Sitting on a train, after a day wrestling with a research proposal, an interesting synchronicity unfolds. Passengers cram in; opposite one starts a crossword puzzle. Adjacent, one opens a laptop and starts programming. A few minutes layer another passenger gets on, sits opposite, and starts a sudoku. A moment later the sudoku solver and the programmer recognise each other; obviously know each other a little; but don’t talk for long, and settle back to their tasks. I’ve been glancing at the programming beside me; its in a terminal window and is full of test cases and assertions. I guess it might be a test harness for an electronic board.

After a while I notice the approach the sudoku player is taking, systematically listing, in small script at the top of each cell, the candidate possibilities for each square, identifying the most constrained cells first – then reducing elements out other cells once one is determined. I find myself thinking of procedures I could use to program that - looping through each column, and row, with an array attached to each cell; - maybe with colour if one just wanted to hint at productive cells…. I glance back at the programmers screen –and it suddenly seems like that is exactly what he is programming  - he flicks a window and I see its called sudoku.py.

My sudden conjecture is that there might be coworkers, since they did recognise each other … even though the common link of sudoku algorithms seems like improbable work  .. so I break the convention of commuting silence and start a conversation.  It turns out their common focus is not these little numerical puzzles - they actually did a computer science course some years ago; the manual sudoku solver now works in a bank; as a systems designer;  the programmer works for a stockbroker, programming automated trading systems  – both are tackling the sudokus for distraction. 

We chat, and I talk about this research, and Sherry Turkle’s reservations on today’s notion of IT– around the that fact that 20 years ago many kids programmed computers for fun –  we all agree on that - but today kids are more likely to be on MySpace or World of Warcraft. I mention my suspicion that the lack of a 'BASIC' – the simple, pre-installed language we learnt with, might contribute to this.  I’m interested in their opinions. The stockbroker programmer indicates, wryly, he is happy with the lack of competition coming through from junior programmers. The sudoko banker rebukes him, and warns that below a critical mass that whole sector of the IT industry will be outsourced to India. Working in a large bank, he sees it already; there are no local programmers below the system designers. He also seems bit conflicted about ICT in schools; since he has fond memories of the control he felt in teaching himself programming language, and spending hours trying to make games, on a Commodore 64;  but isn’t sure there is a future in it now. The stockbroker programmer disagrees – loves the technical work and sees it as a good career option for students.

I feel like I should interview these two, incarnations of the concerns I’ve been reading over for two days; early dialogue in an outcome space.. after they leave at the little satellite town, I travel on, feeling I might be on to something - that the historical tensions around how IT is conceived corresponds to real and current issues,  and the strength of this little debate tells me the issue goes beyond schools - and the idea of visual schematics to examine the tensions might work.

many in education seem set on cheerleading the '21st century ict' ='web 2.0' =transformation' theme - lots of syrupy youtube videos  on that theme - but not everyone agrees, or at least not without reservations about what is missing in that equation. Some have even stepped away from the spin and put it all in historical context. Its quite stabilising to have some sense of the real historical trajectory of educational computing - the popular idea that its all progressed betrays some of the real history. 

My little boy likes 'The Incredibles' brand of superheroes, so I know that Pixar film rather too well. There’s a clever intro to the movie, where the super heroes talk about their alter egos. One of them, glib and suave, complains that “superladies, they’re always trying to tell you their secret identity. They think it strengthens the relationship or something. I tell them,  I don’t even want to know about your mild mannered alter ego. You tell me you’re Mega-Ultra-Lightning-Babe, and I’m good. I’m good.”

The reality of these things is not always so fun. I have a friend who works in procurement for a large multinational company – transacting leases on oil tankers and little things like that. He was recently pulling his hair out as the company was upgrading their super duper finance package, which is a world class, company wide, top of the range product, from version 2 to 3. The result, after endless meetings, change management plans, consultants flying in from the US,  is that they now have a world class system that is much harder to use, takes 16 keystrokes to complete tasks that used to take 3, and has many of the shortcut commands in another language.

So here’s a few thoughts.

I knew a school in Melbourne, close to 10 years ago, that developed some pioneering approaches to IT in general  - all teachers were asked, and required, to work hard to integrate IT in their classes -  and also were progressive with learning in general (they were onto the metacognition, “learning to learn” , habits of mind, middle years sort of approaches early on), as well as new uses of space (open learning spaces, passive supervision of pods etc)

(I was in a Catholic school at the time, which would probably have wished to claim a richer purpose in education, and yet I and others from our school were very impressed with the clarity and focus of this schools purpose and mission – everything seemed to pull in the same direction – and so we ended up, via an ICT project, in some sort of mentoring relationship with the school.)

