Some college mathematics may be required for one of the majors that you are considering or it may simply be required for you to graduate in any major. Even if it is not a requirement at your college, you may find that a basic knowledge and skillful use of arithmetic and math will be expected of you in your natural and physical science classes and in many of your business and social science classes. Math is a common tool which may be used in any one of a large number of the classes offered in college.
So, you may suddenly find yourself facing a math requirement which you hadn't planned for. If you have had a solid and continuous math background during high school, you're in good shape and the study tips in this chapter will just be frosting on the cake. However, if you have had little math in high school, or had it some years ago, or got only a "C" average in the math classes you did take, then read this chapter very carefully. You will discover some very valuable new study patterns.
Renew Your Basics
The first thing to do when you find that you are going to encounter math in college is to review your basics. If you have had a lot of math in high school, it's a good idea to spend part of the summer before your freshman year begins by reviewing the prerequisite courses for the college course you will be taking. If high school algebra, solid geometry and trigonometry are the prerequisite courses for your college course, bone up ahead of time so that the skills you have learned in those courses are fresh in your memory.
Most college math courses move very rapidly. Very little time is spent in class review; you are expected to know it well when you come to class. Occasionally a first day quiz on the basics you learned in high school is given. If you haven't reviewed you may find yourself washed out with the suggestion that you take a review math class before beginning the class you have enrolled in. To avoid this possibility, review before you begin the class.
One useful way to conduct your review is to get out your “old" high school texts and systematically go through a sampling of different problems to refresh yourself. Another useful approach is to go to the college bookstore about a month before classes begin and look over a copy of the math book you will be using in your first college course. Skim the first two or three chapters to see the kinds of things they may expect you to know how to do early in the course, then go back to your high school materials and review the skills covered in those first chapters.
What do you do if you haven't had much math in high school, or you had it and it's been a while, or you took a business math or consumer math class because you really weren't planning on taking any college math? If that is your background, your best bet is to give yourself a thorough review in arithmetic skills, reviewing percentages, proportions, and especially fractions and decimals. If you can quickly and accurately add, subtract, multiply and divide fractions and decimals, you are in pretty good shape to take the next step in math. If you haven't practiced these skills recently, review the material in Appendix B at the end of this book. You will probably find it useful to review your high school math books, too. When you hear college students say: "I've never been any good at higher math," they usually mean that they have not practiced their basic skills in arithmetic. It's easy to forget those basic skills if you haven't used them for some time or never were really clear about how to use them correctly.
Handle Your Math Textbook Differently From Your Other Textbooks
Sometimes college students who are trying to increase their reading speed will try to apply speed reading techniques to their math textbook. It doesn't work. You necessarily will have to slow your reading pace substantially. It will be necessary to stop frequently to note definitions for the very precise vocabulary of mathematics. These definitions can be placed on flash cards for ready reference. However, because there are so many new definitions per page in math texts, you may have to simply take the time out of your schedule to memorize each new definition as it comes up so that you will be able to read the assignment with understanding. Frequently you may find it necessary to reread to clear things up.
When using underlining in your textbook, pay particular attention to new formulas. If a particular formula is used frequently in an assignment, check with your instructor to see if it's one to be memorized. You may be expected to memorize some formulas for your math class, but more often you will be expected to know where to quickly find it in your book and especially to know how to apply it correct1y once you have found it. Don't memorize every formula you encounter; a check with your instructor may save you a substantial amount of memorizing effort. However, all important formulas should be circled so that you can quickly find them when you need to. It's also wise to circle one or two of the most representative problems in each day's math assignment. Pick out a couple of the best examples of the problem types emphasized in that part of the text. Also, star one or two of the problems with which you had difficulty. Later you can review these, or even redo them as practice preparation for your next test.
If your textbook examples aren't too clear as illustrations of particular math concepts, you don't have to limit yourself to that text. Ask your instructor if he knows of some other text which can give you additional examples of the concepts or processes covered in that particular section of your text. Often a different author will give a much clearer example of a given concept or process. The text you are using is only one tool. Feel free to check into other texts so that you are expanding your set of tools.
How You Can Take Better Math Class Notes
Math lecture notes may be more limited than in some of your other classes. Sometimes your instructor may spend most of the hour going through two or three sample problems. As a result you may write less in your math class notes. However, you should be actively thinking through the problem solving process with your instructor. If you get lost in one step of the given problem, raise your hand and ask for clarification. If for some reason you don't get an opportunity to ask your question during the class period, check with your instructor right afterward. If you can't catch him, check with your friends after class. If they don't understand it either, go to your instructor during his office hour. It’s important to get a clear understanding of the class sample problems. If you miss the meaning of a mathematical concept, what you miss may be a key idea and lead to greater confusion later. Remember, the pace is fast and each new day's work builds on the previous day's understanding; so check quickly about things that you don't understand. The next two days' assigned problems may depend on your knowing exactly what the instructor is doing with the example he is presenting.
