Defining "Problem Solving"

Date: 07/30/2007 at 15:21:11
From: Blake
Subject: Definition

Is there a clear definition for problem solving?  Do you know all the 
different strategies for problem solving?

Date: 07/30/2007 at 15:57:10
From: Doctor Ian
Subject: Re: Definition

Hi Blake, 

It's not a clear concept, which is probably why you're having trouble
finding a clear definition. 

Really, the definition of "problem solving" is "solving a problem". 
So you need to get definitions for "solve" and "problem".

A problem, most generally defined, is a situation that you wish was
different than it is!  For example, suppose your car has a flat tire,
and you wish that it didn't have one.  That's a "problem". 

Problems can range from very, very large in scope ("There is a lot of
fighting in the Middle East.  We wish that would stop.") to very, very
small in scope ("If I add 13 and 29, I get some result.  I wish I knew
what that is.").  But they're all problems.

What does it mean to "solve" a problem?  It means you find some set of
steps that, when followed, takes you from the situation you have to
the situation you want.  

Mostly in math, when we talk about "problems", as opposed to just
"calculations", we mean that you're supposed to have to figure out
which steps to do, and in what order, without relying on a formula or
recipe.  For example:

    John is visiting his father's farm.  There are goats
    and chickens in the barnyard.  He counts 20 heads, 
    and 32 legs.  How many chickens are there, and how 
    many goats? 

If you've never seen this kind of thing before, you have to do some
reasoning about how you can use the information you're given to find
the answer you're asked for.  When you can do that, you've "solved"
the "problem". 

Does this answer your question? 

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

Date: 07/30/2007 at 22:47:33
From: Blake
Subject: Thank you (Definition)

Thank you!  I get it.

Blake