Do you find it difficult to prepare for an exam?
Some of the questions most frequently asked in a math class
are: Will this be on the test?, or What will be on
the test? Those are reasonable questions, but chances
are that if you have to ask them you are not spending your
Exams are artificial situations. You do not take a class to
prepare for a particular contrived and transient situation.
Rather you are most likely taking the class so that you can
function better in the long term, for example in your
career. Ideally, you should be taking the class at least
partly because you like the subject. (If not, ask yourself
if you set the right goals for yourself.)
So you should focus on the long term aspects of the class, and on
the subject, and in the process, as a pleasant side effect,
you will become well prepared for the test.
Specifically, I suggest you make a habit of doing the
Before class, read the relevant sections of the
textbook. That way the material won't be so new, and
you'll understand better what's happening.
After class go over your notes and relevant sections of
the textbook and make sure you understand what you did
Look at the exercises of the relevant sections of the
textbook (or perhaps exercises suggested by your
instructor). Think about how you would solve them. Also
think about what each exercise teaches you. If you are
sure you can do an exercise skip it. If you are not sure, do
the exercise. If you don't know at all what to do with
the exercise, think about it,
and maybe get help. Avoid doing lots of repetitive
exercises. You may do easy exercises for fun and the
sense of accomplishments, but the learning effect is
much higher for exercises that you can barely manage.
If there are a bunch of exercises that drill
a certain technique do enough so that you understand how
the technique works, but don't spend your energy
reaching a high level of speed and proficiency. Put
emphasis on correctness and accuracy rather than speed.
Always question and check your answers.
- Whenever you do an exercise, before you start think
about what you expect to happen. There are two
possible outcomes: your expectations turn out to be
correct, which makes you feel good. Or you find something
contrary to your expectations. In this case you may have
made a mistake and now that you are alerted to that fact
you can find it and correct it. Or you may have
misunderstood something and now you have an opportunity
to learn something and understand it better. If you
don't formulate expectations there is a chance that you
don't even notice something strange has happened, and so
you may not realize your mistake or miss an opportunity to
At the beginning of the course, find a study partner.
Get together on a regular basis with your partner and go
over the material. It's OK if one of you is having a
much easier time with the class than the other. The one
having the easier time will benefit from explaining
things, and the other from having explained things one
When you get stuck in your preparations don't spin your
wheels. You are trying to take too big a step and need
to go back and solve some simpler related problems,
perhaps study some more math, talk to your friends, or
talk to your teacher. You may be hesitant to do this
since you are under time pressure, but continuing to
spin your wheels is not getting you anywhere.
Don't hesitate to seek help. Talk to your instructor.
Other help may also be available through tutors or
When you actually take the test:
First of all, relax! I know that's easy to say
and hard to do. But if you've prepared well
taking the test should be easy!
Before you start actually answering the
questions read the entire test. Then answer the
easier questions first! Leave the difficult
ones till the end. This has several advantages.
If you can't answer all questions during the
allotted time you answer more questions
that way, the questions you do answer are more
likely to be correct, and you don't get
flustered as easily or immediately.
- When you get stuck on a particular question,
and it's not the last one, put it aside and get
back to it only after you answer the other
When you are done and have time left, don't
leave! You have allotted that time to the test,
and the test is important to you. So spend the
rest of the available time checking your
answers, and correcting them if appropriate.
Suppose there is a question you don't
understand. Some instructors will let you ask
for a clarification during the test. In my
experience this only causes disruption and
distraction, so I don't answer questions during
a test. So suppose you can't ask. Then write
on your test that you don't understand the
question, describe what part you don't
understand, and answer the question as well as
you can. Sometimes there are mistakes on the
test that make a question non-sensical, or
incomprehensible. It shouldn't happen, but
it does. In that case say that the
question does not makes sense, and if you can
describe what the error or the
problem is. Any clearheaded instructor will
appreciate your insight and your effort, and
give you credit.
Different Kinds of Test
Different kinds of tests have different kinds of strengths
and weaknesses. Here's a brief summary:
Take Home Tests
One can ask more sophisticated and therefore more instructive
questions. The test is more of a teaching tool than an
assessment tool. Students can work together and learn in
the process. Grading tends to be tedious and more
difficult because of the amount of student writing and the
larger scope for partial answers
and partial credit.
In Class Tests - Closed Books and Notes
This is the standard sort of test. The learning effect
comes from preparing for the test, not from taking it. Tests
tend to be short and easy to grade. Students tend to dislike
this kind of test because it makes their proper
preparation more crucial.
In Class Tests - Open Books and Notes
Allowing open books and notes makes it possible to ask
more sophisticated, and therefore more instructive,
questions. Students tend to like this format since it
allows them to think of their books and notes as a crutch.
But actually at least some of the questions on the test
are likely to be harder than in a closed books and notes
test, and students sometimes waste significant amounts of
time searching their materials for items that they
actually could think of immediately if only they
tried. Grading is similar to closed books tests.
This in my opinion is by far the most effective form of a
test. You can adjust your questions according to the
student's answers, and find out better than in any other
way what the student really knows. Often a side effect of
an oral exam is that the student for the first time
understands key issues that were previously not
understood. The major impediment to using oral exams
exclusively is the amount of time it takes if there is a
large number of students. Students tend to be terrified
of oral exams, but they should look at them as
opportunities to prepare in a benign context for similar
situations later in their lives and careers. Every
interview (or conversation with a co-worker, client, or
customer) is a form of oral exam, to various degrees, even
though it is not called one.
Fine print, your comments, more links, Peter Alfeld,