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So you think you’re not good with math. Hmmm.
Well that’s something I hear all the time so you
shouldn’t feel too bad. The truth is, many, many
people, at one time or another, have felt the same way,
and have experienced something which has made them
feel bad about math and numbers in general. So the
common complaint, “I was never good at math,” or “I
hate numbers and math,” is as common as the common
cold and sometimes just as annoying. Interestingly,
what I have discovered from working with students
through the years is that this feeling of inadequacy
often stems from some negative experiences with the
subject. This might very well be the case with you.
Perhaps you had a hard time in one of your math
classes and felt very frustrated by it. Perhaps you
struggled year after year because you could’nt
understand the material being taught, or because the
pace was too fast. Perhaps you didn’t understand
because the subject matter was presented in a way that
did not get across to you. Sound familiar?
My concern with the above scenario is that,
uncorrected, this problem usually leads to feelings of
frustration and inadequacy toward math in general. A
likely–yet very undesirable–end result would be the
drawing of incorrect conclusions about yourself and
your abilities. Do these sound familiar?: “I’m just not
good at math and never will be,” or “I’m just not
smart enough to do math,” or more general and even
more crippling, “I’m just not that smart.”
I cannot count how many times I have
heard such statements, the like of which only
serve to drain the energy and
stunt the educational gains of even the best of us.
Unfortunately, these statements crystallize into
attitudes and beliefs which become difficult to shake
off. However mistaken these beliefs might be, their
burdensome influence remains for a very long time–
sometimes even for life. The end result–math
illiteracy.
This is very unfortunate–even tragic–since the
ability to work with numbers and do math are skills
that have countless benefits. After all, no one should
be doomed to mathematical illiteracy, especially when
the alternative is so near within reach. Let’s consider
the importance of basic math skills in everyday life.
For one, you couldn’t count without math, pay bills
and then balance a checkbook, understand basic
financial matters, such as by how much money will
grow at different interest rates, or even figure how
much change you should get after a simple purchase
transaction. What a sorry state we would all be in if
we couldn’t do these simple things! Now think for a
second. Suppose you could add, subtract, multiply and
divide numbers so that routine calculations were no
longer a bother. Numbers are now no longer your
enemies but your friends. A very likely consequence
would then be that the word math no longer triggers a
bunch of negative impressions but rather positive ones.
You now consider yourself good at a very tough
subject and therefore consider yourself a “cut above
the rest.” The implications of this new self-appraisal
are enormous.
Furthermore, imagine having a simple method
which allowed you to figure percents easily. Then you
could figure discounts in a store and know exactly how
much less you would pay for items that go on sale. As
you will soon see, working with calculations involving
percents is nothing more than understanding decimals
and how to multiply numbers. Of course, rather than
figure the discounts yourself you could wait until you
got to the cash register to pay for the items. This
would always be a possibility, but once again these
methods do not only have one practical use. If they
did, their value would be that much less. Percents
figure in many other areas of the real world, not just in
purchase transactions. In short, these newly acquired
skills, whether they be in the area of multiplication and
addition, or in the area of percent problems, will
certainly open up all sorts of possibilities within the
mathematical realm and unleash capabilities within
you that you never thought you possessed. In short,
this is the aim of Arithmetic Magic: to foster an
appreciation of mathematics through the study of the
basic arithmetical operations.
With this goal in mind, many positive things are
achieved. Specifically, as you learn the techniques in
this book, your new ability to work with numbers will
definitely give you an advantage–an edge, sharp and
cutting–to whatever you do. Aside from giving you a
command over numbers, which will come in handy in
daily life and serve you countless times in your days
going forward, the techniques will pave the road
toward new-found confidence and a boost in attitude
towards your mental abilities. This–more than the
computational ability–is the key payoff. Personally,
it would be difficult for me to estimate the number of
times I have used these techniques or the number of
ways in which they serve me. In fact, I am constantly
coming up with new combinations of the techniques
and teaching both myself and my students new
methods based on existing ones. You will find
yourself doing the same as you read this book with an
open and hungry mind.
For those of you who think the ability to work
easily with numbers is beyond them, think again.
From my experience, I am convinced that the ability to
work well with numbers is not solely a byproduct of
inborn talent. This is in spite of what many might
think. Barring any severe mental abnormalities, an
individual can improve his ability at math. Even the
so-called “classified” individuals, whether they be
considered “learning disabled” or afflicted with ADD
(Attention Deficit Disorder)–whatever such
classifications might mean–have benefitted from
these techniques. Part of the inability to do math
seems to be simply that, when it comes to math and
working with numbers, many individuals concede
defeat before even trying. Because such people “throw
in the towel” before the fight is over and never attempt
to do the math, they reach the mistaken conclusion that
math and numbers are just not for them. An erroneous,
yet very sorry, conclusion.
