Why Do We Have to Study Math in School?

Date: 02/25/2005 at 00:59:21
From: Ian
Subject: Why do we learn advanced math in school?

What I find difficult in school is to understand the concept of
learning advanced math. I'm a freshman in high school and I'm in an
advanced math class.  My teacher said to write to "Dr. Math" if I had
questions about Math, and well, I do.  When I grow up, the job I want
to do will have nothing to do with radicals, algebra, imaginary
numbers, and all this other complicated stuff.

I understand why we learn basic math, but why all this extra stuff? My
job will never require any of that.  Yes, you might say, "Well you'll
need it later in life", but I always have a calculator for that.  In
fact if you go to your local supermarket, they use a cash register
with a built in calculator.  Besides occurrences with money (and I'm
sure I'm not going to have questions dealing with radicals), why are 
we taught this stuff?

Date: 02/25/2005 at 08:32:06
From: Doctor Ian
Subject: Re: Why do we learn advanced math in school?

Hi Ian,

Okay.  First, there's an important distinction to be made between what
you need to know, and what can be useful to know.  Here's a discussion
I had with someone about that, which you might find interesting:

  Math is Power?
    http://mathforum.org/library/drmath/view/62716.html 

Second, I'll tell you a secret:  The reason you're being forced to
study math has nothing to do with whether you'll _use_ it or not.  You
probably won't.  Hardly anyone does.  

What you're actually supposed to be learning in math class is the art
of problem reduction, i.e., starting with a problem, reducing it to a
simpler problem, reducing _that_ to a simpler problem, and so on,
until you end up with a problem that's trivial to solve. 

Unfortunately for you (and a lot of other students), many math
teachers don't understand this, or at least don't emphasize it as much
as they should. 

What makes math such a nice laboratory for problem reduction is that
it's possible to very precisely control the complexity of the problems
that are assigned.  Any real world problem has so many complications
that it's easy to lose track of the forest for paying too much
attention to the trees.  But in math, if we can get you to the point
where you can solve an equation like 

   3x + 4 = 5

then it's just one step to being able to solve an equation like 

   3x + 4 = 5 - 2x

and just another step to being able to solve an equation like

   3x   4       2x
   -- + - = 2 + --
    7   5        9

and so on, and so on.  And this continues on up through calculus, and
analysis, and, well, everywhere that mathematics goes. 

At each level of complexity, what you're _supposed_ to be doing is
developing the habit of looking at the problem in front of you, and
thinking:  "Forget about the solution for now.  What can I do to turn
this into an easier problem?"  

If you can master that skill, then once you're done, you can forget
about all the specific mathematics.

Remember when you were a toddler, developing hand-eye coordination and
a basic understanding of balance by building towers of blocks?   When
was the last time you stacked up a bunch of blocks?  Years and years
ago.  When do you expect to do it again?  Probably never.  Does that
mean the time you spent learning to do it was wasted?  Not at all. 
You kept the basic skills--which had nothing at all to do with blocks, 
per se--and left the toys behind. 

Same thing here. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 02/25/2005 at 19:10:10
From: Ian
Subject: Why do we learn advanced math in school?

Thank you very much.  This basically answers my question.  I'm going 
to print this out and show it to my teacher, maybe we'll get less 
homework or something.  ;-)

-Ian