Reading The Text
In this course, it is absolutely essential that you do the reading assignments.
Your experience with previous math courses may make it seem unlikely, since
it may have been possible to avoid reading the text,
yet do adequately well by copying down examples the instructor did in class
and then doing the homework
exercises by just changing the numbers in those "pattern examples" and
the pattern examples given in the
text. Also, older-style texts subtly encouraged students to skip the reading
assignments by putting
procedures for doing exercises in boxes, thereby essentially telling the
students that "everything you really
need to know to do the exercises can be found inside the boxes; you might
as well skip reading everything
Unfortunately, this approach resulted in students being able to do the
mechanical computations quite well, but having no real understanding of
the material and no real ability to apply it in situations that are even
a little bit different from that covered by the pattern examples. In essence,
students were only being programmed like computers to do computations that
computers can do faster and more accurately anyway. It is this deficiency
in the old-style math courses that led to the national movement toward
reformed courses, like this one, which stress understanding. This modern
approach to learning requires new methods in the classroom emphasizing
learning rather than lecturing, as well as new texts such as the one for
The difference between the text for this course and an old-style math
text is apparent from even a cursory scanning of the first chapter. If
you open the text and just begin turning pages, you will probably be struck
by the following:
Doing the exercises requires an understanding of the material in the text,
not just the ability to change numbers in pattern examples. Also, your
instructor will be counting on you to read the text, since he or she will
not be lecturing very much and will be relying on you to have seen the
material before you work with it in class. Like other courses outside mathematics
(but perhaps unlike other mathematics you have taken), not every small
point on which you will be tested will be covered by in-class examples.
Since the reading is so very important, some hints on how to it might be
helpful. You may find that slight variations on the following scheme will
work well for you.
The amount of text to be read outside of examples is much greater than
in old-style books. Older books would typically have brief explanations,
sometimes single paragraphs, followed by one or more pattern examples.
This book has longer explanations that attempt to convey understanding
of the concepts involved rather than just the mechanics of how to do computations.
The examples tend to be much longer than those in an old-style text, and
they often arise from actual real-world problems.
The exercises, which also tend to be much longer than those in an old-style
text, are often quite different from each other and from the examples in
the text, and use real-world numbers that are not as "nice" as the made-up
numbers in the shorter exercises typical of old-style texts.
If you do not understand something during the second reading, put the book
aside awhile and return to it later when your mind is fresher. If you still
do not understand it after returning to it, ask your instructor or your
homework group members about it.
Do make sure you eventually understand
all of the material. You will probably get tripped up in later reading,
in doing the homework, or on test if you treat material you don't quite
understand as "probably not all that important."
Plan to do the reading more than once, and do not make it an essential
goal to understand everything in the reading the first time through it.
The first reading should be devoted only to getting a general overview
of the material in the section.
After the first reading, stop for a few minutes and attempt to summarize
to yourself, in your own words, what the section is all about. Then immediately
re-read the section.
During the second reading, make a serious effort to understand all
of the material in the section. This does not mean to memorize it,
but rather to understand all of the points before going on.
Do not get discouraged if some points require some time to understand.
It is not uncommon to have to think about a point in a math text for a
half hour (or more, for more complicated concepts) before it becomes clear
what is really going on.
Copyright © 1999-2001 University
of Michigan Department of Mathematics