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How to Read a Math Textbook
HOW TO READ A MATH TEXTBOOK
from Math Study Skills by Alan Bass, Addison-Wesley-Pearson Education,
Inc. 2008. pg. 48-?
These five steps should be followed for every section.
An entire chapter is simply too large for these steps to be effective. You
should, instead, approach each section individually in this manner.
Five Steps to Understanding a Section in Your Math Textbook
1. Survey the material. Begin the section by
taking 5 to 10 minutes to glance through the material. For this step, you
will not do much actual reading at all, but here are a few things you
definitely should read:
• Paragraph or section titles
• Boldfaced words (although not necessarily their
• Instructions for examples (but not the solutions)
• Information that appears in boxes
The idea behind this step is that you will begin to get
an overall idea of what the material is about. You will know whether
graphing is involved. You will know whether fractions are involved.
Certain words will sound familiar, others will not. If you survey the
material and everything you see looks totally confusing, that's okay. You
have still done your job.
2. Survey the homework. Next, turn to the page
that contains the section homework and see what kind of problems you will
be doing in this section. This should only take about five minutes. In
particular, read the instructions for the different problem types. If this
seems overwhelming, you may want to try reading every fifth problem (1, 5,
10, 15, 20,...). This will give you a good overview of the whole homework
set. Or, if your instructor has already given you homework for that
section, you could read those problems. In these first two steps, you will
be accomplishing several important things:
Looking at key words
Getting an idea of the big picture
Getting to know expectations
Again, if you read through these problems and say to
yourself, "Well, I just have no idea whatsoever how to do any of this
stuff" that's okay! The fact that you have surveyed the material and its
corresponding homework is going to help when you actually read the
3. Read the section. Now you're ready to actually
read the material. But don't just read it. Your mind needs to be engaged
with the material beyond the voice you hear in your head when you read. As
you read it is important that you actively keep your mind focused on the
topic. There are several ways to do this. Here are a few suggestions: •
Write boldfaced words in your glossary as you go. If you don't completely
understand the term yet, leave some space below the entry so you can write
in more later.
• Copy down the examples in the book. You don't have to write down
every word of the instructions or every word of explanation in the
solution. But if you at least write down all the math steps that are
done it will help avoid that "Why did they do that?" feeling. Many times
our eyes just move too fast to see math steps that should be simple. If
you write down the math steps in the examples, it will be easier to see
why they were performed. Think about it; it will also be like training
wheels for the homework in that section.
• Write down anything that appears in a box, particularly formulas
and equations. If it looks familiar and you know it will be important,
you could write it on a note card or in a corner of the page where you
know you will do homework. If you are a kinesthetic learner, take the
time to doodle a formula into your notebook somewhere you know you'll
see it again later (but be careful not to waste too much time with
• Read out loud to yourself. This is a great idea if you're an
auditory learner. Make sure you are not disturbing anyone around you
when you do this. But as long as you are not, go for it!
• Writing in your book is a great way to make friends with it. If you
don't mind keeping your book after the course is over and not selling it
back, there are several things you can do: = Use a highlighter to make
important information stand out.
Put a question mark (in pencil) beside ideas or examples you
have a hard time understanding.
Circle key terms.
Using a highlighter is okay, but DO NOT use an ink pen to write in
your book. Use a pencil so you can edit your comments later.
Remember: If you just sit there and read to yourself and that's all,
you are not likely to be successful. Your brain needs to be stimulated in
other ways to keep it active and interested.
College Course Structure
A big part of what makes college math different is. . .
well. . . college. That is, many of the difficulties facing students who
are entering a college level math class for the first time are a result of
the huge difference between a high school class and a college class. With
the help of my students, I have compiled a list of the most important
Differences Between a High School Class and a College
|Attendance is required.
||Attendance is optional and
may not even be taken.
|Teachers monitor progress
and performance closely.
grades, but are often not informed by the professor when they are in
Beginning algebra is covered over the course
of 10 months for 6 or 7 hours a week.
|Beginning algebra is
covered over the course of 4 months for 4 or 5 hours a week
|The students have contact
with the instructor every day.
||The students often meet
with the instructor only twice a week.
|Teachers cover all
material for tests in class through lectures and/or activities.
||Students are responsible
for information whether it is covered in class or not.
|Teachers give frequent
tests and allow make-ups or retests if the grades are poor
||There are often only 2-3
tests per semester and no make-ups or retests are allowed
|Grades are often based
heavily on level of participation and effort.
||Grades are usually based
exclusively on quality of work and demonstration of college level
|A grade of "D" is
interpreted as "barely passing" and the student is moved to the
||A grade of "D" is
interpreted as "barely not passing" and the student is
required to retake the class
|Teachers often offer
extra credit for struggling students.
||Professors almost never
offer extra credit.