Improving at Mathematics?

Question

Greetings,

I would like to ask how one would improve at mathematics.

The reason I ask is because I consider myself extremely bad at maths. It's not a matter of being lazy, either. Whenever I'm given homework, I can solve the basic problems quite easily. However, at even slightly complicated ones, I'm stuck. I spend hours and hours trying to figure it out - I write and erase and try a lot of stuff - it hardly ever works. I don't always spend all my time on that single problem; I often go through other similar ones, and go back to the original problem, yet I still can't find any loopholes.

When the solution is given to me, I'm like "Duh!". Even from there, when I'm given a slightly more complicated one, I'm stumped again.

I don't like to repeat myself, but I have to emphasize that this is not a matter of laziness on my part.

Thank you.

p.s. Any indirect methods, such as games, books, philosophy, etc. (even more radical ones), are also appreciated. Thanks.

Thanks for the answers so far. I should have mentioned my Maths level in the original question - sorry. I'm in a course which is approximately equivalent to year 12 (i.e. right before university).

As for the problems, I'm afraid I can't think of or find any that eludes me at the moment. However, all I can say is that I have maximal problems with trigonometry and complex numbers, because to my mind, they are "abstract". I have no idea why I'm doing it, nor what I am looking for.

Thank you.

Answer 1

Moshin has a good point. The worst time to try doing difficult math problems is when you're up late trying to finish your homework. With a lot of subjects, you can manage to trudge through assignments even when half-asleep, but difficult math puts a premium on mental sharpness. Do the hard math during your peak mental hours. I often find that I think the best when I'm up in the hills walking alone. And if you really want to ace mathematics, do more than simply to solve the problems that you're given. Think of other kinds of problems, or different ways of solving the same one. One of the fun things about mathematics, as is unfortunately NOT stressed in public schools, is discovering an enormous variety of ways of sovling the same problem---and that helps you understand a fundamental feature of mathematics, which is that nearly everything in it is connected somehow with everything else. For example, whether or not a polygon is constructible using only a compass or a ruler is connected with whether or not one can find exact solutions to polynomials, and that is in turn is related to whether or not trigonmetric functions of certain angles have exact expressible values. And if that's not enough, all of that is related to imaginary numbers! They never teach you any of that in public schools, but that is the power and beauty of mathematics, waiting for you to find it.

Answer 2

I'm not sure what your math level is, but on higher math levels problems become so complicated that sometimes you can't solve them without coming up with something creative or asking the prof. for a guide. Creativity generally develops with years of math work.
If your stuck on a hard problem try to solve it for a while, if nothing comes up then leave it alone, have a good nights sleep and try it again. This usually works for me.
And the best time to do math is in the morning, that's the time the brain is most alert. This is because of psychologically we have more energy in the morning then in the afternoon.

Last. Please type in an easy problem that you could do, and then type in a hard problem based on the principles of the easy problem. I might be able to talk you into finding out how to solve the harder based on the principles of the easier.

Answer 3

Try to understand the relations. There is a logic in all math exercises. You don't have to use Yoda's magic power. Try to practice various exercises which will make you familiar with the concepts.
Sometimes is like fighting in a war. Some strong points left behind will capitulate eventually when you are advanced into enemy's territory.
Try to read the similar exercises from book and reflect what is all about. Have patience.
It's nothing wrong with you, in time you will understand better especially since you really want to.
If you're in college this book might be useful:
http://www.amazon.com/Professors-Guide-Getting-Grades-College/dp/0060879084/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1196535795&sr=8-1

Games? If you are old enough, the time for games is gone. Though playing chess might improve your logic and strategy.
Try to practice sport instead. It will fortify your body and mind determination.

Answer 4

The only way is to set yourself surprises. I will tackle my homework and some random topics on the same day so that I am constantly forced to stay up to date with my revision.