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In social science and humanities, I agree with you that self studying is an uphill battle. You'll just sound naive unless (1) you've made a herculean effort in

In social science and humanities, I agree with you that self studying is an uphill battle. You'll just sound naive unless (1) you've made a herculean effort in studying, and (2) you've thought very critically on your own about how you will assimilate and where you will fit into the existing space of thought. There are no definitively correct opinions in these fields but plenty of influential people have theories. My experience is that it's all about how you convince others to join your "team", whether what you say is appropriate and within the Overton window, whose "side" are you on, etc. In some sense the thing that is "taught" is how to argue, what's acceptable to think, and who is on whose side or not. And the punishment for saying the "wrong" thing is more severe than in mathematized fields. Textbooks and/or (current) edtech are not going to be effective there. But in hard scientific topics (mathematics, algorithms, engineering) there are facts and ideas that are taught, and it's equally easy or hard to learn from prose as it is from listening. In my experience you can be very effective self-studying as long as you already have basic background about the field and what's the point. I skipped 2-3 years of math in school by simply reading the textbook over the summer, doing the exercises, and just asking to skip to the next class. You do this a few times and then you realize that in-person classes are also just them reading the textbook to you. I don't regret it whatsoever. I'd argue the difference is how mathematized a field is, probably along the same lines as SMBC: https://www.smbc-comics.com/comics/1483460468-20170103.png https://www.smbc-comics.com/comics/1483460468-20170103.png

deleted 4y ago
[deleted]
syzarian 4y ago
I’ve taught mathematics for over 20 years in higher education and I strongly disagree with your view on the relative ease of learning math on one’s own. Let’s take a simple example. Here’s the distributive property for rings: a(b + c) = ab + ac It’s easy for me to convince someone that because of this property we get the following: 3(x + 2) = 3x + 6 It’s much harder to convince someone that 3x + 6 = 3(x + 2) It’s hard to convince someone that factoring is just using the distributive property reading right to left instead of left to right. It’s much harder to convince them of this just from reading it in a book. The nuance will be lost. They need examples that one goes over in a classroom to see this and a book can’t contain enough examples without being too many pages or without boring the reader with what appears to them to be minutia. They can’t grasp the nuance from reading. They grasp it from doing problems and being guided on the problems at the time they do them. Books and videos can not replace a teacher. Your experience is not the norm and you should not use it as a guide for what is realistically possible for most people.
- rrrrrrrrrrrr2 4y ago
  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.
UncleMeat 4y ago
I feel that this comment misunderstands both hard sciences as well as social sciences and humanities. My wife is a historian. The idea that the way to succeed in history is to just make various influential people like you since there is no actual "correct opinion" is just rank bullshit. And the idea that in, say, computer science, that there is precisely one correct approach to a given problem is also completely bogus once you've moved beyond trivial questions.

deleted 4y ago

[deleted]

syzarian 4y ago

I’ve taught mathematics for over 20 years in higher education and I strongly disagree with your view on the relative ease of learning math on one’s own. Let’s take a simple example. Here’s the distributive property for rings: a(b + c) = ab + ac It’s easy for me to convince someone that because of this property we get the following: 3(x + 2) = 3x + 6 It’s much harder to convince someone that 3x + 6 = 3(x + 2) It’s hard to convince someone that factoring is just using the distributive property reading right to left instead of left to right. It’s much harder to convince them of this just from reading it in a book. The nuance will be lost. They need examples that one goes over in a classroom to see this and a book can’t contain enough examples without being too many pages or without boring the reader with what appears to them to be minutia. They can’t grasp the nuance from reading. They grasp it from doing problems and being guided on the problems at the time they do them. Books and videos can not replace a teacher. Your experience is not the norm and you should not use it as a guide for what is realistically possible for most people.

rrrrrrrrrrrr2 4y ago
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.

UncleMeat 4y ago

I feel that this comment misunderstands both hard sciences as well as social sciences and humanities. My wife is a historian. The idea that the way to succeed in history is to just make various influential people like you since there is no actual "correct opinion" is just rank bullshit. And the idea that in, say, computer science, that there is precisely one correct approach to a given problem is also completely bogus once you've moved beyond trivial questions.