Alan Kay wrote:
"Most adult conventions and forms have huge QWERTY components which make learning more difficult for children. However, eventually the conventions need to be added in. It's imperative to start children thinking in the strongest and most intuitive way -- then we can figure out how to merge in the somewhat ad hoc conventions that adults have devised. Various ways of thinking about numbers, lengths, directions, magnitudes etc is a ideal way to <i>eventually </i>get to some of these conventions. But, e.g. trying to get children started into real numeracy with positional notation is really bad, even though it is a mainstream convention ... the general result in America is that children don't get numerate, even though they are forced to learn how to parrot a few of the conventions."
What do you suggest instead of positional notation? If you get them young enough you can teach them Instant Math[1] but by the time they're 3-4 that's pretty much out, and can put a limit on the size of the numbers they can deal with. I've been experimenting with money--kids understand and like money intuitively it seems--and it seems to be pretty good at bridging the gap between quantities and digital representation of said quantities.
===Blake===