Welcome
to the wonderful world of Mathematics!
In order to help you get the most out of Math, please read and consider the
following.
Some Initial Pointers:
Math
is likely to require that you make a substantial investment of TIME. Probably
a minimum of two hours outside class for every hour you spend in class. Build
this into your life. You should work on it some everyday, whether you have
class or not and whether anything is due or not. One of the advantages of
mathematics is that it can be done virtually anywhere, anytime. You can use
time when you are in the shower or waiting in line to be thinking about
problems or going over new concepts in class.
One
of the best ways to learn anything is to explain it to someone else. Working in groups is a good way to
provide yourself with this opportunity. You can also amaze your friends with
careful explanations of, say, all of the different interpretations of the
concept of a derivative.
Math
is not a spectator sport. You
will need to actively participate, roll up your sleeves and get that pencil
moving. You will also need to move your brain. Expect to have to think about
concepts and problems. Some of the problems you will encounter will teach
you new techniques: like playing scales in a musical instrument, or running
laps around a track. You might not see the point immediately, but they
are strengthening you so everything will come together when it counts. Think of
them as push-ups for the brain and practice them often. Some problems
will require you to think hard and pull concepts together (at this point you
will be glad you did your push-ups). Take some time with them, talk about them,
take breaks if you are getting frustrated, ask for help if you are stuck, enjoy
the process: you are learning.
If
you are in Calculus, expect this to be different. There are likely to be better
prepared students here than in your previous math classes, but remember that
you are trying to learn Calculus and not competing with other students. Expect
to have to do more work and for the course to move at a faster pace.
Many
problems that require Mathematics cannot be solved with simple application of a
“formula”. To paraphrase Albert Einstein, “The only thing you absolutely must
know is the location of the library.” In your situation this means you will
probably always be able to find the formula you need somewhere. However, you
will need to be able to set up your problems so that you know exactly what it
is that you need! Many of you will probably take more courses (depending upon
your future plans) that utilize the concepts from this course. So, it will be especially important to
understand what is useful or applicable in a particular context. This is why understanding
the process for solving a particular type of problem is emphasized over
memorizing formulas. In most cases, if you understand the concepts,
memorizing a formula becomes completely unnecessary because you construct the
necessary tools when needed.
Now for some Concrete Pointers:
A. Classes are held for your benefit.
If attending class weren’t important, all courses would be by correspondence!
During class your teacher will go over examples, which are important, and most
likely not in the book. It often helps to have a new concept explained in
several different ways; the book and the lecture are two different ways that
are readily available. Information about quizzes, exams, and due dates is often
given out in class. This will help you pace your studying. Math courses are
sequential, so the stuff you see in Algebra 2, for example, will enable you
to make sense of a lot of the stuff you will see in Pre-Calculus. As one
teacher was heard to say, “Everything you have learned since you were three can
be used in this class.” Hence you will not be helping yourself if you “cram”
right before a test or quiz and forget the material immediately afterward. As
teachers, we note a definite correlation between grades and class attendance.
What's the point? GO TO CLASS!!
B. The plethora of information to be found
in your textbook is astounding. One might even say it covers nearly everything
you need to learn in Mathematics in one form or another. However, math books
are not meant to be read like novels (even though they are often exciting
and dramatic). It is generally best to read the sections of the book to be
covered in class through quickly to get some idea of what is there before going
to class. After the class read through it carefully, with pencil and paper in
hand, working through examples in detail and taking notes. Make a list of
questions to ask at the next class. One thing to bear in mind while reading
your text is that the result of an example is often secondary to the process
used in obtaining the result. This is one reason you should be sure you
understand all the details the author left out (most likely intentionally).
Also, many techniques for solving problems are displayed elsewhere than in
examples, so read all of the appropriate section. Even though it
sometimes may not seem to be the case, the text does give the tools to do
the homework problems.
C. Just as you must play a lot of
basketball (or Tetris) to be good at it, you must DO a lot of Math in
order to be successful. At minimum, work every problem your teacher suggests.
If you are having trouble or want more practice, work other problems in
that section or get another book and work problems out of it. Most texts also
have “additional” or review problems at the end of each chapter. These may or
may not be arranged by section. If you are having trouble getting a correct
answer to a problem, think about what is going wrong, that way you can
learn something new and prevent yourself from making the same error in the
future. Don't settle for a correct answer that you don't understand.
Work
problems more than once:
a good way to start off a study session is to start by working some problems
from the last few assignments. Work problems until you can do them quickly and
they become your friends. You can even name the most difficult ones. When
reviewing or re-doing a problem, think about why you take the steps
you do, rather than simply repeating the problem in a robot-like fashion.
Remember, the process is usually more important than the result.
The fastest way to get into trouble in Math is to not do the homework. Remember, similar problems will probably show up on quizzes and exams, where you will be expected to work them quickly and accurately, probably without the book in front of you. Also remember that you will get more out of your homework time if you minimize distractions, i.e., turn the TV or stereo off.
D. Contrary to many students’ opinions, your
teacher wants you to succeed. Extremely rare is the teacher who will
intentionally put completely different material on an exam than what was
covered in class. For this reason, pay attention to your teacher and take
notes. Then read your notes and be sure you understand them, filling
in any missing details. Use your notes as well as the text when doing homework.
Review your notes regularly and pay attention to the comments your
teacher writes on your work. Read carefully all supplemental material provided
by your teacher. Remember that if your teacher thinks an example is important
enough to do in class, or takes the time to prepare a handout, it may also be
of sufficient importance to test you on it.
E. Quizzes and tests can be the bane of
your existence, or they can be showcases of your mastery of the
material. When studying for them, work every homework problem assigned
in the sections to be covered (more than once!), paying special attention to
why you take the steps you do, and why it works. Review and work through
examples in your notes and the text, again with particular emphasis on the
process being used. Each section of your text has a central idea or concept. In
many cases, this central idea depends in some way on an elementary concept with
which you are already familiar. For example, finding volumes of some solids is
simply an extension of finding areas of some geometric shapes that you already
know. If you are able to explain exactly what the “nugget” of a section is and
on what basic “stuff” it depends, chances are you are well on your way to a
good understanding of the material at hand.
Getting Help:
Working in groups can be of enormous help in understanding Math concepts. One of the best ways to gain understanding yourself is to attempt to explain it to others. Also, many times one student will “see” one problem, while another will “see” a different problem. In this way, people working together can benefit from having access to several different viewpoints. Form study groups with your classmates.
Meet with your teacher when he/she is available: usually before or after school. Frequently ten minutes of work with your teacher will save hours of frustration and turmoil on your own. Your teacher is a profession educator and is trained to help you figure out your misunderstandings.
Most importantly, don’t wait too long to get help. Often a student will wait until halfway through a course to admit he/she needs help. At that point half of that student’s grade has already been determined. Remember, though, it’s NEVER too late to improve!