However ...Re: [Squeakland] Panel discussion: Can the American Mind be Opened?

subbukk subbukk at
Mon Nov 26 10:08:30 PST 2007

On Monday 26 November 2007 8:03 pm, Alan Kay wrote:
>... So one of the biggest questions
> any math educator should ask is: what symbols should I initially
> employ for numbers to help children understand "number" most throughly?
Coming from a culture steeped in oral tradition, I find 'sounds' better 
than 'symbols' when doing math 'in the head'. The way I learnt to handle 
numbers (thanks to my dad) is to think of them as a phrase. 324+648 would be 
sounded out like "three hundreds two tens and four and six hundreds and four 
tens and eight. three hundreds and six hundreds makes nine hundreds, two tens 
and four tens make six tens and four and eight makes one ten and two, giving 
me a total of nine hundreds seven tens and two". Subtraction was done using 
complements. So 93-25 would be sounded out as "five more to three tens, six 
tens more to nine tens and then three more, making a total of six tens and 
eight'. The technique works for any radix - 0x3c would be "three sixteens and 

In India, many illiterate shopkeepers and waiters in village restaurants use 
these techniques to total prices and hand out change. No written bills.

The advantage with sounds is that tones/stress/volume can be used to decorate 
numbers. With pencil and paper, changing colors, sizes or weights would be 


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