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I've noticed that one of the
things that students struggle with in Math is knowing what is
important. How can you study something when you don't understand
it to begin with?
Let me see if I can make it a
little easier for you. Mathematics is not a class like English,
or History, or even Geography. Math is a language class.
Math is the language that scientists, engineers, accountants,
architects, and even artists use to solve every day problems.
So how does this language work?
Math is broken down into
THREE very basic
components.
First is the
VOCABULARY. If I were to say to
you, "Get out your blue spiral notebook, your red ball point pen, and
draw a line from top to bottom in the right hand margin," it's a
pretty safe bet that you'd be able to follow those directions, right?
Sure it is.
But if I were to say, "If we
multiply the numerator and denominator of these rational numbers,
using the identity property of one to achieve the least common
multiple of the denominators, we can combine them," your eyes would
glaze over and your head would start pounding, your heart rate would
speed up and you'd probably get sick at your stomach. Right?
So what's different?
Simple. The words.
In the first sentence, I've used some very exact vocabulary -- blue,
spiral, notebook, red, ball point, line, top, bottom, right, margin.
And yet, it makes sense. It makes sense because they are all
words you know. At some point in your life, you learned them!
In the second sentence I've
also used some very precise vocabulary, but the difference is, you've
not made the commitment to learning them. Math is a very precise
and exact discipline. The words matter. It does not matter
how many problems you work. If you don't learn the vocabulary,
at some point, you're going to run into trouble.
So the first thing I would
suggest to you is BUILD A VOCABULARY NOTEBOOK.
As you encounter unfamiliar words, learn what they mean.
Put them in your brain and in your heart. It's a sure bet that
you will run into them again in your mathematical career. The
more words you know, the easier this discipline will be for you.
Fortunately, unlike English, Mathematics is very exacting and almost
never open to interpretation. There might be a hundred ways to
interpret "blue" but only one idea for "three."
Secondly, make an effort to use
the vocabulary words you are learning as you ask questions, work
problems, and explain the procedures to someone else. You really
know a language when you can speak it, not just hear and understand
it.
The second component of this
language is PROCEDURES. Procedures
are the structure, order, and rules that we use to construct our
language. In English, the order in which we write words matters.
We'd never say the following:
Brown jumped fox dog the over
lazy quick.
It makes absolutely no sense,
does it? That's because we have a life long understanding of the
way the words should be ordered, and when they don't appear in a
predictable sequence, we're confused. Let me clear it up.
The quick brown fox jumped over
the lazy dog.
In the language of Mathematics,
it's very much the same thing. The order in which we do things
matters. When we don't follow the predicted and universal rules
for constructing the sentences, things get confusing in a hurry.
Procedures are pretty rigid as
well. Things need to be done in a certain way, once we decide to
do them. There are several ways to calculate 10% of 50, but
there's only one correct answer. Regardless of which procedure
we use, if we follow the steps in the correct sequence, we'll always
arrive at the same answer.
So, what this means is this.
When a new procedure is introduced, make every effort to define it,
learn the sequence of steps, and analyze what makes it different from
other similar procedures. When do you need to use it? What
particular components do you have to have in place to apply it?
What does your answer mean when you get it?
The last component of this
language is OPERATIONS. There are
four of them - add, subtract, multiply, and divide. They create
the natural order in which this discipline operates. Think of
them as the gravitational force that operates this world. They
cannot be violated, and they must be respected.
There is no way to route around
them, by pass them, or ignore them. They must be,
MUST BE, learned by heart.
MEMORIZE
your addition, subtraction, multiplication, and division facts.
If you don't know them, learn them now. The sooner you
learn them, the less often you will fall down. The sooner you
commit to learning them, the sooner this language will be easier for
you. If you struggle with 9x6, then work at it every night
until you have it memorized.
There you have it. How to
study Mathematics in a nut shell. On the positive side, because
this discipline is so very rigid, once you learn things, they stay
learned forever. The rules, the procedures, and the vocabulary
don't change. You can count on them staying the same for the
rest of your natural life. Very few things in the world are like
that.
So if you make the commitment,
Math should get easier instead of harder, and not many things in the
world are like that either.
The choice, as always, is up to
you. It's a brand new day. What are
YOU going to do with it?
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