How to study and learn math (or anything,
Professors Warren Esty and Norah Esty
takes effort, time, and concentration.
Most serious students attend every class.
Do the homework.
Good students take the commitment seriously. "Practice makes
perfect." Not doing a homework on time is a
warning signal that you are getting behind.
Beyond the Basics (Important things you might
not know are in blue)
We expect to teach you so much that you
need to study, on
average, two hours outside of
class for every hour of class,
minimum. Mathematics is
just like anything else. If you want to get good at anything, you have
to put in the time working, learning, and continually practicing.
Think of it like a sport. You don't get good at basketball by watching
basketball. Beginners must practice a lot to get good, and even the
best players continue to practice regularly for many hours a
week. Research studies show that the thing that differentiates
from amateurs is not how much they enjoy practicing (they don't; no one
but how willing they are to do it anyway.
you get information sometimes your brain puts it into long-term memory,
but mostly it just forgets it. There are two things you can do
to tell your brain that you want something to go into long-term
memory. First, repeat the
information many times to yourself with intent to remember it. Second,
review it shortly after you learn
it (after 5-20 minutes, or as soon
as possible). Research shows that immediate review (right after
studying something) increases
same amount of
day or more later. So if you have a class in the
reviewing your notes immediately afterward, or as soon as you have free
time. It will help you remember things.
studying. Multitasking works for getting simple
tasks done, but you can not learn
something if your mind is
doing several things at once. In order to learn you need to
give the material your full attention, and that means ignoring
everything else for a block of time. Organize your life so that you do
not expect to be electronically interrupted while working. (Don’t text
or use Facebook or respond to e-mail when you are studying.) If you
cannot commit to doing this, then don't be surprised when you are
unable to learn deeply. Learning takes not only effort and time, but
also intense concentration.
notes. Try doing assignments without looking at the
book, notes, or solution manual. If there is a problem you don’t
remember how to do, of course you look in your text or notes to find
out how, but with the serious intent to remember how. Doing without remembering is not
learning. If you always
do your homework or study with your book and notes open next to you,
you will be left with a false feeling of how much you know.
say "I knew that." To learn, you must do the work yourself. Many
students watch in class, nod, and think "I would have done that." Many
copy the solutions manual or a friend’s work and think "I see how it's
done. I can do that." These thoughts are often wrong. Don't kid
yourself. The proof of your ability to do it is in your doing
it by remembering how.
sleep. Research has shown that learning has a
passive component. While you are asleep tonight your brain will
categorize and file things you "learned" today. At night it makes
connections so that you can recall things later. However, you will
remember far less tomorrow if you get only five hours of sleep.
To learn math more efficiently
you must learn to read math. You learn to read by reading.
Read with two goals:
1) to learn the
practice reading in order to learn to read more fluently. The ideas of
mathematics are best expressed in written symbols (not aloud in
learning to read you learn how mathematics really works.
Think of the book as a well-designed
lecture you can
follow at your own pace.
If you find reading your text
difficult, you can blame the text, or take responsibility and recognize
you are dangerously weak at an important skill – mathematics reading
comprehension. The harder you find
reading math, the more you need to work at it. Don't kid yourself. No
one else will
take time to teach you to read math – you’ve got to do it yourself.
it out! If something in the text does not make sense right away,
time to figure it out. Read it again with your brain in gear. Study the
example again. Go over it, carefully, until it makes sense.
your instructor to explain something
is sometimes necessary, but not as often as students seem to think. If
the text and work on an example with the intent to figure
it out, you probably can. Then your learning will be better and longer
than if you ask someone else to do it. Plus, in the process, you will
learning how to learn! You will find you
are getting better and better at understanding what you read. The
dividends, not just for today's lesson, but for all future reading.
Reflect. Do not walk out of
class and immediately put on your earphones and join the world of
entertainment. Right after class is the very best time to review the
even if only in your mind as you walk across campus, and move it to
gratification" is a reward to be received later. It takes
effort to develop skills for which employers pay well. (Many older students
return to college after learning that the hard way.) Put that effort
Learn to appreciate your developing skills. Enjoy your education. Enjoy
process, and you will do well.