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What is the more efficient way of self-teaching, when the return is diminishing? Keep on trying? or study more basic stuffs?

I am currently teaching myself a few subjects, but I have noticed that the learning curves are quite tricky now and then. Sometimes, it gets steep at the beginning, then it gets quite sucky later on (especially when I am in lack of some background knowledge. usually, I have to either look it up or make my own assumptions). Some other times, I have a humble beginning, but then it goes like rocket (e.g. for mathematics, when I tried to understand it, instead of memorizing it).

More specifically, I am learning writing in science on coursera. I am quite satisfied by the general tips (e.g. one main idea in each paragraph, and I had not known that at all), but when it comes to how "abstract", "method", "result", etc. The tutor's suggestions sound quite alien to me (I have little experience in research); furthermore, I am also not making good progress. Therefore, I am not sure if it is normal for someone learning something completely new, or simply because my English is too lousy (even as a non-native English speaker; hence, I had better to switch to other basic English writing courses)

So what is the more efficient way of self-teaching, when the return is diminishing? Work harder as no pain no gain? or switch to more fundamental things? While I am looking for a scientific answer (backed-up by researches), I would also love any personal experience or insight as an answer.

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    When the curve becomes less steep, isn't that a good thing?
    – henning
    May 1 '18 at 8:54
  • @henning oops! Actually I mean my intellectual gains are getting worse and worse! Did I confuse you?
    – Shing
    May 1 '18 at 8:57
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    Two sides of the same thing. Steep learning curve means as experience (x axis) grows the amount of learning (y axis) greatly increases, but it also means the struggle is great as well. To avoid confusion you can replace with something like "return is diminishing."
    – Penguin_Knight
    May 1 '18 at 9:44
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    @Penguin_Knight thanks for the suggestion! I have edited my question
    – Shing
    May 1 '18 at 10:31
  • Are you trying to learn to write more effectively, or is there some underlying specific subject matter, such as mathematics or chemistry?
    – Buffy
    Jul 15 '18 at 18:11
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I can help you think about math and programming, at least. The key to both is to do a lot of exercises and get a lot of practice. In learning on your own, you need access to someone else who can give you feedback on your results. It is very hard to judge your own work and to draw the correct conclusions from mistakes or to overcome difficulties.

Some online course structures may be fine for getting that feedback, but not all are. You need more than just the correct answers. You need to get a sense of why you went wrong in an exercise and how to avoid whatever that error was in the future.

Reading and watching videos isn't sufficient and it will give you only shallow learning. Then, when you hit the next challenge, you aren't quite ready for it. If you have a good textbook (and there are bad ones as well) try to do every exercise. Try to get feedback.

One way to get feedback, if you are working without a good guide, is to work in a group. You seemed to indicate that this was the case with you. You can each do a few exercises (the same ones for everyone) and then exchange work and discuss what you did and how. But even the feedback of other learners is better than none at all.

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You mentioned, as one of the options, "switch to more fundamental things". In mathematics, this may well be a necessity, not merely an option. Mathematics, unlike some other areas of knowledge, depends heavily on basic material in building more advanced material. If you don't know the fundamental things thoroughly, you have no chance to really learn more advanced things. So I would recommend that, whenever your studies reveal some gap in your understanding of fundamental material, you should interrupt those studies and first learn that fundamental material.

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This is one advantage of an instructor. To make you keep going in doing boring routine things. Working by yourself you tend to quit too soon. This is the same role as a coach for learning a sport, or a physical therapist when undergoing rehab after an injury: without them, you tend to quit too soon.

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