Why Study Algebra?
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.
Jason Gibson www.MathTutorDVD.com
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