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 twelve'.
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 impractical.
Subbu