As a math instructor, I have seen many high ability students do poorly, and many average students excel. What makes the difference? The proper combination of attitude and preparation is key for success in mathematics or any technical field.
In order to do well in a math course, you must have these 10 essentials down:
1) A positive attitude towards the subject
2) The ability to focus on details
3) Practice, practice, practice
4) Proper study habits that go beyond memorization
5) A belief in yourself
7) The drive to seek out alternate sources
8) The ability to check your work
9) Methods for remaining calm under pressure
10) The ability to swallow your pride and ask questions when needed.
Number one is the most critical factor. It is impossible to stay focused on a difficult subject if you are mumbling to yourself about why you have to take it or how stupid it is! If you doubt the importance of mathematics in our world, look around. It is impossible to succeed in most high paying jobs without solid math skills. Look at the beautiful buildings and bridges around you, none of them would be possible without the use of mathematics. Take some time and cultivate a respect, and positive attitude towards the subject.
Number two is difficult for many as we are taught in most liberal arts programs to focus on concepts. Mathematics includes many concepts, but if you get the concepts right and mess up the details, you still get the problem wrong! Carefully review each assignment to make sure all your signs, numbers, and parentheses are in the right places. This takes practice. Yes, there is a body of research that shows that some people are verbal and some are mathematical, but I also believe that we learn to spot that which we are focused on the most. Practice adding up long columns of numbers and see if they come out to what your calculator says they should. Review example problems, and make sure you understand every detail, and why it is included. I have also found that working mathematical puzzles over the Internet or from puzzle books helps to cultivate this type of thinking.
Number three follows directly from number two – practice, practice, practice! Imagine that you are a major athlete training for a sporting event. You wouldn’t just practice once, would you? Getting the right answer once is not enough. Work similar problems over and over, looking for more insight each time. Work on your speed, as speed is definitely a consideration during most college high pressure testing situations.
That brings us to number four – change your study habits. This is not a history course where memorization will bring you an A. Don’t just read the words in the textbook and assume you understand. You may not know what you don’t know until you review worked problems, and try them yourself. This is where you find out if you have a concept, or methodology, backwards in your mind. This is normal for complex concepts, and just takes time to overcome. Buy books of worked problems and work them yourself until they become second nature. Then go back and reread the text to see if it offers new insights.
Obviously, in order to take all these steps, you have to believe that you CAN do it. Tell yourself over and over again that you ARE a math whiz. This will put the suggestion into your subconscious that you can do it, you just need to spend more time. This way you won’t give up when the going gets tough. Stay positive, it will pay off.
A belief in yourself will drive number six, persistance. It never failed to sadden me when I saw bright students give up, right when they were on the verge of a breakthrough. Shaking their heads, they would tell me that they just would never be good at math and why try? Never, never give up. Remember how many times Edison tried to get the light bulb right, and know that your very own personal light bulb WILL turn on.
Number seven is common sense, but I still have students who believe that if they can’t understand the material from the textbook, they never will. We are all different people, and difficult concepts make sense to us differently. There are many sources of explanations for complex mathematical topics, if you seek out more than one, chances are one will make more sense to you than the others. Try www.purplemath.com for logical, easy-to-understand explanations of algebra. Or go to your local library or bookstore and find something that clicks. Remember, math takes persistance!
Number eight is also common sense, but I am still amazed by the number of students who think their job is over when they have arrived upon AN answer for a problem. Runners don’t stop and wipe their foreheads when the finish line is in sight, and neither should you. Be relieved when you have solved a difficult problem, but do NOT make the mistake of thinking your job is done. If you have practiced for speed, you should have plenty of time in the testing situation or after a long night of homework problems to double check EVERY STEP of your work. Measure twice, cut once.
It never fails that I have one or two students who do a wonderful job on the homework assignments and choke under the pressure of exams. This is sad, and a very real situation for those who suffer test anxiety. In order to fight this difficult dragon, I suggest that you get a good nights sleep before the exam, arrive early with plenty of pencils, and sit in a comfortable place. Practice deep breathing before hand so that you can calm yourself. The scent of Ylang Ylang oil is also calming, put some on your pencils so that you can breathe it while you work.
Of course, the best cure for test anxiety is to remind yourself of all your careful preparation and study the weeks before the test!
If you missed a few problems, number ten comes into play. Mathematics and all technical subjects build upon one another. Do NOT go into the new material without scheduling time with your instructor to ask questions about what you missed, and making sure you understand every detail. The only dumb question is the one not asked!