Some tips for learning mathematics (or
- Put in the time. Mathematics
anything else. If you want to get good at it, you
have to put in the time working, learning, and practicing. Think
of it like a sport. Would you expect to be good at basketball
after watching me do a lay-up? No: you have to put in the hours
of practice yourself. I expect you to put in two hours outside of class for every hour
of class, minimum. Studies show that the thing that
differentiates experts from amateurs is not how much they enjoy
practicing (nobody likes it), but how willing they are to do it anyway. A friend of mine
says the following about mathematics courses, and I agree: "You should
expect to work ten to fifteen hours a week if you want to master the
material. Work five to ten if you want to get a C or a B.
If you work fewer than five hours, expect to be disappointed."
- Get stuck, and keep trying. If
you read a problem, try one thing that doesn't work, think "I don't
know how to do that," and stop, you'll never get good. You should
be willing to spend fifteen or twenty minutes trying a problem before
you decide you don't know how to do it. I will expect you to have
attempted your work at that level before you come to office hours.
- Study without distractions.
something if your mind is doing too many things at
once. Study in a quiet place, without your iPod, computer,
television, phone, etc. In order to learn you need to give the
material your full attention, and that means no texting, no messaging,
and no music. If you cannot commit to doing this, then don't be
surprised when you are unable to learn deeply.
- Review right away.
Ever wonder how your brain decides whether or not to put something in
long-term or short-term memory? There are two things you can do
to tell your brain that you want something to go in long-term
memory. First off, you can repeat the information
frequently. Secondly, you can repeat it within a short period of
time (as soon as possible, but certainly within a few hours) of when
you first learned it. This increases retention rates
dramatically. So if you have a class in the morning, try
reviewing your notes just afterwards, or as soon as you have free
time. It will help you remember things.
- Work without your notes. If
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. You won't have that with you at exams! Try doing
assignments without looking at the book or your notes. Once
you've tried, look up the things you forgot and try to learn
them. This will give you a better feeling for what you really
- Don't say "I knew that."
If you get a problem wrong and then you see me or a friend do it on the
board, don't react by thinking, "Oh right, I knew that." When you
do that you deny yourself the chance to actually learn something you
didn't truly understand. Instead, pay attention to what happened,
and try to commit it to memory. Understanding steps when I do
them is not the same as understanding what and how to do them
yourself. Try to work on what you
understand, and not on what you can follow.
- Get enough sleep. It doesn't matter how much
studying you do if you don't get any sleep; your brain won't process it.