learning in progress ….

• allowed children to contruct their own models, in rich and non determined ways
• allowed them to explore incremental changes, via a natural sense of space
• allowed children to program the computer

Most teachers will also have at least a passing awareness of Piaget and his notion of developmental stages (eg “concrete thinking" precedes more abstract “formal operations")

Papert worked with Piaget for some time, and began to think that appropriate use of computers could actually shortcut the Piagetian stages – for example that with appropriate environments young children could productively work with physics ideas normally considered part of abstract maths - like vector calculus. That is, computer environments could be used to remove the mathematical formalism, and get to the nub of the ideas. ( Some research into this 'piagetian hypothesis'  found that with appropriate use of the Logo tools this short cutting of the stages did indeed occur)

Anyway, Bill Kerr introduced me to some of this, via Squeak (containing concepts that seeded both Microsoft and Apple with ideas they have run with since), and Alan Kay, the visionary who led much of this development (of gui, windows, mouse, OOP), and who has thought deeply on computing and education, for decades, in ways that makes much of the current “ICT thinking” look a little simplistic.  (Want to find a way to get early school age kids to think about calculus … minus the formulae)
(and he’s tinkering with a 'high risk high return' project that might redefine IT all again - he thinks the real computer revolution hasn't happened yet) 

(incidentally I came off second best with Alan Kay when I ventured some unresearched opinions at one stage;  and while I think I’m on the reflective side, my opinioning was categorised as infected with the “creeping fungus of web think” when i ventured opinions on the utility of MVC and design patterns, without realising that cluster of ideas had also germinated from their work at PARC Xerox  -  but you do come away with a richer understanding after the exchange ...

 So anyway the Sugar list got discussing constructionism a while ago.  Someone had mentioned a story about Piaget, as a child, “discovering” conservation of number – by counting pebbles on a beach, and being amazed that there was the same number, counting from left to right, as right to left … as an example of the sort of personally contructed learning that could be achieved on Sugar/XO.

And that generated some comments about the role of teachers in ICT discovery learning … and the degree to which teachers are needed in child centred approaches … can we set up kids to learn like this, have deep insights, more effectively than ‘being told’ - or is that a rather naive view of contructionism, which might work in individual cases, but won't 'scale'?  

 Anwyay,  some of the stuff might be worth posting. It started via an article with 'constructionist' examples,  and some comments that were made about that:  

“ what was the role of scaffolding? What exactly is the role of the teacher? Can she just give the task at the beginning or is continual guidance from the side required? I think a deeper understanding of the role of the teacher is crucial in really understanding constructionism. A teacher could pick up the bare bones description  ... and turn these tasks into anything.”

Great question (it seemed to me..)  .... so got me jotting ...

.. seems to me that scaffolding is ultimately superfluous. One ultimately wants the building, not the scaffold. Like training wheels on a bike – a necessary stage that one hopes to outgrow. Or like a well written tutorial – one races through the conceptual steps, and barely looks back – now ready to kick that framework away, since one has now scaled that part of the structure.

But given the scaffolding is needed to start with – since most of us do need help learning to ride a bike or solve maths problems, we are left deciding “how much scaffolding” is needed. Seems to me that this depends on a host of local conditions –current intellectual stage of kids; self perception as learners; local culture of learning; previous balance of transmissive / explorative approaches in the local environment; (teachers willingness to model acceptance of uncertainty without losing face by ‘not knowing’ – related to confidence in the material) and critically, individual student interest and aptitude.

Individual case studies are fascinating – and yet attempts to transfer, or generalize, run into lots of uncontrolled variables – learning styles, cultural preferences etc.

Where maths investigations, physics experiments, programming techniques, are repeatable in key ways, and can aspire to precision and reproducibility, the scaffolding of educational experiences remains a “softer”, more mutable, art – what works for one may be anathema to another.

Even the preceding list of 'hard' knowledge (maths, physics, programming), can be  creative and fragile and uncertain at times – in the pondering over a hypothesis or new problem, the cultivation of a new insight etc. These domains just tend to end up getting worked up into mathematical formalisms -  and maybe that is their natural state, and they do need to be precisely codified in order to contribute to the world of formal knowledge, and take a place in engineering automated processes etc.

But comparing these formalities with the initial insights they derive from, is perhaps like comparing the stages of psychological growth (a reputable and testable theory) with the story of Piaget as a child being amazed at the conservation of pebbles on the beach.

