Throw away your calculator! I know I included
this on my Tips for Students Learning Math
page, but I just love typing it, so I couldn't resist including it here too;
plus it makes sense. Calculators suppress thinking; that's not a good thing
when you're taking a math test. Read my article on
Calculator Syndrome for more on
Please, use a pencil and a good eraser. Don't use a pen, not even an eraseable pen. They just don't erase as well as pencil marks do with a good eraser. My favorite is a mechanical pencil with one of those white erasers. You get consistent line thickness and make a mistake and it erases cleanly away; no smudges or marks. The idea here is neatness and organization showing in your work. When you go back to review what you did, you'll find it much easier when there aren't things crossed out, smudges with faint numbers showing through below what you've written, etc. If it's allowed, have an extra piece of blank paper. It comes in handy for quick, side calculations that you don't want to turn in with the test.
When I say 'read the problem,' I am actually implying a lot here. I mean understand what the real question is. Understand what information you are given. Understand how you're supposed to work the problem, if that is specified. These are the steps involved in reading the problem. It's kind of like knowing where you need to go, where you have to start, and how you're supposed to get there. Once you can answer these questions, then you're ready to proceed.
While you are working problems, you need to be thinking about what you're doing to make sure that you're heading in the right direction. Remember what the question is asking. Does what you're doing make sense. Is it going to give you something useful or will it just be a waste of time? Do mental intermediate checks along the way to make sure that what you've done makes sense. If you're working with distances, and you suddenly go negative, that's a cue that something might be wrong. If you're working probabilities, and you have a probability greater than 1.0, then something's probably wrong. You have only so much time to finish the test; these intermediate checks can keep you from wasting time by continuing in the wrong direction.
We're looking for the benefit of the doubt here.
Partial credit. Suppose you end up with the wrong answer, but you set up the
problem correctly and went through all the appropriate steps. If the teacher
can see that, then you're probably in for some partial credit. The real point
of a test should be to determine if you understand the material. Making an
addition error doesn't necessarily mean that you don't understand what you're
doing. The teacher needs proof of that though to give you credit for
understanding. If there is nothing on the test but a wrong answer, he or she
really has no other option than to mark your answer completely wrong. However,
if the work you went through to get that wrong answer is right there on the
test, then you have chance for some points to reward all your hard work. Even
if you're told that you don't need to show your work, do it anyway. It won't
hurt, but it could help your grade in the end.
When you show work, please do it in an organized and neat fashion. When someone is faced with the task of grading 25 papers, they don't want to have to search for answers. If the search involves more than a couple of seconds, they are likely to just mark it wrong and move on.
Last but not least; watch your mathematical syntax. When you write something down, especially on a test, make sure that it makes sense mathematically. If the work you show can't be followed in a logical order or if it is nonsense from a mathematical perspective, don't count on any extra points. Instead of convincing the teacher that you know what you're doing, you may just convince them that you DON'T know what you're doing. A correct answer worked in a mathematically incorrect way is wrong! Even if you worked the problem in a correct way, if what you have written down is incorrect, then you've just hurt yourself. I guess this is the one time when showing your work could hurt you.
Numbers are nothing without their units. Everything is relative to something else, but without units you don't know exactly how they are related. You would probably agree that 50 is greater than 30. But if I then told that the 50 is actually 50 millimeters and the 30 is actually 30 centimeters, then you'd be wrong. Unless you're working with ratios, there are probably some units involved (even if it's just tick marks on a graph).
As long as you're careful as you work a test, then this is done if you have time left. Never turn in a test with time left without checking all your work. You can accumulate a lot of extra points over time by finding those 'stupid' arithmetic errors that cost you a point here and a point there. If you're going to work hard enough to learn the material, then you should do you're best work on the test to get your just reward. Don't shortchange yourself and your grade to get done a few minutes earlier. Check your work!!
One of the most important things you can do is to learn why you missed a problem and learn how to do the problem correctly the next time. It's part of the process of understanding. When you get a graded test or homework back, you should sit down as soon as possible, figure out what you missed, what's wrong with what you did, and how to do it correctly. You should never miss a problem twice! There is absolutely no excuse for missing a problem a second time. If a problem appears on a test, it's important to know. Otherwise, it wouldn't be on the test! If it's important enough to be on a test once, then it's important enough to be on a comprehensive test later.