I’ve tutored lots of people in math over the years and the one thing that gets most people in math is they’ll look at the problem and think, “I don’t know how to solve that.” So they don’t try anything and instead they just throw down their pencil, fold their arms, and sulk. When, if they just did one or two things to the problem that they already know how to do (without knowing how it even helps them) it would change the problem into one they would recognize and they could immediately solve it.
Now, I’m not saying that you’re going to be able to solve any math problem. Each level of math (and there are infinite levels…) requires a certain base of knowledge within that level in order to be able to solve that problem. For instance, if you don’t know how to manipulate equations (by moving around numbers and variables from one side of an equation to the other and combining like terms, etc) then you’re not going to be able to solve a simple problem like 3x = -2x +1, even if you could solve 5x = 1.
What I am about to reveal is how exactly how I figured out how to do a math problem — one that had previously stumped me for two months — during the AP Calculus BC test. And good thing too because there were three other questions just like it (two of them essays) and I wouldn’t have gotten a 5 without this strategy. This is a strategy I was never taught. I just figured it out. I never thought of it as something I could teach others either as I never thought of it as a strategy. It’s just the way I think about math. I was always better at testing in math than my friends, but I never really knew why (other then I knew I could figure things out on tests even when I didn’t understand them previously). Well, this last semester as I helped my sister through her DEs class, she kept doing what I said above: throwing down her pencil and folding her arms. (Hey, we all, at some point, feel stupid doing math and resort to throwing pencils. It’s okay.) So I ended up unintentionally teaching her how I figure out how to do a math problem even when I have no idea how to do it.
How to solve a math problem you don’t know how to solve
With all that said, what do you do when you’re faced with a math problem that you don’t know how to solve (but you have the basis for). Step one: do the first thing that comes to mind that you know how to do that you can do to the problem. In the case above, get all the x’s on one side of the equation. Then presto! You know the next step because you’ve solved questions like these before. If you don’t, however, know your next move after your first, do the next thing that comes to mind and carry on until you get stuck or have solved the problem. If you get stuck, usually somewhere along the way another thing that you could do came to mind and you can try that or look over the problem and look for ideas where you could try something different. As analytical as math is, it can also be a very creative field. Be willing to just try things.
In the case where you don’t even know your first step, or have any ideas, just rewrite the problem. Something in the rewriting of the problem allows your brain to process the information and sometimes as you rewrite (you can also say the problem aloud as you write which helps your brain focus on the problem at hand), something will occur to you. If it doesn’t, ask yourself, “What can I do now?” And usually an idea will come to you.
Don’t spend too long on a problem wondering what to do. If it’s a test, mark the problem (you can circle it or write the number at the beginning of your test), move on, and come back to it later. If it’s homework then google it. You’d be surprised at the amount of information online on even advanced (I used it for my grad level numerical analysis and probability classes) mathematics you can find online. It’s awesome! You can also check your text book for the examples. Any good math text (they do exist!) will tell you how to solve your problems, er, at least your math ones. 😉
And that’s it. Just do what you know you can do, ask yourself what next, and if you’re truly stumped move on or find out more information.
Don’t fold your arms
No really, don’t fold your arms, even if you’re cold. Get a blanket and some hot chocolate instead. Then open yourself up (mentally and physically) to receiving some inspiration and ideas will come to you.
You can throw your pencil though. That’s fun.
It’s really that easy!
This method really does make math easy, at least easier to think about knowing you don’t have to know everything up front in order to solve a problem. Don’t discard this information because it’s simple. It’s by small and simple things that great things are brought to pass. Those that dismiss little things miss out on everything.