Teaching Children Other Bases

Date: 02/20/2002 at 20:20:52
From: Marie Paese
Subject: Number systems other than base 10

What would be the reason to teach children number systems other than 
the base 10 number system? (For example, base 3 or base 7.)

Thank you for your help.

Date: 02/20/2002 at 23:48:13
From: Doctor Peterson
Subject: Re: Number systems other than base 10

Hi, Marie.

There are several reasons for learning this, just as there are for 
learning languages other than English.

First, just as another language will be useful if you go to a country 
where it is spoken, other number bases are used in certain places, 
most notably in computers, where binary and hexadecimal (bases 2 and 
16) are used a lot. As a programmer, I speak both fluently!

Second, just as learning a foreign language can help you understand 
your own language better, knowing how bases in general work can help 
to clarify the meaning of place value and other concepts. I taught my 
son to multiply in binary before he really learned it in decimal, 
because it's easier - you have only the algorithm (method) with no 
multiplication tables to learn.

Third, just as learning other languages can keep you from the common 
American view that America is all there is, learning other bases can 
prevent what I jokingly call "basism," the false view that whatever is 
true in base ten is true of numbers themselves. For example, a number 
doesn't have a certain number of digits; its representation in base 
ten does. And the metric system is only a good idea because our 
numbers are in base ten; base ten is not even the best base there is. 
(The Babylonians used base 60, particularly for fractions as in our 
hours and minutes, and it worked very well.) Stopping to think about 
what a problem looks like in another base can sometimes keep you from 
making false assumptions.

Fourth, bases are just a good exercise for the mind. There are a lot 
of things we teach just for the exercise.

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