I remember a one senior staff member saying she had to travel to most of the intentional conferences on teaching and learning, to keep abreast of it all.

They also did some really interesting things with intranet / extranets etc; they were early on the block with publishing student timetables to the network, and student / parent portals to the web.

A couple of their own IT staff developed that, supporting the school's general agenda. Its not so hard with some time and support – I recall hearing them say, at a Navconn conference in 2001, that they started in Cold Fusion, a fairly streamlined web environment, and only moved to ASP once they got some skills under their belt. That is, they were just working with the more accessible and flexible tools of the day; aiming at functionality, not necessarily at the most technically advanced pathways.  Rapid application development.

An interesting question arises – how would one scale up some of that intranet / extranet innovation?

To my naïve mind, two approaches seem possible.

(1) encourage other schools to foster the same sort of local skills and development. Given there are really powerful open source apps, and development environments, that streamline the process (one example is Moodle), one could expect schools to have a big jump start on those early developers. Some of those projects use a central repository of modules on the web – so one could harness the innovation across the system, magnify and harness the efforts of those two original developers.

The formal educational system could presumably provide some support in getting platforms established. It could also mandate certain standards on how the data must import / export; such as the flavour of XML that was required to exchange data between, say, timetabling and reporting applications, so that local development produced solutions that could still exchange data with each other.  And then let schools plug and play and customise their modules; and tap each others development and ideas, within a framework that still maintained standards on how data was handled, exported, etc.

(For a weak parallel, one could look at edublogger, as an example of education colonising a common platform, in a way that does leverage an existing open source technology (wordpress) - one that is leaping along with regular enhancements from an active community of supporters, using a standard and yet customisable framework. Edublogger is too limited for this to be a good example, since its more of a training / playground –for example, one can’t even modify the underlying Wordpress plugins or themes. Wordpress MU might be a better example, though it would probably be stretching it a bit to try turn it a large scale content management system for a school - its not designed as an admin tool. Moodle, joomla, dotnetnuke might be better examples – where one could enforce some standards on how the flexible app was used /deployed without killing the range of customisations).

 [i guess the risks are that some schools wouldn't be in a position to do much in the way of developing it; and may  need a fairly standard version, and access to a local skills to customise it.]

 OR (2) – one could attempt to build a big system that packages all that functionality into one bundle, does everything, and distribute to multiple schools from a commercial vendor. Sort of like SAP for schools.  (Cases has tried this, i think ,with various web modules).

I think there are a couple of reasons why the former approach is pretty interesting.It could tap some of the willing creativity in schools, and allows schools to fully customise their own applications, in a way that off the shelf seems to find hard to match.

The SAP model – a system that does everything – would seem to run a few risks –in terms such development time; and also that the standardisation might make it hard to customise and match against local needs.

In my untutored observations of these things, if a company had something really good already built, it might work – but it seems pretty tricky. Watching attempts to standardise other software apps in schools, including NSW and Queensland, doesn’t suggest this is going to be easy.

One of the most astute people I know in the field of intuitive learning and software design is Kathy Sierra. (Her crash course in learning theory is great, and thoughts on software features is interesting). She’s made her name with applying these approaches to the teaching and learning of a difficult and traditionally dry area, object orientated programming –and turned the classic textbook genre on its head with the result.

She has this interesting cartoon on her site:

 I have some feeling for the two developers in the school story - and the notion of proceeding by magnifying their efforts.  I wrote an information system for analytical laboratories, in the early 90s, by extending some common productivity software with scripting. … was an after hours project to start with, for the lab I worked in, then a part time job while I did a Dip Ed; and somewhat to my surprise was installed in 6 labs, and reduced the need for admin staff. It lasted a few years after I left; which is not bad for non updated software. Was replaced few years later with a 'proper' commercial product – which was more secure etc, but was less well received than the inhouse tool. Developing from inside the company, one has the advantage of knowing workflow, paperwork, systems, and where to automate the manual work.  

Disclaimer – i no doubt sound clueless, but its not the commerical verus free open source thing that i'm getting at here. Its the question of how to scale up successful innovation;  seed it again in local environments, tap the creativity in the system, with some means of exchange and feedback,  or deliver it from one standardised centre? -  and also the development and flexibility issues in the two approaches ..   but this is all just my uninformed reflections; and i'm not 100% sure which side of the cartoon i'm on.  

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

  (at the time i saw this as "KLA specialists versus middle years approaches" because that was the tension i saw in the local system - and the way maths teachers spoke of it. I have since realised thats just the local expression of a larger tension about maths - the so called "maths wars".

i think i'll write something else on the "maths wars" thing - but first here's my orginal post :   
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