Self-Taught vs. Academic: The Need for Formal Education in Mathematics

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Academia's necessity for becoming a mathematician is debated, with arguments highlighting the potential of self-taught individuals to succeed without formal education. Critics point out the high costs, lengthy processes, and inadequate resources of university programs, suggesting that self-study can yield similar results if one possesses the maturity and dedication to learn independently. However, proponents of academia emphasize the value of access to expert guidance, networking opportunities, and structured learning environments that can enhance understanding and foster original research. The discussion also raises concerns about the isolation faced by self-taught mathematicians and the challenges of navigating complex topics without mentorship. Ultimately, while self-education is possible, many believe that the benefits of formal education, including community support and resources, are significant for achieving success in mathematics.
  • #151
I think the why is just resistance to change.

That's sort of tauntological. Things don't change because there is resistance to change. The question they becomes why is there resistance to change, and what can be done about it?

It's not tautological because what I am referring to is stuff like habits, social conditioning,
not wanting to take risks, rather than having genuine reasons for continuing the old way of doing things.

Have a FAQ available. Eventually, all conceivable questions will be answered. If that fails, tutoring resources, office hours. Some people would rather show up at office hours, anyway.

But that involves setting up tutoring resources and office hours. One thing about a lecture of 500 people is that I know that if I'm a student in that class that if I show up at the professors office, that he isn't going to be annoyed at me. If I replay a video that was made five years ago, I have no such assurance.

Tutoring resources and office hours are already set up, usually. The only thing I'm subtracting is the lecture. Actually, I'm not assured that the professor won't be annoyed with me.

The thing about running a large lecture class is that the instructor of record does more than just lecture. There's the matter of making sure that you have enough tutors, that they are being paid, etc. etc. This *can* be done online, but it's a lot of work. It doesn't happen by magic.

Again, that stuff is already being done. I'm just saying subtract off the lecture. Actually, teachers are already starting to do this in some cases. Their homework is to watch Kahn Academy and class is used for other things. And the results have gotten better.

First of all, videos can incorporate as much feedback as you want from a good sized sample of people studying the material. As far as feedback that is specific to one particular group of people, that can come from homework performance, for example. With videos, the most popular teachers can teach ALL the classes and you can even give the students multiple teachers to choose from, so few will complain about how incompetent the teacher is.

1) You don't get instant feedback. If you are give a lecture via video, you can't see how many people are nodding off, how many people have confused looks, and how full the class room is. (You can get around this by having a live studio audience, which is why you have live studio audiences.)

2) Homework performance means setting up homework which gets you back to administrative scale problems. One problem is suppose you get 400 homework assignments. Is that good or bad. You don't know because you don't know the number of people that didn't turn in their homework.

Again, this is not an argument against merely subtracting the actual lecture.
3) Lectures scale. Tutorials don't. You can have Walter Lewin lecture to 10000 people. However, much of learning math and physics involves tutorials, and you can't have more than ten people in a tutorial section before quality suffers.

That appears to be an argument in favor of my position, since videos also scale.
4) The trouble if you don't synchronize things is that then you have students listening to different instructors, working different problems, and that kills student-student interaction.

Student-student interaction happens during a big lecture? I didn't seem to notice that as being a big part of it. Actually, the place where all the interaction took place when I took freshman physics was in the lab.
Again, none of these are unsolvable problems. However, I claim that as of 2012, that they are *unsolved* problems, although I think they'll rapidly get solved. It's sort of like tablet computing in 2008. At some point, someone somewhere are going to put all of the pieces together.

I think they have been solved, but haven't been implemented on a big scale. I mentioned those teachers using Kahn Academy to replace their lectures.
What does taking a test have to do with lectures?

Without an assessment, you can't turn knowledge into cash, and if you can't turn knowledge into cash, that limits the amount of money that you can spend on the lectures. The lecture is the easy part since that is a fixed cost. The problem are the tutorials and administrative costs. University of Phoenix figured out the solution for business degrees, but no one has tried applying the model to math and science (not even UoP).

Look at the subject GRE tests. Where are the lectures? Test, but no lectures. Why not just subtract the lecture? Not much needs to be changed. Because professors need to be paid, I suppose. But there we see money reasons taking priority of education reasons.
Or rather, the tricky part is getting people to change their old ways.

Change to what?

But you have to realize that there are reasons why the old ways exist, and we know that the old ways work, whereas anytime you do something new, you end up with risk. One problem is that if say MIT suddenly changed the way that 18.02 is taught and the new way just doesn't work, then you have a disaster. So what you do is to set up experimental groups and pilot projects, and then as you learn stuff, it goes back into the main sections.

I don't really see experiments going on, but maybe that's my limited experience. Some of the reasons, as I said, probably are purely sociological, with little or no actual substance to them, and other reasons are just excuses for the purely sociological ones.
The main problem that I see right now is money. How do you set things up so that either everyone gets paid, or that you have a barter/gift economy in which payment is not necessary? I think it's a solvable problem, but as of 2012, it's an unsolved problem for the undergraduate physics curriculum.

And then there is the motivation problem. Why change? In the 1950's there were *radical* changes in physics, because people believed that without some major changes, everyone in the US would be speaking Russian. There isn't this sort of "light people's pants on fire" motivation that I can see right now.

Money is a problem, yes. Which is why I'm glad I never valued it very highly.
 
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  • #152
twofish, do you ever argue with yourself? I have to ask. In a thread like this, I'm surprised I haven't seen you quote yourself then bring up a counter point of something you posted several days ago. It seems your main motive in a lot of threads is to talk about the social, economic, or "system" aspect of the given topic.
 
  • #153
twofish, for math and science knowledge, do you think it is feasible to have a more exam-based system? Something like say, Calc BC, but on a more advanced and comprehensive scale, so you can show the certificates of exam grades to substitute for a degree.
 

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