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.
The way in which you should read in mathematics is quite different from the way you 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 problem, four, five, six, or more 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 is important, because there are many thoughts condensed into a few words.
Always have a pencil in hand and scratch paper ready, and use them when you read and study mathematics. Test out the ideas the authors are discussing on the scratch paper. 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 yourself on scratch paper. This will help to clinch the ideas and procedures in your mind before starting the exercises. After you have read and reread a problem carefully, if you still don’t see what to do, don’t 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 exerted enough effort to justify seeking help.
Try to master each assignment without assistance. Getting help needlessly, either from your teacher or a classmate, is one of the pitfalls in the study of mathematics. It takes exercise, you know, to develop muscles; you cannot develop them through someone else’s exercise. However, another pitfall is failure to 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 really 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 manner.
Many of the finer points, fundamental principles, and modes of thought will be developed in class. You must pay careful attention to these discussions in order to really understand what is going on.
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 don’t seem to be making any progress after working on a problem for some time, 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 has given you a great deal of trouble.
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 awhile and do reflective thinking about them before they become a part of you. Do not try to learn mathematics by memorizing illustrative examples. You will soon be overwhelmed by this approach, and the further you go the worse it will get. All mathematics is based on a few fundamental principles and definitions. If you concentrate on these fundamentals and try to see how each topic is just a reapplication of them, very little memorization will be necessary. Do not wait until the last minute to do your homework and then rush through it. If you spend just enough time on your lesson to get the answers and do not take the time to really understand it, you will soon become confused. Mathematics is a lot of fun as long as you are “on the top of it” and understand what is going on; otherwise it can be very frustrating.
These are habits that will save you many “headaches” in any field of endeavor. Keep your work organized. Have a special notebook for mathematics. Keep homework papers and lecture notes in the notebook, so that you can refer to them throughout the course.
To be successful in mathematics, you must do your homework every day and make up the work missed when absent. Your grade will be based on homework, as well as on test scores. If you have been negligent in daily work, your performance on tests will suffer and your grade will be lower as a result.
Learning mathematics is not an activity for the intellectually lazy. It requires a strong, steady effort. There is no other successful way. Mathematics is not a spectator sport; you must be actively involved. Do not expect to sit idly by and watch your instructor do the work. This may keep the instructor in good condition, but it won’t do you much good.
There will be no extra compensation for working hard. This is something you are expected to do, as a matter of course. The “reward” you will get will be the mathematics that you learn.