How to Study Mathematics
For an excellent web site with some great discussion of study skills check out the following
site by Martin Greenhow. The site has some occasional comments pertaining to the school Dr. Greenhow teaches out but is non the less a great site that goes into much greater detail that I do here.
Before I get into the tips for how to study math let me
first say that everyone studies differently and there is no one right way to
study for a math class. There are a lot
of tips in this document and there is a pretty good chance that you will not
agree with all of them or find that you can’t do all of them due to time
constraints. There is nothing wrong with
that. We all study differently and all
that anyone can ask of us is that we do the best that we can. It is my intent with these tips to help you
do the best that you can given the time that you’ve got to work with.
Now, I figure that there are two groups of people here
reading this document, those that are happy with their grade, but are interested
in what I’ve got to say and those that are not happy with their grade and want
some ideas on how to improve. Here are a
couple of quick comments for each of these groups.
If you have a study routine that you are happy with and you
are getting the grade you want from your math class you may find this an
interesting read. There is, of course,
no reason to change your study habits if you’ve been successful with them in
the past. However, you might benefit
from a comparison of your study habits to the tips presented here.
If you are not happy with your grade in your math class and
you are looking for ways to improve your grade there are a couple of general
comments that I need to get out of the way before proceeding with the
tips. Most people who are doing poorly
in a math class fall into three main categories.
The first category consists of the largest group of students
and these are students that just do not have good study habits and/or don’t
really understand how to study for a math class. Students in this category should find these
tips helpful and while you may not be able to follow all of them hopefully you
will be able to follow enough of them to improve your study skills.
The next category is the people who spend hours each day
studying and still don’t do well. Most
of the people in this category suffer from inefficient study habits and
hopefully this set of notes will help you to study more efficiently and not
waste time.
The final category is those people who simply aren’t
spending enough time studying. Students
are in this category for a variety of reasons.
Some students have job and/or family commitments that prevent them from
spending the time needed to be successful in a math class. To be honest there isn’t a whole lot that I
can do for you if that is your case other than hopefully you will become a more
efficient in your studies after you are through reading this. The vast majority of the students in this
category unfortunately, don’t realize that they are in this category. Many don’t realize how much time you need to
spend on studying in order to be successful in a math class. Hopefully reading this document will help you
to realize that you do need to study more.
Many simply aren’t willing to make the time to study as there are other
things in their lives that are more important to them. While that is a decision that you will have
to make, realize that eventually you will have to take the time if you want to
pass your math course.
Now, with all of that out of the way let’s get into the
tips. I’ve tried to break down the hints
and advice here into specific areas such as general study tips, doing
homework, studying for exams, etc. However, there are three broad, general areas
that all of these tips will fall into.
Math is Not a Spectator Sport
You cannot learn mathematics by
just going to class and watching the instructor lecture and work problems. In order to learn mathematics you must be
actively involved in the learning process.
You’ve got to attend class and pay attention while in class. You’ve got to take a good set of notes. You’ve got to work homework problems, even if
the instructor doesn’t assign any.
You’ve got to study on a regular schedule, not just the night before
exams. In other words you need to be
involved in the learning process.
The reality is that most people
really need to work to pass a math class, and in general they need to work
harder at math classes than they do with their other classes. If all that you’re willing to do is spend a
couple of hours studying before each exam then you will find that passing most
math classes will be very difficult.
If you aren’t willing to be
actively involved in the process of learning mathematics, both inside and
outside of the class room, then you will have trouble passing any math
class.
Work
to Understand the Principles
You can pass a history class by
simply memorizing a set of dates, names and events. You will find, however, that in order to pass
a math class you will need to do more than just memorize a set of
formulas. While there is certainly a
fair amount of memorization of formulas in a math class you need to do
more. You need to understand how to USE
the formulas and that is often far different from just memorizing them.
Some formulas have restrictions on
them that you need to know in order to correctly use them. For instance, in order to use the quadratic
formula you must have the quadratic in standard form first. You need to remember this or you will often
get the wrong answer!
Other formulas are very general
and require you to identify the parts in the problem that correspond to parts
in the formula. If you don’t understand
how the formula works and the principle behind it, it can often be very
difficult to use the formula. For
example, in a calculus course it’s not terribly difficult to memorize the
formula for integration by parts for integrals.
However, if you don’t understand how to actually use the formula and
identify the appropriate parts of the integral you will find the memorized formula
worthless.
Mathematics
is Cumulative
You’ve always got to remember that
mathematics courses are cumulative.
Almost everything you do in a math class will depend on subjects that
you’ve previously learned. This goes
beyond just knowing the previous sections in your current class to needing to
remember material from previous classes.
You will find a college algebra
class to be very difficult without the knowledge that you learned in your high
school algebra class. You can’t do a
calculus class without first taking (and understanding) an Algebra and a
Trigonometry class.
So, with these three main ideas in mind let’s proceed with
some more specific tips to studying for a math class. Note as well that several of the tips show up
in multiple sections since they are either super important tips or simply can
fall under several general topics.