by jason gibson
"Why study algebra?"
If you're a parent, it's a question that you will no doubt hear as your
children study the subject. If you're a student, it is a very natural
question to ask, "What's the point of learning algebra in the first
place?"

After all, all of the math leading up
to algebra that we learned growing up such as addition, multiplication,
decimals, fractions, and the like, seem to have a concrete meaning. These
concepts all deal with numbers in some way or another and because of this we
can wrap our brains more easily around the concepts. After all, I can pick up
six pencils and give two to a friend and by using math I can figure out how
many pencils I am left holding in my hand. We can all imagine situations
where basic math serves us well  calculating your change in the grocery
store for instance.

In short, basic math deals with
numbers. Since we are all taught how to count at a young age the concepts of
basic math, even though challenging at first, seem to have a practical value
 even to children.

Enter Algebra. Suddenly, we are asked
to deal not only with our comfortable numbers but with letters. And it
doesn't stop with this. You start seeing parenthesis and exponents, and a
whole potpourri of other symbols that seem to make no sense at all. This
single fact more than any other turns many people off to learning algebra. At
the very beginning you are asked to learn certain rules on how to calculate
things in algebra. You must learn which steps are legal to do before others,
and if you do them in the reverse order you get the wrong answer!

This leads to frustration. With
frustration, despair follows in short order. And so the thoughts begin:
"Why do I need to learn this?" "When would I ever use Algebra in real life?" 
What you have to remember, though, is
that basic math is riddled with special rules and symbols as well. For
example, the symbols "+" and "=" were at one time foreign
to us all. In addition the concept of adding fractions, as a single example,
is filled with special rules that we must learn. When adding 1/3 to 1/3, for
example, you keep the common denominator and add the numerators, so that 1/3
+ 1/3 = 2/3. The point here is that when you begin to learn algebra it may
seem overwhelming with the rules that you must learn, but this is no
different from the multitude of rules that you had to learn that dealt with
basic math such as addition and subtraction.

Learning Algebra is achievable for
all, you just need to take things one step at a time and learn the basic
rules before moving on to more advanced topics.

But this does not answer the question
of "Why should I learn Algebra?" This is a difficult question, but
the simplest answer is that Algebra is the beginning of a journey that gives
you the skills to solve more complex problems.

What types of problems can you solve
using only the skills you learned in Algebra? I invite you to take a journey
with me back to your childhood. We've all been to the playground and had a
great time on the seesaw, the merrygoround, and the slide. At one time all
of us were completely fascinated with these trips to the playground, but
Algebra can help you understand them. The physics of all of these playground
toys can be completely understood using only Algebra. No Calculus required.
For example, if you knew the weight of a person at the top of the slide and
you knew the height of the slide you could roughly calculate how fast you
would be traveling as you exited the bottom of the slide.

On the seesaw, let's say that a
person was sitting at one end and you knew that person's weight. You'd like
to sit on the other side of the seesaw, but not at the very end  you'd like
to sit opposite your partner in the middle between the seat and the pivot
point. Using algebra, you could calculate how heavy you'd have to be to
exactly balance the seesaw.

Moving away from playground
equipment, as children we were all fascinated with the magical way that
magnets attract each other. Using algebra, you could calculate how much force
a given magnet would pull on another magnet.

There are examples all around us of
things in the everyday world that you could fully understand using only the tools
in algebra. If you drop a rock off of the roof of a house, how long would it
take to hit the ground? If you dropped a second rock 100 times as heavy off
of the roof of the same house, how long would it take to hit the ground? If
you somehow brought a bulldozer up to the roof of the house and dropped it,
how long would it take for the bulldozer to hit the ground? The answer in all
three cases it takes the same amount of time to hit the ground! The time of
freefall depends only on the Earth's gravitational field (which is the same
for us all) and the height of the roof you drop from. Even though the
bulldozer is "heavier" than the rocks, they all fall at the same
rate to the ground.

Most people would assume that
learning about more "advanced" topics such as rocket propulsion and
Einstein's theory of Relativity would require much more advanced math than
Algebra. It is true that more advanced math is necessary to understand every
facet of these and other advanced topics. However, many of the fundamental principles
can be understood using only the tools in algebra. For example, the equations
that describe how a spacecraft orbits the Earth only involve algebra.

Moreover, many of the central topics
in Einstein's theory of special relativity can be understood only using
algebra. For example, it turns out if you are traveling on a spaceship near
the speed of light time actually slows down for you relative to your friends
back on Earth. In other words, if you were to fly in a spaceship near the
speed of light for some time and then you returned to Earth, you would find
that you had aged very little while your friends on Earth have aged a great
deal! Albert Einstein coined this phenomenon "time dilation" and it
can easily be calculated using only Algebra. This effect is not a theoretical
effect  it has actually been measured many times. In fact, the GPS system of
satellites in the sky that the military and police forces depend on must take
into account the effects of time dilation or else the system would not work
at all! Because the satellites are moving in orbit around the Earth at speeds
much smaller than the speed of light, the time dilation involved is very
small  but it must be accounted for or the system would not function.

Now, you might be thinking, "I never
learned how to calculate things such as this in my algebra class!" This
is in fact true. All of the applications we have been talking about here are
known as the study of Physics. If you had to boil the word Physics down to
one sentence it would be: "Physics is all about studying the world
around us using math as a tool."

Simply put all the math that you ever
learn is really a tool for understanding the world around us. And believe me,
we have only begun to scratch the surface of understanding how the world
works. Algebra is a stepping stone to learning about this wonderful universe
that we live in. With it you have the tools to understand a great many things
and you also have the skills needed to continue on and learn Trigonometry and
Calculus which are essential for exploring other types of problems and
phenomena around us.

So, try not to think of Algebra as a
boring list of rules and procedures to memorize. Consider algebra as a gateway
to exploring the world around us all.

Sabtu, 04 Agustus 2012
Why Learn Algebra?
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