Precalculus -- Preparing Students
for Calculus
Precalculus,
by Warren Esty
Third
edition.
A text designed to produce a deep understanding
of algebra and trigonometry so that students will be comfortable with
their next math. Students will be well-prepared for calculus.
This text is designed to be appropriate for self-study, as well as
classroom use.
The content includes the usual precalculus material
(functions, powers, polynomials, logs, exponentials, trig, etc.).
Graphing calculators play an important role. However, this text is
unlike others because it does not just use calculators to do old-style
problems, but actually incorporates calculators
as a learning tool and not just a "doing" tool.
This text has been used at Montana State University and elsewhere by
five dozen different instructors and thousands of students. A great
deal of experience has gone into making this text an effective learning
tool.
"As a home-schooled junior in high school this
year,
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math.
Up to this year, I considered math to be a distasteful medicine [clip].
No
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enthralled with your ideas, and now I love Math. Precalculus was my
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"A few months ago, I ordered your Precalculus text,
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"I ordered your precalculus book, and thus far it's
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[an adult student]
"I am the teacher who used your Precalculus
text with some homeschoolers over the internet the year before last. I
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Here is a link to information
about ordering a copy.
Of course, the presentation of most topics resembles that of other
precalculus texts. So does the organization, at least after Chapter 1 (which is unique). But it is particularly effective because of its numerous
distinguishing
features:
- An effective new approach that incorporates
graphing calculators as a learning
tool (not just a calculating tool). This may be the first text
to fully adjust to the fact that calculators can do the calculations
and
therefore accelerate learning about algebra, exponentials, logs, and
trig,
but students must still learn and understand the math.
Calculators
can help:
- Concentrate attention on essential points
- Increase the rate at which students gather experience with the
subject
- Focus on learning math that is valuable
(essential!) even though calculators can do all the calculations.
There is still a lot to learn about math, even though calculators can
do a lot. This text clearly distinguishes between learning about
calculators and learning about math with the help of calculators. (Dr.
Esty has given numerous conference talks about learning with the help
of calculators.)
- Emphasis on learning how the symbolic language of math is used. This
is probably the most distinguishing feature of the text. It is an
explicit goal of Chapter 1 that students learn how thoughts about
methods are written in modern mathematical notation. The goal of
Chapter 1 is to have students become able to learn math by reading math.
Let's face it, most students do not learn math by reading it. This text
has explicit reading lessons! They will
- Increase students' ability to generalize properly
- Increase students' ability to learn outside of class. [There
is so much more time outside of class than in class. Wouldn't it be
great if students could learn (not
just
practice) outside class!]
- Illuminating homework in addition
to the usual type of calculation problems for practice.
- (For example, most "B1" problems ask for an illustration, or
explanation, rather than a computation.)
- Memorable visual illustrations
that generate correct concepts.
- Emphasis on connections to lower- and higher-level material.
- (Calculus-style applications of algebra are frequently
discussed).
- Two sections devoted to how to do word
problems. Students who can't do word problems are
missing something important about algebra -- how symbolism is used to
represent operations. The emphasis on symbolism for expressing
thoughts
about operations in Chapter 1 helps students learn how to do word
problems,
and they would never be ready without it. The author's research on word
problems shows that students cannot do word problems just by taking
years
of algebra. They need to study writing about operations in symbols
first.
- Emphasis on graphs and their interpretation, and
effective use of graphing calculators.
- Emphasis on mathematical concepts that will not become
obsolete when the next generation of calculators arrives.
- Instructor-friendly and student-friendly (this
text does not require new teaching techniques or classroom experiments)
- Excellent for teaching yourself.
It is hard to learn math on your own. You must have good (English)
reading skills. In contrast to all other texts, this one has lessons in
Chapter 1 on how math is written and how to read it. This should help
you get
the most of the text even if you don't have a teacher.
Table of Contents.
Six articles by Dr. Esty on learning precalculus with the aid of
calculators have appeared in the recent proceedings of the International
Conference on Technology in Collegiate Mathematics. The
importance of conceptual development that is specifically algebraic is
discussed in "Algebraic
Thinking, Language, and Word Problems," an article by Dr. Esty and Dr.
Anne Teppo in the 1996 Yearbook: Communication in Mathematics,
published
by the National Council of Teachers of Mathematics. They have written
related articles on problem-solving and algebraic thinking in several
issues of
Psychology in Mathematics Education.
Warren Esty is a Professor in the Department of Mathematical
Sciences at
Montana State University.
Here is a link to three paragraphs about the author, Warren Esty.
For information about ordering a copy.
Warren Esty has written another text, The
Language of Mathematics, designed to constitute a core course
in mathematics.
Warren Esty, Dept. of Mathematical Sciences, Montana State University.
e-mail Warren Esty at 