= 27d567bc2d48d9f40e9ccc20ea370b15)
Dahlen comments on Open thread, Nov. 17 - Nov. 23, 2014 - Less Wrong Discussion
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (322)
Advice/help needed: how do I study math by doing lots of exercises when there's nobody there to clue me in when I get stuck?
It's a stupid problem, but because of it I've been stuck on embarrassingly simple math since forever, when (considering all the textbooks and resources I have and the length of time I've had it as a goal) I should have been years ahead of my peers. Instead, I'm many years behind. (Truth be told, when performance is tested I'm about the same as my peers. But that's because my peers and I have only struggled for a passing grade. That's not what my standard of knowledge is. I want to learn everything as thoroughly as possible, to exhaust the textbook as a source of info; I usually do this by writing down the entire textbook, or at least every non-filler info.)
There is a great disparity between the level of math I've been acquainted with during my education, and the level of math at which I can actually do all the exercises effortlessly. In theory by now I'm well into undergraduate calculus and linear algebra. In practice I need to finish a precalculus exercise book (tried and couldn't). While I'm learning math, I constantly oscillate between boredom ("I'm too old for this shit" ; "I've seen this proof tens of times before") and the feeling of getting stuck on a simple matter because of a momentary lack of algebraic insight ("I could solve this in an instant if only I could get rid of that radical"). I've searched for places online where I could get my "homework" questions answered, but they all have rather stringent rules that I must follow to get help, and they'd probably ban me if I abused the forums in question.
This problem has snowballed too much by now. I kept postponing learning calculus (for which I've had the intuitions since before 11th grade when they began teaching it to us) and therefore all of physics (which I'd terribly love to learn in-depth), as well as other fields of math or other disciplines entirely (because my priority list was already topped by something else).
I've considered tutoring, but it's fairly expensive, and my (or my tutor's) schedule wouldn't allow me to get as much tutoring as I would need to - given that I sometimes only have time to study during the night.
Do any LessWrongers have resources for me to get my questions answered? Especially considering that, at least at the beginning until I get the hang of it, I will be posting loads of these. Tens to hundreds in my estimation.
Sorry to jump from object-level to meta-level here but it seems pretty clear that the problem here is not just about math. Your subjective assessments of how difficult these topics are is inconsistent with how well you report you are doing at them. And you're attaching emotions of shame and panic ("problem has snowballed") to observations that should just be objective descriptions of where you are now. Get these issues figured out first (unless you're in some educational setting with its own deadlines). Math isn't going anywhere; it will still be there when you're in a place where doing it won't cause you distress.
I can see how it would sound to an outside observer now that you point it out, but in my situation at least I have trouble buying into the idea that math isn't going anywhere. The problem really is urgent; there are loads of fields I want to study that build upon math (and then upon each other), and it just isn't feasible that I can further postpone deep, lasting learning of basic math concepts any further, until after I'm in the "right mindset" for it. There just isn't time, and my neuroplasticity won't get any better with age. It'll take me at least a decade to reach the level I desire in all these fields. Not to mention that I've long since been having trouble with motivation, or else I could have been done with this specific math in about 2011-2012. I'm not doing well at these topics (despite evaluating them as easy) because I spend less than a few hours per month on them.
How old are you? I think the peak is around 30 years of age.
I'm 21. I thought it began to decline after early/mid 20s. It'll definitely take me longer than that to learn just a few prerequisites thoroughly.
In my opinion, what you probably need is some mix of tutoring and therapy -- I don't know if it exists, and if there is a word for it -- someone who would guide you through the specific problem, but also through your thought processes, to discover what it is you are doing wrong. Not just what are you doing wrong mathematically, but also what are you doing wrong psychologically. This assumes you would speak your thoughs aloud while solving the problem.
The psychological level is probably more important than the mathematical level, because once the problems with thinking are fixed, you can continue to study maths on your own. But this probably cannot be done without doing the specific mathematical problems, because it's your thought patterns about those math problems that need to be examined and fixed.
