Why hasn’t technology disrupted higher education already?

Being prepared for the problem style ahead of time isn't cheating, it's just studying.

If your claim is that this style of studying isn't preparing students for the real world where the problems cannot be easily predicted then I definitely agree. But cramming isn't cheating, students are just trying to succeed within the system.

It's a social problem rather than technology. If something signals higher social status, it will keep going.

I agree with you except for the very last point, that "students need to be guided on problems at the time they do them". I think this issue is fundamental to the tradeoffs of self studying that I've experienced. I want to point out: the guide doesn't necessarily have to be a human. And textbooks accomplish this by giving examples that walk through how to solve problems similar to the exercises. Unfortunately this is a useful secret about textbook and problem design that is not common knowledge to students. (I.e., the principle of charity, principle of relevance, Chekhov's gun, etc.)

I agree with the point of your example, but maybe not the choice of example.

For your example, Gallian (which imo is the standard intro algebra book) includes this property in the definition of a ring: "Property 6. a(b + c) = ab + ac and (b + c)a = ba + bc". (Probably in order to disclaim the confusion you're talking about.) Then he goes on to derive 6-7 other properties of groups that will (of course) be useful in the exercises.

I definitely found it's really important when self-studying to pick the right textbook. Definitely you have to be an experienced educator to write a good book that anticipates most of these things. But I agree that it's impossible for any textbook to anticipate every place someone reading it might get stuck. Let's say for a given student it happens 5-6 times in a really high quality textbook like Gallian or Rudin PoMA. They have 3 options (1) ask on mathematics.stackexchange.com and probably get an answer because it's a great community, (2) try to figure it out themselves, or (3) pay $600 and invest 3h/wk to take an algebra class that might cover the first 1/2 of the textbook in 4 months.

I think where we disagree is what are the constraints of the tradeoff between attending a class vs. reading the book. My experience has been that, if the subject is interesting enough, reading a good quality textbook is cheaper and 2-3x faster than taking a course, but at certain points it can be much more challenging. I think where it depends on which student is how much more challenging, i.e., will they be able to dig themselves out of those holes in a few minutes or a few hours. I was personally in the middle of these two extremes, but I still thought it was worth it to self study after taking 3-4 classes in the math department, then I skipped a bunch (7 semesters) of analysis/algebra/topology and came back and took 2-3 grad courses, where I didn't really understand the main goal of the subjects until I took the classes. And then I went into CS industry and never used any of it again. But I don't regret the experience; it was legitimately interesting to learn about math.

I think you have to be legitimately interested in a subject to self study it successfully. But that's true about studying serious math in general though: you have to be unrelentingly into it, or else you're just really misguided and shouldn't be there, given the high competition, poor odds for any future in math, and no practical use for any of the theory.

That's my experience with it and why I made the argument that I made.

1+1 x 2

this has been doing rounds on twitter how people do not have grasp of basic maths and it points out a good argument for people who have been taught "good basics"... like i recently asked a doctor who says they are bad at maths and they just blurted out 3. i asked why and they responded, "uh.... bodmas?"

its such a small thing really, like in your primary and secondary education, of all the classes you attend, this is just a tiny tiny topic that must've been taught but because you were taught its importance and use it as a building block early on, it just feels like second nature.

like the tables of 2-9. pretty hard for kids to remember but once they do and they are taught to HOW to use it, it really helps them

I think that OP's fundamental error is talking about school vs university. When I started my bachelor's studies in math the professor covered 3 years of high-school math in the first 2-3 weeks of the first semester.

Up to that point I too thought I could just learn by reading the textbook. University (assuming a good one, mine wasn't world famous but has a good reputation nationally & in Europe) level maths is completely different level than high school level math, and having access to the professors makes a big difference (although I was often the only student coming by at their office hours if it wasn't before a test, so I guess not everyone agrees with that).