Problem solving is a major component of many "physical science"
courses. If you don't learn to solve the types of problems
addressed in these courses, from memory, both accurately and
quickly, you will not do well on the exams, even if you think you
understand the concepts. Students occasionally ignore one of
these factors when they are studying: some students work through
the problem sets while looking at the examples in the text,
simply plugging in different numbers, and then quit when they get
the right answer and think they understand the procedure; other
students get to the point where they can work problems through to
the correct solution without referring to the text, but they take
so long -- perhaps from "taking the wrong turn" a few times --
that they don't get finished in the exam.
Guidelines and Tips
Use active reading strategies to read your text. When
you are reading a section in your text, before doing the
problems at the end, first skim the section to find out what it
is about. Then work through it carefully. When you come to a
worked example, write down the question and see if you can work
it out yourself before you see how it is done in the text. Then
compare your work with the example, and if you made a mistake,
figure out where and why you went wrong, and try it again,
without referring to the text. Keep in mind that even
though you understand a procedure when you read it, it is quite
possible that you will not be able to use that procedure in
solving a problem on your own. Then work on the problems
at the end of the section without referring to the text, as
much as possible. If you really need to peek at the text, do
so, but then try doing the problem later without peeking.
Use any strategy you need to understand the concepts,
problems and procedures. It is perfectly legitimate to
refer back to examples, work towards the correct answer, get
someone to help you, use another text, or to use any other
strategy that works, to figure out how to work through a
problem so you understand what you are doing. But, do
not stop at this stage.
Practice doing problems from memory. Here is some
advice from a student who reputedly does not get less that 97%
on math tests. "Most students do too many different problems of
one type. Pick five problems of a particular type (one easy
one, three medium ones, and one hard one). Then do them over
and over from memory until you can do them in your sleep."
Realize that you haven't quite got it until you can solve the
problems quickly and without using an example.
Practice doing problems until you can do them both
accurately and quickly. Students often run out of time in
math exams. A likely reason for this is that they have not
practiced working under exam conditions -- in this case, with
an emphasis on speed. If you practice problems until you can
work quickly as well as accurately, then you will finish early
and have extra time to check your work, or spend extra time
working on that one difficult problem.
Resources Related to Problem Solving
If you have problems in this area and would like help,
please contact us. This problem can be fixed, and it is not a
good idea to let a fear of math keep you from doing what you want
to do in your life. Check our schedule for this month, call us
(250-721-8341), or drop by the Counselling Services.
If you would like to participate in a workshop focused on
learning effective problem-solving strategies, make a request at
the receptionist desk, Counselling Services.
appointment with a Learning Skills counsellor for help in developing a repertoire of
strategies that meets your needs. We are familiar with the
resources available at the university, and can also suggest
qualities to look for in a tutor.
The Modular Learning Skills
Course contains information related to problem solving:
Module M, Problem Solving, will be of particular interest.
Updated: May 2012