Consequently, if you’ve been frustrated by math–
and its fiendish counterparts, numbers–it should be
refreshing to hear what I have discovered regarding
this particular illness: you can do math and you can
work with numbers. This is something I am sure of
and, by the time you’ve read this book, something I
will have proven to you. I can state this positively
from experience. What you need, and what is
absolutely essential, is the right approach. Time and
time again, I have found that many people cannot work
with numbers because they have simply convinced
themselves that they are bad at math. Why? It seems
that these unfortunate individuals experienced some
frustration with the subject early on. Because these
early failures have far outweighed any successes, these
same individuals come under the mistaken notion that
they cannot do math. This situation now sets in
motion a negative cycle. These early failures–or
“lack of successes”–snowball to the point of no return
and form a downward spiral. Once this happens, the
individual is then certain that math is not a fun subject
and one to be avoided at all costs. After all, you can’t
do something if you believe you can’t.
Admittedly, mathematics is not an easy subject.
Math has its roots in numbers and although the more
abstract branches of this subject might find themselves
far removed from numbers, the foundation in numbers
is still there. You cannot escape them. There is even a
whole branch of mathematics devoted to the study of
numbers and number properties called Number
Theory. It would seem then that the royal road to
understanding math lies in understanding numbers and
that the two were inseparable. I say royal because
even such famous mathematicians as Pythagoras–you
know the one with that famous theorem in geometry–
have written that numbers and counting formed the
foundation of all mathematics. Moreover, since
math–with its many branches and applications–
serves as one of the principle tools to explaining the
world around us, and since these things we call
numbers find themselves intricately woven into all of
mathematics, a good understanding of them can
certainly help pave the way to a better understanding
of mathematics in general. Even doing calculus
requires that you understand the basic arithmetic
properties of numbers. As though this were not all,
one very real and definite benefit in learning and
studying mathematics comes from the educational gain
made in rational and logical thinking. Now that’s a
nice payoff!
What I have laid out here in four simple chapters is
the basis for understanding numbers. This is done
through a study of the four basic arithmetic operations:
addition, subtraction, multiplication, and division. As
you will soon see, each of these operations finds itself
related by special properties to the other. This
relationship allows us to simplify even further the
study of these basic operations. I do use some basic
math terminology but I deliberately avoid getting
weighted down in special names. Far more important
than memorizing any terminology is understanding and
learning the techniques and knowing how and when to
utilize the methods.
As someone who struggled with math–who understands
the frustrations and feelings of inadequacy
that this subject can rain upon you–I put this book
together with the confident hope that it will help you
gain a whole new perspective on math and numbers.
This new attitude might foster a desire for further
study, and this would ultimately lead to a higher rate of
math proficiency. I am delighted to tell you that in
overcoming my frustrations toward math and numbers,
I have benefited enormously from gains made in selfconfidence
towards this subject and many others. I
now approach any subject matter or challenge–
whether personal or academic–with a feeling of “I
can do it.” If after reading this, your attitude towards
math and numbers has changed to a more positive and
less fearful one, then my goal will have been
accomplished.
One final note that should set you in a very positive
frame of mind before reading is the following: the
arithmetic techniques presented here are not only
empowering but also mind stimulating. They are
confidence boosting. Now I am quite aware that in the
high technology world of today, calculators are readily
available and found everywhere; even cellular
phones have these built-in devices ready to serve you.
But the truth of the matter is that even though
technology is everywhere, the use of such technology
is sometimes limited. The point of this
discussion is that there is something special about
knowing how to do something, and this is particularly
true when you can do something that others think is
hard. Such as mathematics. The other point is that
knowledge in and of itself has a very rewarding aspect
to it, one that often cannot be thoroughly evaluated or
appraised. So you are not learning these techniques
solely to do away with your calculator, as this device
will always have its uses. You are learning them so
that you come to understand that what you thought was
undo-able is actually do-able and what you thought
might be impossible is actually possible. This fact is
very empowering indeed and can serve as the very
bridge to higher achievement.
So let’s get going and begin our journey into
Arithmetic Magic. May you never be the same again.
See more at Arithmetic Magic
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