Here is some great advice
for math students I received from a teacher (Terry Guay) on the AP Stats
listserve:
”You need to do so many problems that there is nothing that can be thrown at
you that you haven't seen before. Do every problem you can get your hands
on. This also reduces any anxiety during a test. You know you've prepared
well, so you are more likely to try the tough problems and not fear them,
AND you actually know quite a bit of stuff since you studied well and that
knowledge will help you figure out new “stretch-type” problems.
My list of math studying advice:
1. You
can never do too many problems.
2. Do
several problems of each type until you are VERY comfortable with a
technique, then do a couple more so it is cemented in your brain and becomes
automatic.
3. Always
do the homework that is assigned. If you have any difficulties, do MORE
than what was assigned.
4. Check
your answers - ALWAYS. If you have answers in the book, check them. If the
teacher provides an answer key in the classroom or online, check them. If
there is a classmate who does quality work, check answers with them.
5. Make
a list of the types of problems you are responsible for- every kind and
their variations. Then write down an example of each and the steps involved.
6. Make
a list of math techniques that you can apply to problems in the chapter you
are studying. This is your bag of tricks. Memorize them! If you are
working a new problem (or are taking a test) and get stuck, go through your
list and see if any of those techniques might apply.
7. Write
yourself little notes as you learn little important things, little tricks,
and things to remember.
8. Find
outside resources when available. Use all your resources. If there is
stuff online from your teacher, be sure to use it. If there are outside
review books, get several and use them. If the teacher has old practice
tests, do them. You can never do enough problems. If you have an older
sibling or a parent that can do this stuff, by all means take their
assistance.
9. Take
notes in class. Put the date on your notes. Have your friends take notes
and date them also. This helps when comparing notes. Write down everything
that the teacher puts on the board or overhead. The more material you have
to work with, the more you can study. You need material to study from.
Sometimes the more difficult types of problems are modeled for you in
class. Study these. When you are stuck on a homework question, check your
class notes. Sometimes problems done in class are previews of test
questions.
10. When
doing a problem, you don't need to know how it will turn out when you
start. Just start and see where it leads you. Remember to simplify (but
not round) as you go; you may get to a point where you "see" what to do
next by what form your intermediate work is taking.
11. Sometimes
you can work a problem from both ends and meet in the middle.
12. When
possible, do not round until the end of the problem. Work your calculator
or your math on paper so that you keep it as exact as possible.
13. Study
and do homework with a study partner. Find someone you can work well with.
Do homework simultaneously - checking each other's work. Talk about
different methods. Be sure you discuss the little details. This will help
you remember.
14. Spend
about 2 hours studying per section in a math book. Another rule of thumb is
to spend 2 hours studying for every 1 hour in class. It might take you less
time if you are efficient, but don't be afraid to spend a lot of time
studying math. You need to go over concepts - make a list of the techniques
- and do a bunch of problems to practice, and list anything else you feel is
important to remember. That could take 2 hours per section. Each section
is a separate concept with techniques and variations. Give it its due
time. The goal isn't to "get by" but to learn it well.
15. You
need to analyze what it is that you need to know. MAKE LISTS. MAKE SHEETS
of all the important things in the chapter. This will help you study for
the current chapter test and will help you review for the final later.
16. When
studying for a test, you should be reviewing stuff you already learned -
this is not the time to learn something for the first time. Be sure to keep
up with class, doing and checking all homework as you go. Be sure you can
do all the types of problems you are responsible for. Master the material.
Then when you are at the end of the chapter, you are simply reviewing and
bringing it fresh in your mind.
17. Go
see the teacher if you have any questions. If you study 2 days before the
test, then you can still ask questions on the day before the test.
18. Be
sure to go back through class notes and chapter quizzes when you make your
lists to study for the chapter. Don't leave anything out.
19. Once
you've made your list, study it. Memorize techniques, go over the tricky
problems enough so that you'll recognize them on a test and you'll remember
what to do.
20. Another
quote: "Studying is what you do to firmly fix new information in your
memory. You study to learn and to improve your ability to recall what you
need to know." I often ask students, "How will you remember this?" Find a
way to get it into your brain so that you'll know it the next time you need
it.
21. Never,
ever, say you "looked it over". You need to DO IT, and do LOTS of it.” |