Self Help-Math Study Skills

Math Study Skills

Read what the instructor will be lecturing on before you go to class.

Read slowly. Reading mathematics is not like reading a novel or even history.
Speed reading techniques are not appropriate. Every word and symbol is
important to the meaning. Do not skip the symbolic part of the text. This
is often the most important part. If you do not understand a symbol, look
in the glossary or in the earlier part of the text. Symbols are often
explained when they are first introduced. If you still can not find out
what a symbol means, ask!

Read with a pencil in hand. Every time the author does a problem,
do it on your own—either before or after you read his or her explanation.
This makes sure you know what steps have been shown and, more importantly,
which ones were omitted.

If there is something you do not understand, try to formulate a question
about it. Often if you can ask a specific question, you can answer it
yourself. If you can’t answer it, you know what part of the instructor’s
lecture requires your complete attention. Your question is ready if
the lecture does not clear up your misunderstanding.

Understand the concepts

Don’t be satisfied with vague ideas about how to work problems. Do the
examples yourself, understand the concept illustrated, then try making
up your own examples. Keep in mind that the questions on the exam may
be very different from the example in the book.

Practice

Be sure you understand the concepts before you practice. Then practice
will help you remember and give you confidence in your mastery. Force
yourself to remember the methods as you work problems; don’t look back
in the book.

Keep up with assignments

(whether they are graded or not)

The pace is much faster in college and keeping up to date with assignments
helps you to better understand what is going on in class. Mathematics
is not a spectator sport. The only way you can learn mathematics is by
doing it. Following are some suggestions for getting the most out of the
time you spend on homework.

  • Understand the purpose of homework. Homework in mathematics classes
    is assigned to help you understand certain concepts and to help you
    build certain skills. Homework is not assigned to you because it is
    important to get the right answers. Your instructor already knows
    the answers.
  • Try to understand the process, not the specific problem. Classify
    problems in the assignment by problem type. Although this is often
    done for you by the directions, it is not always. Do each assigned
    problem and then check it in the back of the book. Try to figure out
    why you missed the ones you did instead of just working toward the
    answer. A similar problem may be on a test or quiz.
  • Mark homework problems you still do not understand and get help
    with them before the next class. The next lecture may build on a concept
    or skill you did not understand in the homework. When you do get help,
    make notes on what you learned, so that you can study them for the
    test.
  • Before closing the book, look back over the assignment and try to
    explain to yourself what the assignment was about, what each kind
    of problem was asking, how you got the answers and what the answers
    tell you. This process will help you understand the material and will
    help you discover what you don’t understand.
  • Keep your homework in a convenient and neat notebook so that you
    will be able to find questions or difficulties you have quickly and
    easily. This will also provide an invaluable study guide for tests.

Ask questions

Do not hesitate to ask questions. Ask your instructor for help after you
have tried to pull class notes and textbook explanations together for
review and still don’t understand. Write down specific problems so you
have them ready; don’t be vague and say you just don’t understand.

Don’t hesitate

Get help right away. Tutoring and help sessions are available. The longer
you wait before getting help, the harder it will be to get caught up.
Most of the time when you feel lost, it is just one concept that you are
missing, so get help quickly. One missed concept in a math class will
make the rest of your math career a hardship. Don’t feel embarrassed to
ask questions and get help; even the best mathematicians have felt completely
lost at some point.

Suggestions for Preparing for and Taking Math Tests

  • Keep a list of things to remember - problems stressed by the instructor,
    definitions, terms, diagrams and graphs, formulas.
  • Keep up with the work - some courses can be passed by cramming,
    but math isn’t one of them. Skills in math, as in sports, must be
    practiced.
  • Study copies of old exams, chapter tests from the book, or make
    up your own. Then practice them with the same limits as the real exam.
  • Get a good night’s sleep before the test so that you are rested
    and alert; a quick review before the test should be a summary only.
  • Arrive at the test early so that you can be relaxed when the exam
    begins.
  • Quickly look over the test and budget your time - don’t spend too
    much time on any single problem or section of the test.
  • Do some work on each problem - try to work at least part of each
    problem because partial credit is better than none.
  • Check your answers and look for careless mistakes during the last
    few minutes of your test time (budget this important time).

Suggestions for Word Problems

Solving problems is a practical art, like swimming or playing the piano;
you can only learn it by imitation and practice. There is no magic key
that opens all doors and solves all problems. The major goal in solving
word problems is to translate the written words into a mathematical equation
that we know how to solve.

  • Read the problem for a general sense of what it is about; sometimes
    putting it into your own words will help.
  • Then re-read it to pick out specific information:
    • What you are asked to find? Usually you choose a variable to
      represent one unknown and other unknowns will be represented in
      terms of the first.
    • What information is given? Make a list, then organize it into
      a diagram, picture, or chart.
    • What are the relationships among the information given and the
      information to be found? Sometimes it helps to think of similar
      problems from arithmetic and the formulas needed there.
  • Translate the information into an equation - get into the habit
    of doing this for easy problems. The longer problems will not seem
    as difficult.
  • Solve the equation you have written and label your answer - then
    find any other quantities to be found.
  • Return to the original problem and check your answer(s). Do they
    make sense in the original problem and answer the question posed in
    the problem?

Adapted from On Your Own in College by William C. Resnick and
David H. Heller.