Playing a role? Yes. Becoming universal? No.

- If you're dealing with many students at once, you have to lecture some of the time. Explaining the same thing to every student, or even by small groups, simply takes too much time for the teacher, and wastes time for students that aren't getting the teacher's attention at that moment.
Of course, even giant lecture classes are typically paired with discussion sections, which are driven by student questions. Those need some mixed styles as well; left to their own devices, you'll get the same few students involved every time, and the rest passive.

- Student motivation matters. Students through high school have to be there, and some of them will always be marking time. College students can skip classes more freely, but they're still often taking it for a requirement, interested only in meeting some standard. It's very hard for a teacher to reach an unmotivated student at all. AoPS doesn't have to worry about that, by the nature of what you offer.

If your first line is referring to the role of AoPS, then I pretty much agree. We'll play a role. We won't be universal. We aren't for everyone. One of the shortcomings of the current educational system is believing that *anything* is universal.

If your first line is referring to the author of that article's view of how education will change, then again... I pretty much agree. I'm usually skeptical of "the internet is going to bring about the end of X in the near future" stories. This one is no different. I also agree that there will always be a role for lecture. But I do think that role will change. For example, the Alcumus videos are essentially lecture. But they're short and delivered on demand, with indication to the student when he/she ought is "ready" for them. As another example, cut-the-knot is essentially a collection of lectures in a different medium.

Richard,
This industrial model of education (K-12 and then the proliferation of the universities) was something America never had until it was forced upon us beginning in the late 19th century. I think the best source of how all this came about is told by John Taylor Gatto, who was a public school teacher for 30 years up in New York City (http://www.johntaylorgatto.com/). Just go to the site and read the introductory paragraphs on his newest book, "Weapons of Mass Instruction", and you get an idea of why the industrial model fails to meet the needs of our kids and whey AoPS is really an example of what education used to be like in America, albeit with the enhancements of modern technology. His book, "The Underground History of American Education" is one of the best books I have ever read. John is brilliant, I am amazed at both the research that went into "Underground History" and how he was able to take all of this information and put it into a coherent whole.
I think people confuse schooling with education. Schooling is a part of education, as education never stops (hopefully). Basically, after people finish schooling, learning becomes self-directed. People have to decide, for themselves, what they want to learn and to what depth and breadth they want to learn. They also have to self-evaluate the quality of their learning (this is another reason why I hate grades, it short circuits this process). The industrial model delays this process at best and in the worst case causes people to become too dependent on an instructor. I am not saying having an instructor is a bad idea, as they can increase the speed at which people learn, however, as far as I know most really good instructors try to move their students to independent learning as quickly as possible.
The sooner we move towards a personalized model of education (what we used to have over a 100 years ago) the better off we will be. I think AoPS offers a conceptual template of what this might look like.

I just read the Gatto book. Very thought-provoking... Maybe a dangerous book for me to read, but it helped bolster my conviction that we need to hire someone to focus on Alcumus, at the very least...

Murray Rothbard made some arguments very similar to Gatto's in "Education: Free and Compulsory" http://mises.org/story/2226

The article is interesting but I think some caveats are in order, though mostly in a way that would favor programs like Alcumus. I know many people who teach at the undergraduate and graduate level, and by all reports the "digital generation" is coming up short on critical reading, thinking and writing skills. Students can find things on the internet, but their ability to separate the excellent from the mediocre from the B.S. is not highly developed. There's a high level of consumerism (a degree is a product they're buying, and since they're paying tuition, they're entitled to be entertained and really catered to by professors). These students are a product of the educational system Gatto describes in Dumbing Us Down, not it's opponent.

If lectures have become a one-way street it's because students generally EXPECT to be told what they need to know for the exam, so they can regurgitate it back, or more likely, pick it out on a multiple choice test, collect their degrees, and get on with their lives. My spouse teaches former history majors who tell him they have never written an essay exam before. And many are mortified at being asked to speak in front of classmates. (Welcome to law school!) No wonder the brightest undergrads find they can skip lectures, if they have more efficient ways of memorizing the material and have better things to do with their time.

I think that at the university level most professors would love to have more of a conversation with students, but that would require that the students actually work on learning the material themselves (and not some lightweight version they found on the internet, either). In theory the digital age should open up more avenues for communication and for keeping students learning at a level that is challenging to them -- and for some it does. But that doesn't seem to be what the kids who facebook each other in class are really looking for. These students as well as their professors would have to adopt a different approach for something like the "just-in-time" approach to work. I suspect that most conscientious professors would welcome a several-hour heads-up on the hard questions they might be asked in class as well as the picture they'd get of where, as a group, their students are in their understanding of the subject matter. And conscientious students would also find classes more engaging. But there's a group of students who would find it quite a change, actually to have to prepare well ahead of class and send in their questions, and to use class time to learn -- not just to comment on the professor's attire and mannerisms and figure out what time to meet their friends at which bar that evening. (The really bright ones would of course do all of the above . . . . )

In many fields I'm sure the large lecture class has simply seemed the most efficient way to make sure the majors in a subject all know the basic material they need in order to proceed in the field. (There was a time, I think, when some educators believed that in the information age, this step could be skipped entirely in favor of just learning research skills, but I think the pendulum has swung back to the view that students do need to amass a body of working knowledge as well as skills. I worry a little about medical students trained entirely on problem-focused learning without some systematic instruction in pathophysiolgy, pharmacology, etc. On the other hand, course material works in specific clinical cases both motivates learning and takes it to a higher level.) It could well be that in many cases something like an Alcumus model, perhaps accompanied by small-group problem sessions, could replace large lectures in many fields, not just math.

(As for the Mark Taylor piece cited in the article -- I did graduate work in religion at a neighboring -also secular - institution 25 years ago, when the PC had just been invented and there was no internet, and graduate classes were always interdisciplinary and problem-focused. I think he wants to remake the university in the shape of his own field. He's right that the humanities have been producing far too many graduates, most of whom will not find work in the scholarly field for which they've received high-level training. The connection between the growth of large graduate programs and the growth of large lecture courses, all too often taught by grad students or non-tenure-track PhD's, has been noticed by others. If the end of the university is in sight it's because this system has simply become too expensive to be sustained. On the other hand I don't know anyone who finished a PhD in the humanities and ultimately had trouble finding something satisfying to do, either inside or outside academia.)