Your textbook is one of your most valuable resources, so you should make sure that you use it to its fullest. Before the semester begins, familiarize yourself with the contents. Look for any useful features such as a glossary, mathematical tables, formula lists, an index, practice exams, or homework solutions. Make certain that you know where these resources are located and how to use them.

Reading your textbook can make a huge difference in your performance. When reading the text you need to keep in mind that math textbooks differ from most other literature in three main ways.

1. Math texts present information in a very condensed form. Every sentence is important.
2. Math textbooks use a very precise technical language.
3. Math texts attempt to teach skills as well as to convey information.

Because of these differences, math texts must be approached in a different fashion than most other texts. The approach below uses several techniques to improve understanding.

1. The text is read multiple times improve retention.
2. The text is read in a different manner at each reading to maximize understanding.
3. The text is read actively so as to develop your problem solving skills.

One reading schedule that incorporates these techniques is given below. It can easily be customized to fit your personal preferences. Find an approach that works for you and stick with it.

First Reading: Preview

Preview the text before the lecture. At this stage you want to skim the text for broad ideas. Survey the topic headings, examine any diagrams or example problems and familiarize yourself with the vocabulary. When done you should have a good idea of the type of problems that you will solve, a basic idea of the approach to solving them, and some of the applications of these techniques.

Interlude: Lecture

If you have previewed the material, you will find lectures to be more informative. During a lecture, instructors typically overview the material and work selected problems. The lecture will help to give focus and direction to the vague ideas that your previewing will have spawned.

Second Reading: Outlining

Your second reading will be the most comprehensive. Here you will carefully read every sentence. This reading should be an active process and will require that you have pencil and paper (and maybe a calculator). You should record every new vocabulary term and its definition as you encounter them. You should also work through every example problem.

Interlude: Homework

Homework is the first place to apply what you have learned. While working through the problems you will probably use your book as a reference. Try to more than just copy the techniques illustrated by the example problems. The goal of homework is to help you learn how to apply general principles to specific situations. Try to keep your eye on the big picture.

Third Reading: Highlighting

During your third reading the idea is to review topics and examples which are still giving you trouble. When you complete this reading you should be able to answer every problem in the homework and the lecture.

Later Readings: Review

It is a good idea to read the text again before each quiz or test. At each reading the concepts will become more clear and memorable.

As you read through the rest of these study tips, you will notice these readings have already been included.

During the lecture your instructor will attempt to give you an overview of the current topic. Being adequately prepared for the lecture and taking full advantage of the opportunity to interact with your instructor will make later parts of the learning process go more smoothly.

Preview the text before the lecture.

At this stage you want to skim the text for broad ideas. Survey the topic headings, examine any diagrams or example problems and familiarize yourself with the vocabulary. When done you should have a good idea of the type of problems that you will solve, a basic idea of the approach to solving them, and some applications of these techniques. If you have previewed the material, you will find lectures to be more informative. During a lecture, instructors typically overview the material and work selected problems. The lecture will help to give focus and direction to the vague ideas that your previewing will have spawned. Come to class prepared to ask questions about any new concepts which are not clear after reading the text.

Attendance.

Lectures are an important component of the learning process. Make sure you attend class. Be on time and remain until the end of each session. Eliminate any distractions during class (no texting, etc.). Taking notes can help you organize the material, but it can also prevent you from listening to all parts of the lecture. You need to find a balance between these two outcomes.

Ask questions.

If you have questions about the homework problems, get your questions answered as they arise, either in class or in your instructor's office. Many colleges offer tutoring, and you should take advantage of such services. Don't save up your questions for the day before the exam.

Read the text after the lecture.

This reading should be more comprehensive than the preview was. This is an active process and will require that you have pencil and paper (and maybe a calculator) handy. Read every sentence and record every new vocabulary term and definition as you encounter them. Work through every example problem.

Homework is the first place to apply what you have learned. While working through the problems you will probably use your book as a reference. Try to do more than just copy the techniques illustrated by the example problems. The goal of homework is to help you learn how to apply general principles to specific situations. Try to keep your eye on the big picture.

Do your homework.

Do all the assigned homework problems immediately after the section has been discussed in class. When you work the homework, you should work a group of problems at a time before checking your answers with those in the back of the text. Be sure you make an honest attempt at a problem before looking up the answer. Many students become very good at working backwards from the answers to obtain the solutions to problems. Unfortunately, the answers are not provided on exam and quiz problems.

Manage your time wisely.

Spend some time every day on the course. Spending comparatively little time each day will be more productive than saving up all your work for the weekend or for the week or day before the exam. You should expect to spend at least three hours outside of class for each hour of class time.

Review your homework.

Athletes and musicians often record their performances so they can study them later. Your homework can serve the same purpose. After you've finished the problems, examine the results. You will notice that the problems tend to be grouped together. Ask yourself why the text grouped them that way. What was similar about the problems in one group? What was different about the problems in other groups? What clues would tell you which type you were solving on an exam? Are there faster ways to solve these problems? Learning to analyze problems this way will help you see how to approach problems in the future.

Try using spiral review.

Each time you finish a homework assignment, go back and work a few problems from previous assignments. This technique is known as spiral review. It helps older material remain fresh in your mind, and can also help you see connections between different topics. Repeatedly returning to a topic over an extended period of time is one of the best ways to fully assimilate knowledge.

Review the text.

After you have finished the homework, it is a good idea to review topics and examples which are still giving you trouble. When you complete this reading you should be able to answer every problem in the homework and the lecture.

Focus on the big picture.

