I am currently a "self-studier", so the manner in which I learn is I have a textbook and I work through it in a relatively linear fashion. As I am introduced to new concepts I ask questions (sometimes I go down the "rabbit hole", but I feel I've got a good handle on this now) and I attempt to answer these myself and if all else fails I ask Maths SE. Most importantly, only after I've understood a certain topic do I then use Anki to make flashcards to ensure I retain most of what I've learned. Learning like this is what seems to work for me, however I feel like this could be optimised.

So, I have a few questions:

  1. When exposed to a new topic what kind of questions should one be asking oneself? What are the most incisive kinds of questions that cut to the core of a matter? How do I ask the right questions?
  2. Is there a proven effective way of learning? How does one learn something inside-out?
  3. How does one learn to think really analytically?
  4. What is the best way to make connections with things you've learned previously? I feel that with Anki (a spaced repetition system) that I make all these flashcard decks full of bite-sized bits of knowledge that I can recall on demand, but just because you can recall something on cue doesn't mean you can use that knowledge when a certain context demands it. How does one make strong connections between all these disparate bits of knowledge? I want to build a strong "network" of knowledge if you get what I mean.
  5. What study-habits should you instill in yourself if you want be an effective learner?

P.S. If this is too opinion-based is it possible to place this in community wiki or something?

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    $\begingroup$ This seems somewhat off topic: these same questions do not seem math education specific. One thing which I would definitely add to your list though is "narrative structure". You should have a story about why things are important, how you would think of this definition, or that theorem, how various pieces of the subject connect. For me developing these kinds of compelling narratives is a huge part of learning. Often asking the right questions becomes easy: try to fill in the holes in the plot, so to speak. $\endgroup$ Commented Aug 15, 2014 at 20:43
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    $\begingroup$ These are very broad questions. Your previous inquiry (matheducators.stackexchange.com/q/4093/262) asked six large questions about creativity; this one includes five large questions about a variety of topics (self-inquiry, ways of learning, thinking analytically, making connections, study-habits). There is certainly a literature around all of these ideas, but I think you will need to pick one (ideally of a mathematical nature) of them -- and then focus even further -- in order to ask something that is tractable. I'm afraid this post is too broad. $\endgroup$ Commented Aug 15, 2014 at 22:18
  • $\begingroup$ @Benjamindickman okay I'll try! Thanks! $\endgroup$
    – seeker
    Commented Aug 15, 2014 at 22:22
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    $\begingroup$ frr the record, while I voted to close, I think these questions asked one at a time with a more mathematical focus might well be on topic. $\endgroup$ Commented Aug 16, 2014 at 1:00
  • $\begingroup$ I agree with Benjamin and James. It is broad, but I would like to see these as five focused questions. $\endgroup$ Commented Aug 16, 2014 at 2:53