learning in progress ….

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]

I went back to my desk the other day, and found half a dozen large art works had been placed there, to return to some year 8 students.

The glowing creativity, and the teachers effusive praise, made me pause, since I’d just been ruling perpendicular axes on the board, and the same students were learning how to handle y=mx+c, plotting sets of numbers, drawing letters on graph papers, decoding graphical puzzles etc; and even with these variations, it all seemed relatively dry by comparison .

Looking at the art, I wondered again, about a topic I've considered in the last couple of years – why do we not use more ICT to explore the world of maths, from the "inside" – that is, get kids to build the simulations, build the models?

Seems that approach should be congenial in Maths, of all places. ICT and maths share some similarities, derive from the same imaginative heritage. There’s also a serious challenge in teaching and learning either well enough to really do the hard stuff.

Maths though, enjoys enough respect that we still take the top end seriously. (Most of the population might wince at the memory of simultaneous equations, and maths teachers might get bad press for being recalcitrant in the face of demands to be more "integrated", "collaborative" or other progressive terms – but overall, it seems that higher maths is justified, by whatever percentage go on to further studies).

And although ICT looks a bit more popular, with its web pages and animations and video conferencing, we seem we seem to have bought the idea that a much lower threshold of difficulty will do. As long as the kids can make something novel out of the glittering array of tools, that their parents didn’t know how to do; there is no need to remember that this flexible software is built on computer science.   

(More generously, maybe ICT supports the thinking in other subjects – helps to gather or display data in science, or write essays in English, supports creativity in photoshop images or media video etc. All of which is great).

But the art on my desk, got me thinking - i googled "interactive flash art" and recalled these beautiful, dynamc art works

I know this is built on a synthesis of programming and maths - iteration of functions, rendered with flash's nice vector graphics. The interesting maths is a little hidden - one needs a decompiler to get at the code, to see how it was done - make the parameterised drawing routines visible.

Or take the apparently simple but very popular lineRider game, also coded in Flash, which the students - and a few teachers - seem to love playing. Behind the scenes, all that free flowing sketching and intuitive physics is stacked full of maths; equations for wind resistance etc ( i have had a look at this one- and its full of nice maths we could use).

Its a pity the maths isn’t more visible; not hidden away in the finished product; (although its not hard to decompile with ASV). Recalls Papert – the mathematician – and his brilliant ideas of Logo for children. That fact that "Logo" now sounds like it a relic of a dim era, rather than a high point or seminal approach to educational technology , is part of another story.  To use a logo term, we are inclined not to make a serious effort to grapple with the "flip side" of ICT; the detailed control side; which Papert hoped would render geometry and physics and other fields (dynamic systems etc) open to intuitive play - or the play would inform the code -  without the excessively formal pathways that are often the way in school.

These days we usually let someone else produce the code - we don't see that as part of the learning; maybe because we think ICT is meant to be simple. Graphic calculators, or Graphmatica - interesting as they are, they tend to provide a short cut to the results; and so we are limited to "using the application’. The irony of this is it can kill the promise of building it; of taking the challenge of students being producers as well as consumers of digital simulations, as this visionary school puts it

Anyway given these art and lineRider game examples, I thought, why not use flash, with its slick vector graphics, in maths? - its just as powerful as the old turtle wandering around, but might be more familiar today. Lots of kids already know how to use the drawing tools in Flash, and can animate cartoons – little South Park skits. Its rare for them to tacke the drawing commands, though they are simplicitly itself:

 moveTo (x,y)       //moves the virtual pen to x,y
 lineTo(x,y)           //draws with the virtual pen x,y

nothing hard there – in fact almost too simple - but the essence of wandering around the plane, drawing is all there

(the equivalent of the old "pen down" or pen color" commands is :

lineStyle (thickness, color, transparency)   

using nothing much more than that, one can make a simple cartesian grapher :

(a minor point for the curious– Flash, like lots of computer graphics, puts 0,0 at the top left corner of the screen – so I’ve used an empty movie clip called ‘origin’ at the mid point of the screen – and by drawing there we inherit its idea of 0,0 at the centre of the screen)

Anyway, the point of this is not that we needed yet another graphing tool.

Its to see how easy it is to make a zoomable linear grapher, in a few dozen lines – about as much as a page of working - final file is only 5k.

A little more extension, and it would be able to plot any function – exponential, sine, whatever - might be a nice task for some programmer kid somewhere. So if an ordinary teacher – who is certainly no maths genius - can do it, and could of on the old Commodore 64 - what of our "digital natives"? Why do we not see them there? Students seem to teach themselves, or watch siblings and friends, use Flash from a design point of view; but might need help to get started on the coding side; but I argue its no harder than the maths they’re being asked to do – and empowers it; both for learning and attractive application

if ever a rationale was needed, try this –

(a) in the space it takes to wrestle through a few problems, you can write your own graphing tool

(b) getting kids to do this forces them to grapple with the concepts and modelling involved

(c) can be extended into art or games.

(d) gives an inner perspective on wrestling with functions and space

(e) If this is the information age, modelling simulations should surely be a useful tool, and valid in maths

(f) taps the natural engagement many minds have with a computer

(g) can be extended and modified. (eg first version of this didn’t have zoom –which made it easier to start off - and then extend; unlike a pen and paper problem which stays fixed)

(i) Maybe there’s an inter-disciplinary approach sitting dormant - computer art & maths - here – but would take more than a semester to unlock, given where we are starting from.

So just a little proof of concept.

