Parenthesis

Date: 03/09/99 at 09:26:18
From: Jeremy Ravenscraft
Subject: Parenthesis

I know how to do parentheses, but the problem is that I have to teach 
a class for the day, and I really have no idea how to explain how they 
work. Can you help me with that?

Date: 03/09/99 at 12:54:12
From: Doctor Peterson
Subject: Re: Parenthesis

I have all sorts of ways to describe parentheses for people who have 
trouble grasping the concept. One good way is just to write an 
expression on the board and turn each pair of parentheses into a circle 
enclosing the parenthesized part completely. You will end up with 
something like this:

             -------------
            /             \
           /               \
          |  -----          |
         |  /     \          |
     2 + ( ( 9 - 5 ) / 4 + 2 ) / 3
         |  \     /          |
          |  -----          |
           \               /
            \             /
             -------------

You have to turn the contents of each circle into a single number, then 
replace the whole circle with that number and continue. You can do this 
step by step, each time redrawing the expression with less stuff in it. 
You can make up a silly story about black holes collapsing or 
something, to make it fun. You might even want to start with just the 
circles (not parentheses), and after showing this, erase the top and 
bottom leaving just a little curve at each end of a circle - the 
parentheses!

Other ways to talk about parentheses include "boxes within boxes," each 
box having to be opened in order; this is most useful if you are 
talking at the level of algebra, with some variables inside; you solve 
equations by "unwrapping" one box at a time (undoing the operations) 
until the variable inside is revealed. Or you can make diagrams like 
this:

     2 + ( ( 9 - 5 ) / 4 + 2 ) / 3
            \_____/
               4
          \_________________/
                   3
     \___________________________/
                   3

Since I am not sure of the level of your presentation, I have probably  
missed some of what you want to talk about; but this may give you some 
ideas of your own.

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