Learning
takes effort and time.
The Basics
Attend class.
Most serious students attend every class.
Learn during class. Don’t just take notes – pay attention and learn during 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
Review very soon after studying. It is hard to get things you “learned” into
long-term memory. Immediate review (10-15 minutes of review right after
studying something) is far more effective than review a day or more later.
Research shows that, with immediate review, 83% of class discussion is retained
9 weeks later. Waiting even one day drops retention to only 14%!
Forming
a memory takes about 17 seconds of close attention. If you don’t linger on a
thought for 17 seconds you won’t remember it.
Do the homework by remembering how, not by looking up how as you go along.
You
don’t know math if you don’t remember it. Learning requires
remembering.
This
has important implications for how you should do homework. Doing homework by
looking up how to do it as you go along often fails to result in learning
because it fails to emphasize memory. Getting homework “done” is not the same
as learning how to do it!
That is
why you should try to do the homework without looking at the text or
solution manual.
•
Study all the
material first (concentrate on key points for at least 17 seconds each) and
then
•
Do the homework
by remembering how.
•
If there is a
problem you don’t remember how to do, look in your text or notes to find out
how, but with the intent to remember how. Doing without remembering is
not learning.
Review after 15-30 minutes. When you find out how to do something (say, a
homework problem), there is a good chance you will forget how to do it almost
immediately after you finish. Reinforce your learning before you forget by
reviewing it after 20 minutes of other work. For example, if there is a
homework problem you have to look up how to do, look it up and do it, but
resolve that you will come back to that topic. Then continue with the rest of
the homework and 20 minutes later return to that topic and try a similar
problem to reinforce your learning before it fades. Immediate review really
works for moving thoughts to long-term memory.
“Seeing how” often doesn’t
work.
To learn, you must be engaged with the work. Many students watch in
class, nod, and think "I can do 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.
Serious Students
• Figure
it out! If something in the text does not make sense right away, take the
time to figure it out. Read it again with your brain in gear. Study the text's
example again. Go over it, carefully, it until it makes sense.
Asking your
instructor to explain something is sometimes necessary, but not as often as
students seem to think. If you read 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 lasting than if you ask someone else to do it. Plus, in the process,
you will be learning how to learn! You
will find you are getting better and better at understanding what you read. The
effort pays dividends, not just for today's lesson, but for all future reading.
Believe it!
•
Devote
substantial time to learning (not just doing homework) outside of class.
At a university you
are expected to work two hours outside of class for every class hour. Two hours
may seem like a lot of work, but that is what it takes – even if you finish the
assigned homework in less time. Study in addition to doing homework. Do the work
and reap the benefits. School is a serious job for which the pay is your
education.
To learn math more efficiently
you must learn to read math. You learn to read by reading.
•
Read your text.
Read with two goals: 1) to learn
the current material
2) to practice reading (to learn to read
more fluently). The ideas of mathematics are best expressed in written symbols
(not aloud in English). By learning to read you learn how mathematics really
works.
•
Think of the book
as a lecture you can follow at your own pace.
•
Read with
pencil, paper, and calculator. Do the
calculations with your own calculator. Reproduce the graphs on your calculator.
Try to fill in missing steps. Take notes. All this is designed to encourage you
to think while you are reading. And, it works!
(Reading math is much, much slower than reading a novel.)
•
Pay special
attention to theorems. Theorems are a
mathematical way of summarizing general methods that apply to many examples.
They tell you what to do and when to do it.
If you find reading your text
difficult, you can blame the text, or take responsibility and recognize the
strong signal that you are dangerously weak at an important skill – reading
comprehension. The harder you find
reading, the more you need to work at it. Don't kid yourself. Not reading is a
sign that you are not comfortable with an important mathematical skill. No one
else will take time to teach you to read – you’ve got to do it yourself.
Reflection. Research has
shown that learning has a passive component. For example, while you are asleep
tonight your brain will categorize and file things you "learned"
today. However, you will remember far less tomorrow if you get only five hours
of sleep. Get enough sleep.
Right
after class you can "mull over" the lecture and later find you
remember it much better than if you proceed straight to a different sequence of
thoughts. (This is related to the “review after 20 minutes” idea.) Driving
home, if the car radio is off, you may find your thoughts returning to the
lecture. This sort of repetition is very valuable.
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
material, even if only in your mind as you walk across campus, and move it to
long-term memory.
Success. At MSU, about
30 percent of the students are "over traditional age." Many retake
math courses they did poorly in years ago, and do very well the second time
around. What is the explanation?
Attitude.
They want to learn it this time. They do the work. They pay attention. They
have learned how to put their brains "in gear."
"Deferred
gratification" is a reward to be received later. Many of the returning
"over traditional age" students have learned the hard way that it
takes serious effort to develop skills for which employers pay well. Put that
effort in now. Learn to appreciate your developing skills. Enjoy your
education. Enjoy the process, and you can excel.
