Questions about Listening To Presented Material [closed]

I find that during seminars I attend, I often feel like the slowest person in the room. 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?

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.

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).

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.