(I’m not, though, about to reinvent the year 8 course on these 'lines" , for a few good reaons:  

- in the current curriculum, with its boundaries (this is Maths, this ICT) there is not enough time or access to layer the programming mindset into maths

- its not as easy trying a new approach ; needs some support to make it work - eg a few people to bounce it around with - since canonical maths approaches, and content, both get modified in the process - and notwithstanding the promise of taking control at this level, in the world of "using applications" ("i just want it use it")  it looks too slow and laborious (and while i'm suggesting the payoff would be worth the effort, it doesn't seem a common angle for some reason).

might be of interest - rob

ok. this is rather exciting, i think

Some of the Whitehills cluster schools (and a few schools in Mildura) have been involved with a pretty cool virtual world project called River City - immersive 3D world for learning science, where you engage in enquiry learning tasks via avatars (virtual characters). Kids and teachers have really liked it, and there is also research confirming it is particularly effective in communicating science concepts to kids who might be at risk of dropping out of science (they've tested control classes etc)  (i've described it here before)

 Access to their simulation has been free but is limited – its developed and run by Harvard graduate school of education - we’re the only Australian schools they’ve taken on and they are having some resource issues supporting that (eg our access clashes with them upgrading or testing software at night etc) At one stage it looked like they could give us a full copy of the simulation, which was going to go on the Flinders Uni servers, at the Aus Science and Maths school – but that fell through – turned out the legal people weren’t quite as ready to give away tools like this, even though the researchers liked the idea of a greater pool of student data as a trade off

so, they offered to give some advice if were interested in building our own "next generation" version - ..... which was nice - but felt a bit huge.. right - so we'll just go out develop an enquiry learning, immersive virtual world, simulation project, here. Sure, no problem.  But unlikely as that may seem ... it seems to be happening...

The principal of the Australian Science and Maths School, Jim Davies, suggested we try to tap the “Science by Doing” / enquiry learning agenda . to cut a long story short, we've been talking with a few people about developing a simulation in the same style (with a sustainability theme) and Swinburne uni have just committed themselves to definitely taking this on – fits very well with their expertise and desire to take their games and multimedia dept into developing educational simulations - in short they think they can make a rich and immersive and customisable simulation - in fact a flexible simulation producer -  for very minimal costs, using their inhouse and student expertise, graduate projects etc, for schools

(i met one of their lecturers when i took a programming class to the ACMI - has bubbled away since then) - the official "science by doing" agenda hasn’t got behind this yet - but Swinburne are keen to build a prototype by middle of next year  - using student and inhouse labour. ASMS is also partnering and sponsoring this. it will be a simulation builder - and will leverage our experience so far.

River City is engaging and well designed – but as a user (or trainer) you can’t change anything in the design or curriculum. (there was also a tech problem that stopped it working from some locations). We’re planning to keep this model more easily customisable. The first version will be around "sustainability" and will be customisable in itself. River City is also built on older technology which has dated somewhat - good as it is, the new stuff will look better, allow richer interactions, has a full physics engine (the Unreal engine) inside it etc.

Swinburne's expertise is the technical side - i saw what the 3rd year students are doing on global warming simulations etc and so i can well believe that. We'll need to develop a group to look at curriculum for science learning in this environment, comparable to the River City curriculum and training docs  

Didn't look like it was all going to come off for a long time ... but now looks it will ... which is great. Spin offs should be interesting-  eg maybe linking in programming students - some real project examples for them - and swinburne looks likely to allocate a 3rd year student via an industry placement to work on it - so we can aim to get the secondary students to meet the undergrad developers etc - and of course the science currculum needs development and testing by teachers etc. we also can get an explorable model of one of the new Bendigo schools in there as well (technically, its quite easy, apparently, if we can get enough access to plans). .. have discussed that with a the regional office staff etc . Weeroona, or loosely Whitehills cluster, and the Aus Maths and Science School, are the nominal "client" (ie between us we will provide the design brief, look at developing curriculum etc)

the harvard "River City" person i met through video skype and email, Ed Dieterle, is also willing to give some general support  ... so no shortage of ideas flying around at the minute  - he just wrote an email, from Chicago airport, as i finished this at midnight ... so all interesting developments. (Like River City, it will most likely be targeted at middle school - upper primary to mid secondary - and maybe older as well - the appeal of RC was pretty broad. ) 

links  :
 story of how we got involved
Education Times article (p15)
background on our attempts to tap the Science by Doing agenda     (and Swinburne rebuild project)
River City site (this is not the simulation - just an info site, with movies, overview etc)

A few of us just visited the Aus Maths and Science school in Adelaide; an open plan, highly connected / immersive, ICT rich environment, that we seem to be heading for. Even there, though, integrating maths and science is proving difficult; and i'm not sure IT is fully harnessed, yet, for maths.   

I also read a book recently, what “Video Games have to teach us about Learning and Literacy”. It  takes a reflective view  - a player’s view - on the challenges of learning video games; why do people pay good money for long, difficult learning experiences? how do game designers scaffold the levels so the experience is hard but learnable? what might schools learn from this? I like his thoughts on role and identity – you get to “be” something cool from day one; similar to when schools allow you to work as a scientist, rather than learning 10,000 things “about science” for the “future”. David Perkins of Project Zero had similar ideas of letting students “play the whole game” in school, albeit in a cut down form, not just endless “learning about”. Traditional technology offers the same role based learning, you get to be the cook, or the metal worker. Anyway, I wonder if we can do the same with maths; maybe using computers for modelling.    

(warning - long post!)
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