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What Can Math Do for Me?

Date: 11/24/2005 at 23:52:58
From: Todd
Subject: What can math do for me

How can math help me in the future?

I feel some of the problems we are doing in my grade 11 math class 
seem to be quite ridiculous.  Although I understand them I cannot
possibly paint a picture in my mind of how I could use it in my
lifestyle.  The only way I feel I could use it is if I became a
scientist or something where math is a huge factor, or of course if 
I became a mathematician.



Date: 11/25/2005 at 10:08:17
From: Doctor Ian
Subject: Re: What can math do for me

Hi Todd,

>How can math help me in the future?

That depends on what you think your future is going to be like.  
Unless you can predict the future, it's hard to know ahead of time how
math might help you.  About the only thing you can say for sure is
that the less math you know, the harder you're going to have to work, 

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

  What is Mathematical Modeling?
    http://mathforum.org/library/drmath/view/61551.html 

and the easier it will be for other people to take advantage of you,

  Understanding Graphs
    http://mathforum.org/library/drmath/view/61632.html 

  Is Algebra Useful in the Real World?
    http://mathforum.org/library/drmath/view/61611.html 

>I feel some of the problems we are doing in my grade 11 math class
>seem to be quite ridiculous.  Although I understand them, I cannot
>possibly paint a picture in my mind of how I could use it in my
>lifestyle.  The only way I feel I could use it is if I became a
>scientist or something where math is a huge factor, or of course if
>I became a mathematician.

An analogy I like to use is this:  When you were very young, you
probably spent a lot of time stacking up blocks and knocking them
down.  You might ask yourself:  When was the last time you did that? 
Probably a long time ago.  When do you see yourself doing it again? 
Probably never.  Does that mean it was a waste of time?

Not at all, because you were using a very specific and somewhat
useless skill (stacking things) as a way of developing a very general
capability (hand-eye coordination).  And that very general capability
is something you _do_ use, every day of your life. 

Math is pretty much the same way.  You're using a very specific skill
that is useless to most people (setting up and solving equations) as a
way of developing a very general capability.  What capability is that?
You're learning to use abstraction to turn the problem in front of
you into some version of a problem you already know how to solve.

That is, math is providing a _context_ for learning about something
else--in sort of the same way that in Japan, learning about archery or 
tea ceremonies or flower arranging provides a context for learning
about Zen Buddhism, which is the real goal.  

(In that tradition, there is a metaphor for this kind of learning,
which is that you use a boat to get you across a river, but once
you're across, you don't take the boat with you.  Once you've realized
the essence of Zen, you can arrange flowers or not arrange them.  It
was just a boat to get you there.  Similarly, once you've realized the
essence of mathematics, you can leave the techniques behind.)

What makes math a good context for learning about problem-solving? 
There are at least two things, I think.  One is that the amount of
complexity can be very precisely controlled.  That is, you can take a
math problem, and introduce one new wrinkle, and it becomes a slightly
harder math problem.  Most "real world" problems aren't like this at
all.  In fact, any truly realistic problem introduces all kinds of
complexities that can easily overwhelm any regularity that we might be
trying to exploit. 

A second thing that makes math good for learning about problem-solving
is that it is formal, in the sense that when creating mathematical
systems, we aren't bound by what happens in the "real world".  By
altering our axioms, we can create new systems in which our intuitions
don't always work, which can force us to move beyond common sense and
into more sophisticated and systematic kinds of reasoning.  

Let me know if this helps.

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