Best ways to study math and science?

[pakmingki2]

is the best way to study math and science really just to do tons of practice problems?
BEcause I've always been told by my teachers, especially when preparing for standardized tests to do as many problems as possible.

Is this really the most effective way to become "good" at math and science?

 

[mr_coffee]

For me, it was all about solving the problems.

Reading did nothing for me. Once I do the problems, I see a pattern, then I can apply that pattern on other problems.

Physics is the same way, without doing tons of problems, and just reading about it, I don't see how that's even possible.

When I would study for an exam, I would re-do ALL my homework, over and over again.

 

[TMFKAN64]

Yes, definitely, do as many problems as you possibly can. As you do this, the concepts will become second nature to you...

However, you need to find a good source of *different* problems. You won't learn anything by plugging different numbers into the same basic equation.

 

[kuahji]

For algebra it was all about plugging & chugging. Simply doing as many problems as possible. But for trigonometry & calculus, at least for me, I had to do a bit of reading. It was still do as many problems as possible, but its still VERY important to understand the underlying concepts, or else the applications just don't make sense. I mean I suppose you could still do them systematically, but its important to understand concepts like what is a derivative, integral, etc.

Yes, definitely, do as many problems as you possibly can. As you do this, the concepts will become second nature to you...

However, you need to find a good source of *different* problems. You won't learn anything by plugging different numbers into the same basic equation.

I agree with this as well. I always try to keep two sources of problems. Usually the textbook for class, & another old outdated one that can be found really cheap online. Or if your school has the complete solutions manual, usually doing odds & evens work.

 

[zhentil]

The goal is to understand the material inside and out. For 99% of people, this involves doing practice problems to understand how it works. I don't know any mechanics or cooks who learned by watching a video. You have to dig in and get your hands dirty.

Personally, I always try the problems before I read the section. Sometimes I can do them, most of the time I can't, but it always gives a vivid demonstration of the need for the more sophisticated techniques that were introduced.

There are some people who can read a math book once and understand it all immediately with no further effort. I'm guessing you're not one of these people, since otherwise the problems would be so trivial that no teacher would ever recommend that you actually prepare for an exam. But here's a rule of thumb: if you don't understand the material completely after reading the section once, you won't understand the material any better by reading it again.

So far, I've only considered doing problems and reading theory. But what else is there?

 

[CompuChip]

And even if you are on of those people that understands everything after having read the text once (or n times, for that matter), understanding the material and being able to follow a proof is something entirely different from being able to solve problems yourself and provide proofs yourself.

 

[sadhu]

the best way to study maths and science , is not just cramping the book or just doing the same kind of problems again and again ...

what worked for me was 25 min of understanding, 15 min of thinking about the topic and to
dig deep into it ,and 20 min of practice...

i usually just read the heading of the topic and then try to figure it out on myself.

these days regular college books just repeat the same problem , making only a slight change
in it , its of no use doing same thing again and again without knowing what it is .

try to manipulate the topic yourself and generate new methods of doing tougher and tougher problems of the subject.

 

[Shackleford]

Yeah, it has helped me a bit on my Calculus courses to step back and qualitatively rehearse everything - I do this to do that because I want to do this, blah blah blah.

 

[zhentil]

And even if you are on of those people that understands everything after having read the text once (or n times, for that matter), understanding the material and being able to follow a proof is something entirely different from being able to solve problems yourself and provide proofs yourself.

If one can't solve problems or provide proofs, I would hardly say they understand the material.

 

[zhentil]

the best way to study maths and science , is not just cramping the book or just doing the same kind of problems again and again ...

what worked for me was 25 min of understanding, 15 min of thinking about the topic and to
dig deep into it ,and 20 min of practice...

i usually just read the heading of the topic and then try to figure it out on myself.

these days regular college books just repeat the same problem , making only a slight change
in it , its of no use doing same thing again and again without knowing what it is .

try to manipulate the topic yourself and generate new methods of doing tougher and tougher problems of the subject.

I'm not sure what textbooks you're talking about, but after Stewart's Calculus I had no textbooks like that. I didn't take too many science courses, but what I've read of Jackson's EM textbook did not strike me like that either.

 

[Poop-Loops]

I liked Stewart's Calculus. Having that many similar problems was great. You can't make a line with 1 point, and similarly, I need to understand at least 2 problems before I can say I understand the concept behind them. More is better.

Boas was like that, too.

Griffiths E&M and QM, Tipler & Llewellyn's Modern Physics, Schroeder's Thermal Physics, and Kibble & Berkshire's Classical Mechanics have all just had one problem per concept and then you move on. Don't like that much...

Or even worse. The example given is something completely trivial and then for the homework problem you have to solve this completely different thing.