I happen to have a background in math and psychology and teaching, so if you would like to try a free Skype lesson or two, send me an e-mail to "viliam AT bur.sk". Don't worry about wasting my time, since it was my idea. (Worst case: we will waste two hours of time and see that it doesn't work this way. Best case: your problem with maths is fixed, I get an interesting professional experience.)
Thanks for the offer! Yes, this sounds interesting. One of the things I've tried to get out of my math tutoring experience was to see how the teacher looked at the problem before beginning to actually solve it and see if it works out. But they never actually thought out loud for me to understand their thought process; also, I often can't tell what mental resources someone else uses when solving a difficult/tricky math problem. (Experience? Sudden insight? Additional notions I don't yet have?)
Find somebody else who is in the same situation and study together.
Have you looked into Physics Forums? They have Homework & Coursework Questions subforum.
Yes. Recently made an account there, started off by asking a homework question. Wouldn't want to spam it, though.
I'm wondering whether you're expecting some math to be effortless when you're actually still at the stage of trying one thing and another, and need to be less focused on how you want the process to feel.
Effortless, no; however, some of it is sufficiently familiar by now that I don't think there is additional value in rehearsing the same material. (Example: I first encountered derivatives on Khan Academy, before they officially taught them to us; then in 11th grade as an intro to calculus; then on several tests and exams; then in freshman year of college. I don't think I need to be given the intuition on derivatives one more time, and if I took a test in derivatives I'd ace it without much effort.) I'm not expecting new notions to be very easy to learn -- moderately challenging and definitely not impossible, but not easy.
Maybe you should post here about one or two or the problems you're stuck on.
I'm wondering whether you're demanding too much facility of yourself before you go on, but this is only a guess.
Have you looked into Khan Academy?
Only if the LW Study Hall organized threads like that; I've been considering joining it, but never got around to it. Otherwise, I'd feel it would be a waste of people's time. There are lots of exercises I might get stuck on, and it's usually not as if any particular one of them represents a key insight to me; the answer/solution/hint to any given exercise is low-value to me, but the answer to all or most of them is high-value.
Been on Khan Academy since 2012, I think. Earned a Sun Badge and everything. (That type of performance didn't constitute my real challenge, though; I've been struggling for these two years to earn the modest Good Habits badge, to no avail to this day.)
In general having a goal to exhaut textbooks by copying them is stupid. That's not what they are for. Get rid of that strategy.
Most forums have rules that prevent you from asking questions without deeply thinking about those questions yourself.
On math.stackexchange you are allowed to ask all maths questions provided you search before for similar questions and put in the effort to write a decent question.
Asking decent questions is a skill. Learn it and people will answer your questions.
Suspected as much... but I am not sure what strategy to replace it with. I definitely plan on doing all the exercises, and sometimes if I also write down some of the theory/proofs it helps with recalling them later. I'm guessing good rules of thumb are: stick to the essentials; use common sense; review at appropriate intervals.
I'm fine at asking a question that doubtlessly won't get removed. A question. I'm not sure that asking 20 (good, rule-abiding, thought-out) questions per week in a given forum would last me very long. That's about how often I might get stuck if I do some exercises every day.
On stackexchange nobody has a problem with someone asking a lot of question provided they are good, rule-abiding and thought-out.
You can also answer questions of other people. It might even be better than textbook problem because someone well tell you when you are wrong via comments.
Have you tried using WolframAlpha? If you get the pro subscription (~$66 per year - ~$45 a year for students) you gain access to their step by step solutions and unlimited problem generator. I am currently studying a Masters of Biostatistics (which has a heavy calculus section) and found this service invaluable.
Examples http://i59.tinypic.com/2yuniv9.png http://i60.tinypic.com/c5i7n.png
You should go on to more advanced topics without being fluent in less advanced topics. You can always later go back to the exercises that stumped you. The typical student taking calculus without being fluent in adding fractions is a mistake, but that don't over-correct that mistake.