Hello, folks. I'm one of those long-time lurkers.
I've decided to conduct, as the title suggests, a quick and dirty survey in hopes of better understanding a problem I have (or rather, whether or not what I have is actually a problem).
Here's some context: I'm a Physics & Mathematics major, currently taking multi-variable. Lately, I've been unsatisfied with my understanding and usage of mathematics—mainly calculus. I've decided to go through what's been recommended as a much more rigorous Calculus textbook, Calculus by Michael Spivak. So far I'm really enjoying it, but it's taking me a long time to get through the exercises. I can be very meticulous about things like this and want to do every exercise through every chapter; I feel that there's benefit to actually doing them regardless of whether or not I look at the problem and think "Yeah, I can do this." Sometimes actually doing the problem is much more difficult than it seems, and I learn a lot from doing them. When flipping through the exercises, I also notice that—regardless of how well I think I know the material—there ends up being a section of exercises focused on something I've never heard of before; something very clever or, I think, mathematically enlightening, that's dependent on the exercises before it.
I'm somewhat embarrassed to admit that the exercises of the first chapter alone had taken me hours upon hours upon hours of combined work. I consider myself slow when it comes to reading mathematics and physics literature—I have to carefully comb through all the concepts and equations and structure them intuitively in a way I see fit. I hate not having a very fundamental understanding of the things I'm working with.
At the same time, I read/hear people who apparently are familiar with multiple textbooks on the same subject. Familiar enough to judge whether or not it is a good textbook. Familiar enough to place how they fit on a hierarchy of textbooks on the same subject. I think "At the rate I'm going, it will take me a very long time to get through this."
Here's (what I think is) my issue: I don't know whether or not I'm taking too long. Am I doing things inefficiently? Is there a better way to choose which exercises I do and don't work through so that I learn a similar amount of material in less time? Or is it just fine that I'm taking this long? Am I slow and inefficient or am I just new to this process of working through a textbook cover-to-cover, which is supposed to take a very long time anyway?
I spend more time than I should learning about learning, instead of learning the material itself. I find myself using up lots of time trying to figure out how to learn more efficiently, how to think more efficiently, how to work more efficiently, and such things—as opposed to actually learning and actually thinking and actually working, which ends up being an inefficient use of my time. I think part of this problem stems from the fact that I don't have much of a comparison for when I can say "Ok, I'm satisfied and can stop focusing on improve how I do this act—and just do it already." I want to solve that issue now.
Which brings us to...
Here's my attempted solution: A survey! I assume many people here at LessWrong have worked through a science or mathematics textbook on their own. Mainly I'd like to gauge whether or not you thought you were taking a very long time, how long it took you, etc. I'd also like to know what your approach was: Did you perform every exercise, or skim through the book finding things you knew you didn't know? Did you skip around or go from the first chapter to the last? Do you have any advice on how one should approach a given textbook?
Here's the survey: https://docs.google.com/forms/d/1S4_-7_dxgmgprMbNhL1dNmX_0Zq9QrA9lpTl9ZHHxMI/viewform
I'm not sure how interested anyone but me is in this, but on a later date I could make another post showing the data. I considered checking "Publish and show a link to the results of this form", but I wasn't sure if that kept everyone anonymous or not. Also, feel more than free to post any criticism, shortcomings, improvements, etc. Have I left anything out? Is there anything you'd like to see me add? This is my first attempt at a survey like this and I'd appreciate any feedback (though I know it's not necessarily a rigorous survey, just a quick data-collection, I suppose).
I strongly encourage the posting of any textbook-reading tips or guidelines in the comments. I left that out of the survey so that anyone who's interested has immediate access to tips.
Here's an edit: Thanks for all the responses, everyone. Not only was my original question sufficiently answered (that is, it doesn't seem like I'm taking too long; there were only a few survey takers, but in between the comments and the survey answers, I'm not going at an extraordinarily slow rate). There's some very solid advice for different methods I might try to optimize my learning process. One that especially hit home was the suggestion that the large amounts of time spent "learning about learning" are such because it feels more comfortable than actually learning the material. In short, it's a safety blanket that makes me feel like I'm doing something productive when I'm really just avoiding what needs to be done. Some other useful pieces of advice are:
- Try being open to learning a broader range of materials without necessarily mastering each one. It might be the case that you need to know one thing in order to master the other, and need to know the other in order to master the one—trying to master either of them in isolation ends up being somewhat futile. Not everything needs to be "brick by brick" structured. (This was a lesson I found useful when I first learned that a number raised to the "one half" power was the square root of that number: Trying to master it in terms of the rules I already knew ended up in a thought like, "... Two to the third power is two times two times two. Two to the one-half power is two... times two one half times?"
- Though it may be uncomfortable at first, it could make learning easier to try the exercises before reading the chapter super-carefully; trying them before you feel ready to try them. You don't necessarily have to fully comprehend all of the proofs in the chapter to get through some exercises.
- Textbooks might just be the wrong way to go in the first place. Try resources like Wikipedia, math blogs, and math forums.
- "Don't use the answer key unless you've spent a significant amount of time trying to find the answer yourself!" (This may seem obvious, but a few years ago, I'd spend a couple of minutes on the problem, not understand it, look to the answer key, and wonder why I wasn't learning anything.)
- Skip exercises when you feel you could solve them, but randomly check whether this estimate is correct by doing the problem anyway. (I like this one a lot).
- Talk to a professor!
- It may be the case that you learn well via just reading, and not spending so much time on the exercises.
Here are some websites/blogs mentioned:
(Blog) Math for Programmers - http://steve-yegge.blogspot.com/2006/03/math-for-programmers.html
(Blog) Annoying Precision - http://qchu.wordpress.com/
(Math Forum) Mathematics - http://math.stackexchange.com/
Excellent, excellent stuff, though. Thank you. :) There's a lot of material and advice for me to work with—while simultaneously making sure I don't avoid my work by hiding under the guise of productivity.