need them).
But, yeah, pooling resources. Definitely something we should do more of and WHY HASN'T THE FREE MARKET SOLVED THIS 10 YEARS AGO?
(1) Fermi estimate is as follows: Cursory search indicates Harvard offers a bit over 3k undergraduate classes. Round it up to 5k to include secondary school and the few undergraduate courses not offered at Harvard (for instance, I can't find an equivalent to 8.012.) Multiply by 4 for different levels, and we arrive at 20k camera-people needed to tape all these courses. (It's actually less than that, since most courses are one semester.)
Cursory Googling indicates there are 3700k teachers in America; add in other English-speaking countries and eliminate primary- and graduate-level teachers should bring you to 4M teachers (I'm guessing that we add more teachers from English-speaking countries than we lose from not considering primary- and graduate-level teachers, since most classes are at these levels.) Assume that half their teaching job is replaceable by the videos we've created, and we've freed up the equivalent of 2M full-time jobs.
This is very much a Fermi estimate, but I feel I was liberal enough with the camera-people portion (we're only hiring them a few hours a week!) to say that the cost of getting high-quality video of all secondary and undergraduate courses is 1% of the savings it should theoretically yield every year in the future. This upper limit goes down once we start writing textbooks instead of taping lectures, especially since most secondary and undergraduate courses already have very good textbooks to work from.