I ask this because I find myself to require allot of time and thinking before I am fully comfortable with a mathematical concept. There's always this feeling of discomfort towards a new concept that I have to vanquish by thinking about it for hours and hours. It's not that I can't apply the concept; it's more that I spend allot of time trying to understanding its every details and implications. What worries me is that once in college, this kind of learning will not be possible. For someone who tries to get a deep understanding of things, is it normal or am I just a slow learner?
I do that too, and it drives me nuts, because the class keeps pushing forwards and you have to learn about new material while still thinking about old material. Keep doing what your doing. After a while you will find that it becomes easier and faster to learn new things because you understand the things you already know at a deeper level.
Actually, I believe that's perfectly normal. The catch is that you sometimes don't have time to do this in college/university. So, you learn to get by (even do well) without even fully understanding what's going. Totally normal. You have perseverance it seems, so that's a good skill. Also, although you think you're learning this little concept while thinking all that time, you're actually learning a lot more than you think, and that will come along later. Don't sweat it.
I agree with Jason, I'm taking the last part of Calc 3 now, i took the first part about a year ago and I found its easier just to go with the flow and not question it. Some girl sits besides me asks every little question and we get no where. I just see a pattern and apply it. I think calculus is the only math subject where I can just see patterns and apply them, without really thinking about what i'm doing but seems to work quite well.
When you start appyling this math to physics problems where they are no longer numbers and symbols but physical things that represent something you're going to find it much more difficult than the girl that spent time considering each detail. If your not thinking about what your doing, you dont know what your doing. You're blindly using equations, and thats dangerous.
Cyrus, I already made it threw Physics Mechanics, Q&M and quantum all with A's so i'm past that stage of just using formula's. I was just stating what is easily done in calculus. That I havn't found possible in any other type of math, such as discrete or diff EQ. But while I was taking physics I was doing this in my calculus classes, but during physics, he would explain why we are doing it.
wow... passed quantum with A? I heard quantum is hard, hope you can help me out in the future on this forum!
it does not matter how slowly you learn. if you are learning you are doing well. it is those of us who have stopped learning who are in need of sympathy.
Me Too!! Hi there... I have classified myself as a "slow learner" as well. Where some seem to "just get it" ..I have to look at things for SEVERAL hours to understand them completely. I have only made it to Calc II (with A's), but this is what I do: Before each class, I review each chapter, working the examples, writing down the formulas, just like I might in class. This helps me in two ways: a) When I get to class...I have a clue...albeit usually a small one. b) I can take less notes in class and pay more attention to what's going on on the board. This has helped me keep my averages very high. I'm an excellent math student, but not because it comes natuarlly. It takes hours of prep on my part. Good luck...oh...and I was a C and D student in math in high school. Go figure. :surprised
I was a Comp Eng Major who switched a semester ago to Comp Sci. Comp Eng majors only needed 2 credits of calculus 3, not the full 4 credit course. Now i'm going back to take the 2nd half of calc 3. So even though right now im in calculus 3, I've already taken Linear Algebra, all the physics needed and then sum because now i'm comp sci (which only needed Mechanics and E&M), Diff Eq, Discrete math, so after this semester i'll be done with all the math except I still need 2 300 level stat courses. So right now i'm classified as a senior and yet i have 44.5 credits left to complete my major :\ Oh well as long as I'm not paying for school I'll go as long as possible! Also at Penn State your not required to take all your calculus courses before your physics like i've heard some universities do. You take the physics courses concurrently with your calculus 1-3 sequence. The physics coursses here will give you a quick "crash course" on what you should know even if you don't know the subject, you don't need to have completed all of calculus sequences to do physics. ha, i took it about 1.5 years ago but paste it up and i'll see if i can :) (but don't paste in this section paste in the physics section of the forum.)
as long as you get good grades and you understand the material, it doesnt matter to anyone if your'e a slow learner or a fast one.
Take your time and learn slowly. You may spend 3 hours thinking but that is alright. It is the same deal in my Thermal class. At the beginning, I was behind because I cannot allow myself to just blindly computing and plugging things in formulas. Now that I have spent so much time doing extra reading and thinkings. I have a much much greater understandings in the material than most other people. right now, I seem to be one of the few who ACTUALLY have a complete understanding on what is going on and now other people are falling behind me instead of I falling behind them. Honestly, it's okay to feel uncomfortable and it is good to be uncomfortable (it means you are actually trying to learn something instead of cramming something in your head). The difference between a smart student and a normal student is how he/she deals with this uncomfortable-ness. you either go grab a book from the library and study like hell. or be lazy and let it slip by. I did the former one and I am ahead of most of my classmates.
I tried searching for information about this "slow" learning of Roger Penrose; I did not find anything relating to any slowness of his learning. Do you have some comments about it, or any website links? How slow is too slow? At what measure of slowness should one choose to not continue studying Mathematics or Physics?