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I find that during any class I take, I'm quite often the slowest person in the room, even though my overall performance in the course may be in line with the average. For example when seeing a technical theorem on the board, I often forget it by the time we are but a few lines into the proof. This is problematic because by the time I look back at it, I've fallen behind when I look back to the proof.

When studying material on my own, I have plenty of time to commit notation to my long-term memory so that I can see the bigger picture behind a proof and then there is absolutely no problem.

But I'd very much like to be able to sit in a seminar or lecture however, and not feel like I am just sitting there pretending to understand (AKA feel like an idiot). Has anyone else experienced this and come to any conclusions that may help?

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I seriously doubt there's anyone who has studied mathematics, but hasn't experienced what you describe (and doesn't still do that once in a while). The part about feeling like an idiot and falling behind, anyway. –  tomasz Jun 15 '13 at 23:39
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Maybe all your classmates think they're the slowest person in the room. –  Michael Hardy Jun 15 '13 at 23:44
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This is the zombie theory in reverse, the other one being how do you know everyone else is feeling like an idiot when you understand something?, or vice versa more info en.wikipedia.org/wiki/Philosophical_zombie –  Arjang Jun 16 '13 at 0:10
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I was going to say what Michael Hardy did. My experience has always been that when I don't understand, and I frequently stop the lecturer to ask questions, that the other people in the room are relieved and grateful, because they didn't understand either, but were afraid to ask. It often seems like asking a lot of questions will display to everyone how dumb you are, but in my experience it seems to have had the opposite effect. –  MJD Jun 16 '13 at 2:51
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Mathematics has a way of making everyone feel stupid, from those who learnt how to multiply fractions and then gave up forever to those high-ranking academics doing groundbreaking work at the forefront of their field. Most people simply don't talk about it. –  Billy Jun 16 '13 at 3:47
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closed as off topic by mixedmath Jun 16 '13 at 11:02

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5 Answers

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While you haven't said you are taking notes I will throw in a bit of my experience relating to notes. I often find that taking notes (writing everything from the board down) is counterproductive. Maybe I am just a terrible multitasker, but I find that if I am writing things down I am not really paying attention to the material and not trying to "internalize" the material. Instead I pay close attention to what is going on, try to think ahead and see where things are going and how they are connected. I am not saying I don't write anything, but what I do write is normally just little sketches, diagrams, or questions to ponder latter in order to better under stand what is going on. As others have mentioned preparing before class is really helpful. In short, I think the main idea of my post is to do things so you have more time to actually think and consider what is going on in the moment. Anything that makes it so you can ask more questions and think about more concepts during class should make the lecture more rewarding.

One other thing to point out is that you (probably) won't understand everything perfectly the moment the professor shows you, math takes time to understand (maybe just get used to).

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Came to write the same. Yes, notes are really counterproductive. If you don't make them to show your precis somebody else, that is much better to note just some key moments. –  Harold Jun 16 '13 at 3:40
    
Yup, I've noticed that my comprehension goes down as I take notes. However, if I'm not taking notes, then my mind is wandering to other things (ADD maybe?) Thus the best thing for me, and I'm not even joking, is to print off a puzzle (e.g. from puzzle-shikaku.com/?size=5) and do it while listening. Perhaps coloring would work too. –  Daenerys Naharis Jun 16 '13 at 5:37
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I can relate to learning better from books than from lectures, and I can certainly relate to the feeling of not having any idea what's happening on the board. Here are two tips that have worked for me:

Read Ahead: The easiest way to be able to keep up with the lecture is to read ahead and know what's coming. Even if you don't understand all the nuances after the initial reading, knowing what's coming and having some idea of the bigger picture in advance is a big help. If you have some idea of what the "punchline" of the lecture should be (most lectures usually have some important theorem or definition at the end that the lecturer builds up to), then you'll have a much easier time understanding what steps need to be taken in order to get there.

Participate: I can't speak for anyone besides me, but I find participating to be a good way to keep myself on task. Obviously, this means raising your hand when some of the questions are asked, but it can go a little further. If there's something on the board that doesn't make sense to me, I ask about it. It's easy to be embarrassed about speaking up, but the payoff makes it worthwhile. If you get a question wrong after an educated guess, the right answer is much more memorable, and nobody is going to think less of you for trying. Also, if something confuses you and you're not sure about whether you should ask about it, chances are that somebody else is in the lecture is in exactly the same situation.

Again, this is what has worked for me, and I can't recommend it for everybody.

