How to understand underlying concepts of math?

Question

I read somewhere that people who are really good at math understand the concepts behind it, rather than simply knowing how to do it? What does this mean? Tips on how to do this?

Answer 1

If you don't mind an analogy, there are people you know who write well. Some of them come up with simple ideas, then look up synonyms of words in a thesaurus, plug them in, and what they write looks impressive, but isn't really. Compare this to someone who actually understands the nuances of all the words and phrases they use... picking the exact right ones for the right places in their writing.

At first, to the untrained eye, both might look good, but only one is of high quality. The same holds true in math. People who understand the concepts behind what they do will have fewer lines in their proofs and will be crystal clear in their explanations... they'll be able to create as they go and have the ability to figure out math answers beyond what they're taught in a classroom. Those who "just use" the formulas are trapped by the limitations of what they already know.

As far as tips on how to get there, the best way to read a math book (your text, for example) or to be a student in a math class is to be skeptical. Don't take anyone's word for granted, especially that of the author or of your teacher. Make sure you question anything and everything you don't completely understand, even if it seems to be the dumbest thing. Don't worry how it makes you look in class, either. The thing is, while your classmates roll their eyes at any new question, they'll be droning out the key information you're gathering. They won't "get it," but you will.

Finally, make sure you never, ever use any formula or theorem that you personally haven't proven to be true. When you know the "why" behind an answer, the "how" is a piece of cake!

Great question, and best of luck in your studies.

Answer 2

Everybody learns differently and you may just have your own unique learning style that isn't working too well with algebra right now. You also said "it seems like everyone is doing it wrong except me." but in Math, there are rules to follow, and if you follow those rules you will get the desired outcome. That may not mesh well with your learning style. I would go to a learning center like Sylvan and get some advice. If that doesn't work, then possibly think about getting evaluated by a psychologist who specializes in learning and education. It could be something simple.

Answer 3

Yea I know what you're talking about. Being able to just do math means that you know a few steps and can somehow get to the answer following your procedure, but you may not know why the answer is what it is or how to solve the problem without those steps. A person who understands the concept can visualize the problem and know why the answer is what it is.

Answer 4

Anyone can memorize the Quadratic Formula: [-b +/- sqrt(b^2- 4ac)]/2a, but if you don't know what that formula really means then you are missing out on some secrets to algebra.