what difference has ICT made in school maths?
In spite of the smoke, just about none.
We just use the technology for more efficient representation of the same content. Hundreds of years of pen and paper has deeply shaped the way we think of maths, and we're not sure of how to unleash the new thinking that ICT provides ... such as the power of modelling in an era of spreadsheets and recursion. Although the practice of science and engineering is highly transformed in places, we've barely modified the content or approaches to 'problem solving' in maths education....barely scratched the surface of how these tools overlap with the school subject we call 'maths' . We have some interactive whiteboard demos, but not much has changed in secondary maths...we have lots of little disconnected 'learning objects' that illustrate a concept or two(the Learning Federation spent $100 M on a set of very ordinary, disconnected 'learning objects'... which tend to be feel scripted, artificial - not much of the rich constructivist thinking that ICT can offer)
Compare this with the rich interactvity of game engines.... the huge and sustained development that makes a world fluid and believable and compelling ... where are the versions tweaked to make maths explicit?
school barely even attempts to go there ...-
(here's a minor example of what i mean)
Alan Kay thinks the real computer revolution hasn't happened yet... and we're still in the early days, like the first 50 years after the printing press, when it just looked like a better way to make manuscripts....
.. when there is a realm of ideas and approaches that can be tapped - click the pic to see what 6 simple building blocks can do, when we move beyond the computer as reproducing text, to having tools that allow new ways of thinking, new ways of seeing the material
this is literally, a few building blocks ... click to see ... year 7 and 8 kids got this at first go...
there are 200,000 other projects shared in this space, and some rich maths ones...
in spite of the limitations of the tool, Scratch is rich enough to allow
- expression of creative ideas
- tinkering
- experimentation
...attributes often rather lacking in school versions of maths
I’ve often noticed a few kids in school – often totally under the radar of their teachers- have quite strong skills at programming, largely self taught - even though they might be mediocre at maths or english, as judged by results.
just about no-one in school tries to the leverage the overlap...since education still tends think of 'mathematics' as manipulating symbols according to the same rules ... and computing has become a black box, where we are 'users' and others to the work of developing the simulation and model
Contrast with this
"(If you like programming, but you hate mathematics, don't panic. In
that case it's not really mathematics you hate, it's school. The
programming you enjoy is much more like real mathematics than the stuff
you get in most high school math classes.) In these books I try to
encourage this sort of formal thinking by discussing programming in
terms of general rules rather than as a bag of tricks."
http://www.cs.berkeley.edu/~bh/v1ch0/preface.html
Papert of course had strong views on this - that school maths was too
dry, and that playing with the turtle gave even young students access to
ideas like vector calculus, in a more intuitive way, without the
formalism normally associated with these ideas....
for example,
Repeat 360 [fd 1 rt 1]
Is an alternate and possibly more intuitive way for kids to explore a circle, than the classic analytical description
(x-a)2 + (y-b)2=r2
(and when differentiated according to the rules for doing this...
dy/dx = --- [an expression too full of indices, brackets and square roots, to be formatted into an email (where some of this was drafted) ]
and so what intuitive meaning does a student see in the rate of change of y with respect to x
and which version will a child most likely see in school?
The former approach gives more "feeling" for the differential changes; and so maybe in later years 'curl' and 'div' and all that would be likely to make more sense, if one had played with the 'feeling' of curves like this ... or at least, maybe one is more primed for some sense of the mathematical objects ... maybe ... (like paperts 'gears' becoming the mental tool he spun to appreciate what 20=4x+5y meant)
why is the mapping between these domains, across them, so weak in school maths - with all the effort expended in both ICT and maths ... why not better allied ...
I know I move into a more creative place when i model or program maths ideas - and have ever since my own schooling - and thus find the maths makes more music ... and I want the kids to experience all this via modelling and programming ...
will take some more permeation of ICT into maths... not as a presentation tool, but as modifying the discipline itself...
Papert and David Perkins describe this as "2nd order" change - not just using the new tool to more efficiently represent traditional paper based content, but allowing it to interact, modify the content and discipline itself ... will sound like sacrilege to many maths educators; less so, i suspect, to pragmatic scientists and engineers, whom we like to think we are preparing..