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 see-saw, the merry-go-round, 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 see-saw, 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 see-saw, 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 see-saw.
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 free-fall
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
Jason Gibson is the founder of http://www.MathTutorDVD.com,
the leading producer of educational math tutorial content on DVD. Jason has
earned a BS and MS in Electrical Engineering and a MS in Physics.
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