i wondered recently, and ages ago, about the unrealised potential of tinkering with software to learn maths etc, from the "inside"; more of a modelling approach using iteration etc. So here's an example of that ... taking the popular internet game LineRider -which is full of neat, but hidden, school level maths - and adding a cartesian grapher in the left corner to make some of the maths a little more visible to the kids who can't see where y=mx+c kicks in
(click the pic to launch it, then click the little icon on the left hand edge)
[if you want to download the swf, you'll need this file as well]
so ... my point is really, not that we can make demo's like this, though its fun... but that we could, in principle, teach whole courses like this ... a hybrid of maths with computers ... or even this sort of interactive art, -ie not just apps that demo "key concepts" ... but maths thinking and "IT thinking" -(programming etc) supporting each other ... thats the boundary i think we still haven't crossed in school yet; reconceptualising how maths and ict could relate.
Nothing much novel here - Papert and Kay were suggesting it 30 years ago; just don't think we've gone there in any significant way -programming feels a bit out of favour, for various reaons - and so i think we are missing a key aspect of what software really is; limiting kids to being software "users" - not experimenting with the most flexible and expressive symbolism devised ... (i'm certainly no expert at this - just feel that in order to take control in creative ways kids need to be exposed to the art and discipline of programming; its what this ICT stuff is made of after all; they need to be literate here, or least get a chance to be - empowered so "behind the scenes" isn't out of reach - and this world of functions and variables could also be very useful for exploring maths in particular; could also mix into art, word games, media stories etc)
(here's a compelling story on how we got to where we are .. where the software experience is reduced to "using applications" - i'm just finding out there was a huge educational vision around the initial explosion of IT ... not just logo ... which had the idea of kids making and exploring their own tools - which has largely gone by the wayside)