Teaching Children Other BasesDate: 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/ |
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