Mathematics: Guidelines for Study   back

The University of Alabama
Center for Academic Success
124 Osband
348-5175

As a first step to learning mathematics, it is important to realize that mathematics is easier to study in small doses. While this statement is true of almost any subject, it is particularly true of mathematics. Two hours a day is a lot more productive than 10 hours one day a week. Although you may be able to read two novels in one weekend for a literature course, it is almost impossible to catch up on two weeks of math in one weekend. The study of math is cumulative with concepts building on those previously learned. You also need "soak time", a chance to think about concepts and ideas before another is presented.

Second, mathematics is not a spectator sport; it is a do-it-yourself subject. You must work the problems for yourself and recognize that there is no easy road to success. The following guidelines, however, should be helpful to you in studying math. These techniques are related to previewing, note taking, text reading, problem solving, and problem analysis.

1. Previewing
Previewing is an important, but not a very time-consuming part of your study. Before class, glance over the text material that will be covered in the lecture. Get an overview of the material by reading the introductory and summary passages, the section headings and subheadings, and the diagrams. Look at the problems at the end of the section to get an overall idea of the point of the lecture. This preview should serve as a general base for anchoring the new information presented in class.

2. Note Taking
In class, listen actively while taking notes. Intend to learn from the lecture. Write down explanatory remarks about the problem. Note any particular conditions of the problem, how to get from one step to another, and why the approach to the problem is taken. Try to anticipate the consequences of a theorem or the next step in a solution. During a proof, keep the conclusion in mind. If you miss or don’t understand something in the lecture, jot down what you can and fill in the missing material later. As soon as possible after class, review and edit your notes. Use the margin or the back of the opposite page to summarize the materials and to list key terms or formulas. You can also use this space to take notes from the text, thus supplementing your lecture notes and creating an integrated study source. Review your notes at regular intervals, particularly as soon as possible just before and just after each class.

3. Reading the Textbook
When reading the math textbook, first scan the material to obtain an overview. Then read carefully, making sure that you understand each part as you go. Since much of math is concept building, reading past a concept that is not understood may prove to be wasted time and effort. As you read, take notes on new definitions and symbols. It is especially important to translate abstract formulas into your own verbal explanations. Pay particularly close attention to derivations and sample problems. You should analyze the sample problems in the text, explaining each step in your own words and drawing diagrams to accompany these explanations. For practice, close the book and rework the examples in your own terms. Finally, note how the material relates to previous material, and stop periodically to recite the material to yourself.

4. Problem Solving
Most of your study time should be spent working or studying problems. When working a problem, first read through the question to get a general overview. Second, state the unknown in your own terms and write down every piece of information that is given. Next, devise a tentative plan to solve the problem by using one or more of the following tactics:

  1. Form relationships among all facts given.

  2. Consider formulas or definitions that might be relevant.

  3. Work backwards, asking yourself, "What do I need to know in order to find the answer?"

  4. Relate the problem to a similar textbook or lecture example.

  5. Solve a simpler version of the problem using small numbers.

  6. Break the problem into several simpler problems. Work part of the problem and see if it related to the whole.
  7. Check each step of the solution for correctness and clarity. Then, rewrite the solution from beginning to end, editing out blind alleys and false leads.

5. Problem Analysis
After you have worked a problem, analyze it. Focus on the processes used (not the answer) and ask yourself the following questions: What concepts, formulas, and rules did I apply? What methods did I use? How does the solution compare with those in my text and notes? Can I simplify what I did? Explain each step using your own words. In this way you will sharpen your understanding of the problem and aid future study.

The study tips suggested in this handout should help you to improve your performance in your math class. But remember that math courses are cumulative; if you have trouble with the material at the beginning of the course, it is likely that these problems will multiply later on. Consequently, you should seek help early if you encounter difficulty. The Center for Academic Success has instructional material on arithmetic, algebra, trigonometry, calculus, differential equations, geometry, statistics, and math preparation for standardized entrance exams. In addition, the Center for Academic Success has qualified tutors available to help you. Stop by CAS in 124 Osband or call 348-5175.