Math: An Attempted Definition
What is math, anyway? I believe math is nothing more than relationships. It’s a lot like the animal world. A gorilla is bigger than a grasshopper. You’ll never see a grasshopper bigger than a gorilla, unless you read the supermarket tabloids on a regular basis. A leopard is faster than a cow. Most fish swim much better than most elephants.
In a somewhat similar way, you began to learn the basics of mathematical relationships even before you went to school. You knew that having two apples was better than one (and three was even better). You knew 10 was more than 5, and a million was bigger than any other number you could imagine.
Eventually you got all the numbers straight in your head and developed ways to judge their relative size, so that now, you instantly recognize that 14,744 is larger than 7,928, even though this is the first time you have ever seen those two numbers together in the same room.
You learned to add numbers, and soon realized that the result of adding two or more numbers gave you a bigger number. So addition changed the mathematical relationship by creating something larger. Subtracting, on the other hand, did the opposite. If you had seven candy
bars and your mother took five away, you had only two left. (It seemed irritating at the time. We knew two apples were better than one, so why were we always having our candy bars confiscated?) Subtraction, then, made things smaller.
The following year, we learned that multiplication made things way bigger, and so we knew that five times eight must be bigger than two times eight. Division was a little more mysterious because it used that strange symbol that from the back of the classroom looked like a plus sign. Long division was even more confusing. It put one number under something that resembled a carport and the other outside the carport, and then you had to divide, put more numbers on the roof, then multiply, subtract, bring numbers down, and divide again. This was getting to be work, but we eventually conquered long division and found ourselves at the top of the
mathematical world. At least for the rest of fifth grade.
But around sixth grade, things began to get out of control. They started talking about fractions, decimals, common denominators, square roots, and factors. When we began to accept those things as pretty normal, they gave us negative numbers. Then letters instead of numbers. Then letters and numbers. Then adding, subtracting, multiplying, and dividing letters and numbers. Some of the letters had little raised numbers next to them. They told us we could rearrange all these symbols into expressions that could help us figure out how much older Sally was than Billy, or who had more goldfish, Brian or Monica. (As if we really cared. We just wanted to get our candy bars back.)
Next, they showed us pictures of squares and triangles, and for about five minutes we began
to feel comfortable again. We already knew what squares and triangles were. We had colored many of them with large crayons in kindergarten, and then at home while showing off for our aunts and uncles. But our comfort was not to last. These squares and triangles were not for coloring. They were just another excuse to add and multiply with letters and numbers. We had to find the perimeter of the rectangle and the area of the triangle, and soon, the circumference of a circle. Our heads were crammed and confused and for many of us, this was where it all
came tumbling down. We spent the next two or three years just bluffing our way through math, trying to stay out of the way, sliding by. We never raised our hands in class and always made sure our eyes were looking down whenever the teacher asked a question. We had gotten lost so long ago, we couldn’t even remember where we were trying to go. There was no hope of finding our way out of the forest. We would just sit and wait for someone to clear the trees and build condominiums.
And we would’ve made it, too. Most teachers were perfectly willing to give us a C in math just to get rid of us. Next year’s teacher would surely fix the problem. We continued to succeed in this giant slalom of failure, somehow making all the necessary turns, just nicking the poles, but never knocking them over. We were almost down the course.
Then came the SAT. That miserable concentration of torment and frustration. One small test, one major influence on future events. Why is it so important? Why is it so difficult? Why do I have to take it?
The answers are: Because. It isn’t. You don’t.
The SAT is useful because colleges seek to gauge your math and language skills in a way that doesn’t give anyone an advantage. An “A” average may not mean much because at your high school, maybe almost everyone gets A’s, while at another school, almost nobody does. With a standardized test, everyone answers the same questions and is rated against the same scale.
Why does the test seem so difficult? Because it’s tricky. It requires you to think. It isn’t always what it seems. It can’t be trusted, and that’s a new experience for you in the
If you have no intention of ever going to college, don’t take the SAT. Save the registration fee and buy yourself a nice tee-shirt. But if there’s a chance you might go to college someday, it’s probably best to take the SAT now, while the stuff is still fresh in your mind (I make certain assumptions there).
Let’s proceed on the premise that you are going to take the SAT, and sometime within the next twelve months. What can you do to improve your chances of scoring high on the math part? A lot. My book, 100 Math Tips for the SAT, will take you on a tour of a hundred typical SAT math questions. It will point out the traps built into each problem, and it will help you ask (and answer) the four key questions you should be asking yourself:
What are they telling me?
Recognizing the information given often requires some translation, and rearranging. This is vital to setting off in the right direction.
What are they asking me?
Frequently, questions are designed so that the goal isn’t clear. Or if it is, you end up doing so much work you forget what the question was. Problems that require several steps to solve will take you past a few partial solutions along the way. Usually, these partial solutions will appear as answer choices. It’s extremely helpful to restate the question to yourself before marking an answer choice, especially with the more complex problems.
What do they want me to be thinking?
Again, the SAT is designed to lead you in the direction of an incorrect answer. In order to do this, the testmakers try to get you to think about the wrong things. They know you know the math, but if they can disguise the question cleverly enough, you won’t realize you know how to solve it, and will be tricked into thinking about concepts that aren’t going to help you.
What should I be thinking?
When you’ve done enough practice questions, you will be able to look at most SAT math questions and the concepts you need to solve the problem will leap out of your mental toolbox — instantly. And ultimately that’s the key: getting those tools out quickly and using them properly. (If you’ve ever tried to hammer a nail in with the handle of a screwdriver, you know exactly what I’m talking about. And if you haven’t, well, go try it.)
Once you’ve mastered these four elements, you will be on your way to a great SAT math score. The secret is to practice. In addition to 100 Math Tips, get a copy of The Official SAT Study Guide, the one published by the College Board, and do as many of the questions as you can. The more practice questions you do, the more comfortable -- and the less intimidated -- you'll feel when test day rolls around.