How to Study Mathematics

Many people have trouble learning mathematics because they never develop the particular study habits, which are conducive to success in mathematics. If you practice the following suggestions they should prove invaluable to you.

Read carefully and deliberately.  The way in which you should read in mathematics is quite different from the way you may read a history book, newspaper, or a novel. In mathematics you must read slowly, absorbing each word.  It is sometimes necessary to read a discussion, or a problem, many times before it begins to ''make sense" to you. In some types of reading, such as a novel, it is desirable to skim and read rapidly, because there are usually a few thoughts "sprinkled" among many words. However, in reading mathematics each word or symbol is important because there are many thoughts condensed into a few statements.

Think with pencil and scratch paper.  Always have pencil in hand and scratch paper ready and use them when you read and study mathematics.  Test out the ideas on paper that authors are discussing. When they propose a question, try to answer it before going on. Even though an example may be worked out completely in the text, work it out for yourself on scratch paper. This will help to clinch the ideas and procedures on your mind before starting the exercises. After you have read and reread a problem carefully, if you still do not see what to do, do not just sit and look at it. Get your pencil going on scratch paper and try to "dig it out".  If, in attempting to solve a problem, you have nothing written on paper, then certainly you have not yet exercised enough effort to justify seeking help.

Be independent.   Try to complete each lesson without assistance. If you seek help needlessly, either from your teacher or a classmate, you will not gain the maximum benefit from your work. It takes exercise, you know, to become strong. You cannot do it through someone else’s exercise.  However, you must ask questions when necessary. Sometimes little things cause considerable confusion. Do not be afraid that your question may sound  "dumb". The only ''dumb" action is to fail to ask about a topic that you have tried to grasp and still do not understand. Some people seek help too soon and some wait too long. You will have to use good common sense in this matter.

Listen in class.  Many of the finer points, fundamental principles, and modes of thought will be developed in class. You must pay careful attention to those discussions in order to understand what is going on

Persevere.  Do not become frustrated if a topic or problem may completely baffle you at first. Stick with it! An extremely interesting characteristic of learning mathematics is that at one moment the learner may feel totally at a loss, and then suddenly have a burst of insight that enables him to understand the situation perfectly. If you do not seem to be making any progress after working on a problem for sometime, put it aside and attack it again later. Many times you will then see the solution immediately even though you have not been consciously thinking about the problem in the meantime. There is a tremendous sense of satisfaction in having been persistent enough and creative enough to independently solve a problem that had given you a great deal of trouble.

Take time to reflect.  To learn mathematics well you must take time to do some reflective thinking about the material covered during the last few days or weeks, It takes time for some ideas in mathematics to "soak in".  You may have to live with them for a while and do reflective thinking about them before they become a part of you.

Concentrate on fundamentals.  Do not try to learn mathematics by memorizing illustrative examples. You will soon become overwhelmed by this approach, and the further you go the less successful you will be. All mathematics is based on a few fundamental principles and definitions. Some of these must be memorized. But if you concentrate on these fundamentals and try to see how each new topic is just a reapplication of them, very little additional memorization will be necessary.

Be neat and accurate. These are habits that will save you many headaches in any field of endeavor. Most people must deliberately practice neatness and accuracy before they become a habit. Keep your work organized. Have a special section in your notebook for mathematics. Keep today’s homework paper in the same place in this section everyday so that you can turn to it immediately. No excuses for not having your homework will be accepted  (even though they may be true) such as-, “I know I've got it in here someplace.”, “I lost it.”. “ I left it at home.”, “I put it in my book, but it must have dropped out.”, “It's in my locker.”, “ Didn't have time.”, “It's in the pocket of my other shirt.”, ad infinitum.

Take time to do your work and do it on time. You must do your homework regularly and make up the work missed when absent. No sympathy will be given anyone failing to do his homework. Do not wait until the last minute to do your work and the rush through it. If you spend just enough time on your lesson to get the "answer" and do not take time to understand the underlying principles, you will soon become confused. Mathematics is a lot of fun as long as you are "on top of it" and understand what is going on; otherwise, it is very frustrating.  Learning mathematics is not an activity for the intellectually lazy. It requires a strong, steady effort. There is no other successful way. Neither is mathematics a spectator sport; you must become very actively involved. Do not expect to sit idly by and watch your teacher do the work. This may keep the teacher in good condition, but it would not do you much good.  There will be no extra compensation given for working hard and conscientiously doing your homework. This is something you are expected to do as a matter of course. The "reward" you get will be the mathematics you learn.

Good Luck!!

Thank you Mrs. Wright for these excellent suggestions.