Mathematics: Guidelines for Study
The University of Alabama
Center for Academic Success
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.
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 donít 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.
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:
relationships among all facts given.
formulas or definitions that might be relevant.
backwards, asking yourself, "What do I need to know in order to
find the answer?"
the problem to a similar textbook or lecture example.
a simpler version of the problem using small numbers.
- Break the problem into several simpler
problems. Work part of the problem and see if it related to the whole.
- 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 Teaching and
Learning has qualified tutors available to help you. Stop by CAS in 124 Osband or call 348-5175.