One more note: just because you feel like you are the slowest person in the room, doesn't mean you are; there are almost certainly other people in the room who feel the same way.

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The bottom line is that math is hard. Not having a clue what's happening on the board at the time is pretty common, even among students with very good grades. I can vouch, at least out of personal experience, for the suggestions of reading ahead whenever you can (sometimes this can take the form of reading an entire chapter or two and tackling some exercises on your own before the semester begins - other times it might just be reading a few definitions) and asking/answering questions during lecture. Reviewing your notes after the lecture on the same day as a lecture is also a good idea. –  Omnivium Jun 15 '13 at 23:53
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The thing about participating, sometimes when it's really not my day, I ask a lot of silly questions and sometimes find others laugh at me, but I don't really let that bother me, as it still helps my understanding greatly. On other days, I can make up for it by picking up the lecturers' mistakes. That kind of participation makes it much easier to follow. It's easier to understand something if you're the one thinking it up. –  tomasz Jun 15 '13 at 23:53
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Read ahead...participate..."you're not alone" $\implies (+1)$ –  amWhy Jun 16 '13 at 0:25
    
@tomasz Surprisingly, most of the people that laugh are the ones that ask the least questions as a result of themselves being scared to ask questions. Better yet I have found in my own classroom experiences the ones that find the most humor out of others questions are the same ones struggling to pass the course. –  nitrous2 Jun 16 '13 at 0:44
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I will start with some stuff that's not directly related to mathematics, but very relevant, at least for me.

From my perspective, first and foremost you should try to make sure you've had a good night's sleep, and if not, try to take a short nap before the lecture. I've had cases when I couldn't follow any lecture, at all, after having slept for 0 to 3 hours, but after having a 15-minute nap while on a break (or even during the lecture in some more extreme cases), I had no trouble listening and participating.

Second thing is, make sure you eat well. Even if you're well rested, if you're stomach is growling, it's hard to think about anything other than rushing to the cafeteria to buy something to eat, fast. I also try to carry around something nutritious to snack on, just in case I suddenly grow hungry during a tough lecture.

Thirdly, I find that it helps me a lot if I try to work the proofs on my own. How I do it exactly depends a lot on the style of the lecturer.

If he's the kind that explains everything carefully and in detail, I usually try to think ahead and when he's writing some complicated calculations, I try to anticipate what he's getting at and do them myself. Otherwise, I sometimes can't really follow, as when he writes the entire equation down, there's just too much to write down and understand at the same time. At other times, I just skip the parts that I find obvious, so that I can think about the harder parts more.

On the other hand, if the lecturer is more spontaneous kind, I listen and at the same time look for pitfalls he might or might not mention and call him on them if I find any, sometimes writing down more detail than is given on the blackboard.

In both cases, I find it helpful to try and develop an intuition for all things described, including definitions as well as proofs; if I believe I can wrap my mind about something, but am not certain, I ask, as I do whenever I find something completely non-intuitive.

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(+1), getting sleep is definitely important. Unless, of course, you prefer your proofs in haiku form xkcd.com/622 –  Omnomnomnom Jun 16 '13 at 1:44
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Here's what I would do if I were you:

1) As mentioned before, read ahead. Get a basic idea of the concepts in what you'll be learning about in your next lecture and how they relate to what you know currently. This will make theorems easier to remember (at least, in my experience), since if you understand the basic concept, you will pay attention to the finer details in lecture.

2) Ask questions and research on the topic before you start your lecture (and during your lecture). Especially for a course which you struggle in, find some resources online pertaining to your topic. When I was learning Calculus I in high school, as the class was learning limits, I was learning derivatives already and was asking the professor how to do a few questions. (This is usually a little overboard for some college courses, as there typically isn't enough time.)

3) Ask the professor if he/she would be willing (and/or able) to provide lecture notes before you start your lectures. One of my professors had a good habit of leaving all of her "fill in the blank" lecture notes online so that we could bring them to lecture.

What I suggest to you may seem extreme, but you shouldn't spend more than an hour or two doing all that I mention above (for an advanced undergraduate math class, at least).

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I suggest video recording the lectures (with permission from the professor).

One of the best math classes I ever took was John Benedetto's graduate introduction to wavelets. I could never keep up in class. But John let me record the lectures, so I never worried about taking notes and instead participated in the class and then reviewed the videos at leisure.

Maryland still has those videos posted on-line:

http://www.norbertwiener.umd.edu/Education/wavelets/

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