Concentrate on learning the concepts behind the solutions to the problems rather than the solutions to individual problems. The point of the homework is to help you master these concepts, not to obtain answers to every problem in the text. After working a series of problems, ask yourself what concepts were illustrated in the problems. Make sure that you understand not only how to apply a certain procedure to a given problem but also why the procedure can be applied and why it works.

Preparing for a math exam can be as important as preparing for a track meet or a musical performance. Attending class, reading the text and working on homework problems will all help you succeed, but there are additional things you can do to improve your performance.

Review the text.

It is a good idea to read the text again before each quiz or test. At each reading the concepts will become more clear and memorable. After you have mastered the details of each problem type, reviewing the text can help you see them in their larger context.

Study with others.

It is often said that two heads are better than one. When studying for a math test, it is certainly true. Working in a group provides you with multiple points of view that you can draw on during an exam. Too large a group can become unwieldy, so you might want to limit the size to around four people.

Randomize chapter tests/reviews.

On most homework assignments similar problems are grouped together. A student will read the instructions for the first problem in a set, and then work out the rest of the problems using the same instructions. The result is that the student only read the instructions one time. This can make it difficult to recognize a problem when it appears out of context on an exam. Randomly select problems from the chapter review or chapter test, and try to identify the type of problem from the instructions. It can be difficult at first, but this skill will save you time and stress on an exam.

Positive attitude.

Thinking positively won't make you a math whiz by itself, but it can help you overcome the nervousness which might prevent you from showing off your math talents. Try thinking of the exam as a chance to demonstrate how much you know, rather than a judgement of your person. It can help if you practice making positive statements out loud. For example, "I can't wait for this test!" and "I am going to ace this exam!" You may feel silly at first, but you'll find it hard to be afraid of a test when you keep hearing yourself say positive things about it.

Get a good night's sleep.

If your body is not well rested then neither is your mind. It is often tempting to stay up all night cramming before a test. The fact is that this approach is rarely useful. The relationships between mathematical concepts are very complicated and it takes time for your mind to assimilate them. If you have not grasped them yet then one more night is probably not going to make much of a difference. On the other hand being so tired that you can not think clearly can significantly lower you test score.

Eat right.

Taking a test is work and like all work it requires energy. You need to keep your blood sugar up so that your brain has ready access to fuel when it needs it. Do not skip meals out of test anxiety. You might try having a healthy snack like nuts or fresh fruit shortly before the test.

Exercise.

A little nervousness isn't necessarily bad (it can keep you alert), but too much fear overwhelms your ability to think clearly. Exam anxiety has physical aspects as well as mental. Physical activity can help you focus that nervous energy. Some people like to jog or swim a few hours before an exam. If you already use some technique to help you relax before a sports contest or artistic performance, then try using the same method before an exam. Otherwise, experiment with different activities until you find one that works for you.

For many students, exams are the most stressful and frightening part of a math course. But exams are merely a chance for you to demonstrate the skills that you have put so much time into mastering. Here are some simple practices which can make your testing experience less threatening and more successful.

Read the entire exam first.

Give yourself a few minutes to read the entire exam. It will enable you to strategize about which problems to do first, help you manage your time, and let your subconscious process the questions while you work on other problems. Investing these few minutes at the start of the exam can save you many more minutes later.

Skip around.

Everyone has strengths and weaknesses when it comes to math. On a test you need to capitalize on your strengths and minimize your weaknesses. You can do this by identifying the problems that are easiest for you while you read through the entire test. Early success on these problems will help you build the confidence to tackle the tougher questions.

Read each question carefully.

Students often lose points on exams simply because they do not read the question carefully. When solving a problem the first thing that you should do is to identify the quantity for which you are looking. Do not stop working until you have found that quantity. Since math uses a very precise language, it is also easy to misread a question. If you rush through a question, you could easily misread the square of x as the square root of x, but these will produce very different results. Remember that you won't get many points if you do not answer the question that was asked.

Move your pencil.

Many math problems can't be solved in your head. You have to reorganize the information before you will see the solution. Try writing the given information in a different form (a list, a table, a picture, etc.). Often you will find that when your pencil starts to move your mind will follow.

Manage your time.

Time management is critical. If you have one hour to complete a one-hundred point exam, then a pace of two points per minute will enable you to complete the exam and still leave ten minutes to check your answers. So you want to spend about ten minutes on a twenty point question, five minutes on a ten point question, etc. This is only a rough guide - many problems will require eother more or less time than this rule suggests - but it gives you a framework for assessing your progress.

Breathe.

Don't forget to keep breathing deeply and slowly. Relaxation is important for your concentration. Be aware of your physical reactions to the experience of taking an exam, and try not to let them interfere with your work.

Check your answers.

Whenever possible, verify your conclusions. Sometimes this only requires substituting your solution into the original question, and other times it requires checking every step. Knowing that you have successfully completed a problem will free your mind to move onto new challenges.

Be careful changing answers.

It is common for students to second-guess themselves, erase their work, and either replace it with incorrect work or leave the problem blank. Having any answer is at least as good as leaving it blank, and if your mistake was small and near the end of the process it might be worth nearly all of the points. So even if you have determined that your answer is incorrect, follow this simple rule - don't change an answer until you are sure you have something better to replace it with.

Use the full time.

Just because you finish the exam early doesn't mean you have to turn it in. Time is a precious resource when taking exams, so you should use it all. You'll never have those particular minutes back. Re-read the exam and make sure that you answered the questions which were asked. Re-check any answers that can be checked, and re-work those that can't. Remember that an exam isn't a race - there aren't any prizes for finishing early.