If your math instructor is using some examples which aren't in your text, try to get each step of the example down in your notes as he presents it. Then quickly recheck his blackboard work to see that you have not left out some crucial symbol or step. Above all, listen carefully to what he is saying about the steps in the example. Sometimes the very act of copying the example causes you to divert your attention and tune out what he is saying about it. With a little practice you will find that your copying will become somewhat automatic while you listen carefully to what's being said. If at first the listening and copying are too difficult to do at the same time, either wait until the end of the period to copy the board work or bring a portable tape recorder to class for recording and later replaying the lecture.
Doing Math Assignments
The amount of assignments may be greater in college than it was in high school. You will find that you are moving through your college math text much more rapidly than you went through your high school text. Many of the assignments will not be collected or graded in your college classes. In college they assume that you will do all of the practice exercises and assignments on your own. The answers to the questions are usually given in your text or workbook. However, it’s very important to do the assignments even when they are not collected. If you don’t do the assigned exercises, you won't pass the math quizzes and you won't pass the course. They leave it up to you.
Keep Up With Your Assignments
Mathematics assignments usually cannot be postponed. One day's assignment frequently builds on the past day’s assignment. If you get behind on your assignments for one week you may find it difficult and sometimes impossible to understand the following week's work. There are probably some classes where you can safely postpone your work, but if you try to put off your math it may be disastrous.
How to Approach Your Assignments
Review the problem examples you have in your lecture notes and compare them with the same kinds of problems covered in your text. Make this review complete and be certain that you have a clear understanding of what you are doing when you actually begin the practice problems. If you get a wrong answer, go back to the examples given in your text and lecture notes and see if you can figure out where you made your mistake. Don't spend hours going back over the same problem. Review your steps, try it couple of times and then either check by phone with some of your fellow students from math class or temporarily pass up the troublesome problem and go on to other problems which you can do correctly. It's easy to get "hung up” on very insignificant error which may be perfectly obvious to one of your friends. So don't waste time straining one problem when you find that you aren't making any headway with it. Put it aside, consult some buddies and come back to it later.
How Working With Friends Can Help You on Your Math Assignments
Study with one or two other friends when doing you math assignments. Try to study with someone who knows their math as well as or better than you do. Don’t simply arrange to meet them and copy all of their work. If you try that tactic, you won't learn anything and they will soon peg you as a loser and drop you. Unfortunately you won’t be able to copy someone else's work when test time comes.
So, try the first five problems and then compare your work with your buddies. Then try the next five and repeat the comparisons. If you frequently come up with the wrong answer, they may begin to think you are a little "thick," but if you are really trying they will usually be glad to help you over the hump. In return for their help, you might occasionally do them some special favors or help them with a subject which you know better than they do. Whenever you check with your friends, look for patterns of errors. If they say "Hey! You made that same kind of mistake yesterday," listen and try to correct the pattern.
How You Can Prepare For and Take a Math Exam
One of the best preparations for math exams is to be continuously reviewing your practice problem assignments. At the end of the first week, go back over a sampling of the practice problems. At the end of the second week, go back over a sampling of the problems covered during the first two weeks. At the end of the third week, redo a few problems from each of the first three weeks' assignments, etc. In addition to this systematic review of practice problems, it's also useful to give yourself a regular review of the definitions and formulas worth memorizing and a weekly review of the examples your instructor has given you in class. Pay particular attention to the sequence of steps to be followed in correctly doing a particular problem. Try to understand the underlying concept or general rule when you are doing the computation. Occasionally ask yourself "What principle is involved here?"
Lay your problems out on lined paper. Use enough space so that a part of one formula or computation doesn't run into a part of another one. Care should be taken with even simple computations such as adding a column of decimals. If you don't keep the column straight you may come up with the wrong answer. Also, if a series of steps are involved in obtaining the answer to a problem, keep your steps separated clearly and neatly so that when you finish you can review and be certain that you have composed each of the steps. A related common error is to complete all but the last step. A spot check when you have finished each problem will help you to avoid this error. Credit is frequently given for having the steps in the problem carefully and correctly laid out even though you may make a simple error which gives you the wrong final answer. It pays to show your work step by step so that the person grading the test can clearly see what you were thinking as you worked toward the answer. If you skip several steps by doing them in your head, you are more likely to make mistakes and you will get less credit if you miss the answer.
There is a danger that you can get completely absorbed in computing a section or a step in a problem that you begin to plod through it without thinking about what you are doing. You can avoid this if you make a "guess estimate" as to the approximate outcome of each step in the problem as you go through it. When you have enough information, make a guess as to what the final answer will be. These guessed approximations will keep you from making large errors which you would immediately recognize as being impossible answers if you have your head in gear as well as your pencil. For example, if you guess that the answer must be a fraction of one point, you will immediately be aware of a decimal error if your computed answer comes out as 25 instead of .25.
As you finish a problem, it's useful to reread the problem to be certain that the answer you have found is the one that they want. This is especially true in the case of word problems. If the question asks for a measure of speed and you have figured a measure of distance, you obviously have the wrong answer.
By incorporating the ideas in this chapter, you will find that you are able to handle your math class materials more effectively. Being prepared for a new course by reviewing the basics, listening carefully in class, keeping up with assignments, and working with friends will help you to succeed, even in a difficult math class.
