> 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.