Some final comments:
Many problems arise from not understanding what is being asked for.
If you do not have a clear idea of what is wanted, it is unlikely that
you will get the correct answer --- or indeed a relevant answer.
Read the statement of the problem carefully (it sometimes helps to read
it out loud), breaking it into component parts and figuring out how
each part works.
Many problems can be readily understood, if not solved, by breaking them
down into subproblems.
For advice on how to solve problems, see George Polya's How to Solve
Write things down on scratch paper.
A lot of people try to do as much as possible in their heads.
But things are never as clear in our heads as we think they are: that old
line, ``it's in my head but I can't get it on paper,'' is always a delusion.
If it really was in your head the way that a rehearsed speech was in your
head, there would be little difficulty getting it on paper.
What is often in your head is a vague notion, together with a subjective
feeling of `having it': but until you develop it, on paper, you don't
really have it.
So make notes of things, write things down so that you can actually look
at your ideas, and organize them in front of you.
(It rarely helps to stare blankly at a wall for hours: its much better,
when you are blocked, to write something, anything, anything relevant,
down in notes, and try to organize the notes.)
There are several ways to do this.
Marcel Proust wrote sections of his novels on easels.
Ludwig Beethoven kept journals to record his struggles with his music.
Both Emily Dickenson and James Joyce wrote notes on scraps of paper
which they carried around.
Whether you use white boards or index cards, write things down.
One qualification, though.
Some who do not believe that the Unconscious needs to be badgered.
They claim that a person may not pay enough attention to their
Unconcious, and that it would be wise to spend time in contemplation
and meditation, and eventually all will be clear.
For a Japanese Zen point of view, see Eugene Herrigel's Zen and the
Art of Archery; for a more modern and `scientific version of this
argument, see Guy Claxton's Hare Brain, Tortoise Mind.
(The Church of Christian Science has similar suggestions.)
Their advice would be: if you can't solve it right now, put it aside, and
do something else, and it will come.
Sometimes it does.
I realize that there is an anti-picture school of mathematical pedagogy,
but many of these hair-shirted types are themselves secret picture-drawers.
We are primates, and most of us think visually: practically the entire
back of the brain is devoted to vision.
So take advantage of your resources.
Finally, it is often a wise idea to do homework in a place with few
distractions: e.g., no stereo, no television, no conversations, etc.
Many people are used to paying bills, writing personal letters, cleaning
house, and so on, to the sound of music.
Many retail outlets have music running all day long.
But doing homework, like doing anything that requires unusual concentration
(writing poetry, composing music, reading German metaphysics), becomes
hopeless if one's thoughts are always being interrupted by noise.
Some people take extraordinary steps to avoid distractions during their
work: Marcel Proust did his writing in a special room insulated by cork
panelling, while Gustav Mahler would do his composing in a small hut in the
If one is used to doing homework accompanied by Star Trek, going solo will
take getting used to at first, but in the long run it should make homework
Use lots of paper.
Many people try to put their answers in as small a space as possible, making
it very hard to read (and in fact, very hard to write).
Don't try to squeeze double columns on an 8 x 11 sheet of paper, and give
yourself plenty of room.
Here are a few words about homework grades.
Homework is more useful if you get feedback, but increasingly, homework is
not graded in many courses.
The reason is simple: grading homework is very labor-intensive, so at the
college level, it is done by graders.
And many places, like community colleges, can't afford graders (this is why
many community colleges have courses in which homework is not graded).
But if you are lucky enough to take a class where the homework is graded,
the grader will usually grade a selection of problems (that's all the time
the grader is paid for).
The grading will not be as fine as the grading for exams, but it should
give you some information about what works and what doesn't.
Usually, at least in math courses, homework counts only enough so that
students are encouraged to do it: it is not wise to obsess over homework
The true value of homework grades is feedback.
For more on grades and scoring, click here.
Finally, here are some links to some other sites you may be interested in.
About.com's page on homework has links to many short articles on
It is very busy and rather commercial.
Davide Cervone of Union College has a page of
Advice for students,
largely maxims and short bits of advice.