One wonders if the clarity of that moment influenced his key ideas of conservation, of formal and concrete stages; if the genesis of this branch of thinking, a sense of its weight and importance, came in personal flashes of insight like this. (Which is not to suggest that these ideas are “only” personal intuition – no doubt psychology has confirmed their validity in various ways – just that that the genesis might come from here).

I don’t know if that was the case, but Poincare says of mathematical thinking, that sometimes a key insight would come in a sudden flash, delivered up from the unconscious – usually after it had been primed with long formal attempts to study the problem, and then left to germinate.

One wonders if Papert’s Logo had its genesis in his childhood experiencing of picturing gears – he starts Mindstorms with a chapter on “the gears of my childhood” discussing the love for these mechanical devices; would his knowledge structure (including the spatially orientated  Logo) have developed the same way without that precursor of gears as ‘objects to think with’?

There is not much of this awareness of the unconscious in current thinking on maths teaching and learning, as far as I can tell  (though Koestler demonstrates in his investigation into scientific creativity that it is a common experience among mathaticians and scientists).

A few things emerge for me:

(1) School is often too “formal” in its approach to learning. Not enough space – physical or conceptual - for reflection. Maths and science, for example, is delivered as received body of knowledge that tends to kill the creative spark of enquiry. The sense of pondering, of ideas being turned over, with a sense of wonder and curiosity, and exploring the unknown, is often curtailed by the structure of things. One obstacle to learning these things can be a culture of “clarity and completeness” around received wisdom – it seems so logical and complete once its been generalized, formalized, polished up, put in a textbook with theorems, that one loses the original sense of wonder and enquiry and uncertainty. It can lose the sense of being sketchy, provisional, alive, and seem immutable,  precise, pedantic. In this sense AN Whitehead says that formulae obscure, as well as encapsulate, meaning.

(2) Losing the story of gradual historical development of knowledge is also a problem – losing the partial, sometimes contesting insights that had to be reconciled and integrated, and which mirror our own attempt to reconcile partial understanding.

Thermodynamics, for example, is presented as though it had always been a complete theory. The fact that Carnot had part the story – that heat flow achieves work like water does in a water wheel (published in a book disregarded in his own lifetime)– and Joule’s counter insight that heat was transformed into motion, by spinning objects in his brewing tank, and these insights were reconciled by Kelvin, are lost in the integrated “laws of thermodynamics” – and so is the sense that this structure built up gradually, from partial insights. That sense can make it seem more accessible – since we often learn by progressive integration of gradual insights - and that awareness is lost too, when the big picture is presented as a 'once for all' completed theory.

This gradual structuring of the history of science, or history of knowledge, (and the way it helps an individual to sense its ok for it to open up gradually), can take the awkward name of “genetic epistemology” - a term that might well obscure more than it clarifies, but simply means that knowledge grows from a point of genesis, in both individual and historical realms. ...

“Piaget  ... is concerned with the genesis and evolution of knowledge, and marks this fact by describing his field of study as "genetic epistemology." …. But it does not see the two realms [historical and personal knowledge] as distinct. It seeks to understand relations between them. These relations can take different forms. In the simplest case the individual development is parallel to the historical development, recalling the biologists' dictum, ontogeny recapitulates phylogeny”. (Papert : Mindstorms)

(3) So constructionism is perhaps finding conditions to dissolve the meaning that is crystallised in a formula back into some personal sense of meaning. (Re)discovering the insight wrapped in a formula for oneself – maybe by expressing it a different way – and in wrestling with this, making it ones own, having some measure of the original experience of mapping of new conceptual landscape; now I see it. Reworking things back to state of creative uncertainty.

So this involves :

• learning with others - or with their written materials and example
• “Learning by doing” – (doing all this by making things)
• Reflecting – finding things hard; walking away; coming back to them; grappling with them.

(4) While education is social and collaborative, its also highly personal, individual.
Can we assume that students of the right age, left on a beach with pebbles, or with gears, or computers at home, will have  similar insightful experiences? Can we cue them up to this? Or will the scaffold over-ride, oppress, the “moment of insight”?

Can we tell when and where and for whom the formula will have personal meaning. Personally, I don’t think we can.

Also don’t think there is enough time for any but the most gifted to rediscover, or explore, all the meaning that is now embodied in the scientific and mathematic formulae and principles in a typical education. Many teachers report finally “getting” many aspects of their subject, when they had to teach it – since they bring a more reflective pondering to what they had previously “learnt”.

I’m not sure that this is always a bad thing – not sure that its feasible to aim for “deep learning” in all that we do. I think we could aim for far more though, by aiming for less breadth, and more depth – which translates to spending more time on smaller quantities of curriculum.

Teachers, present or virtual or via tutorial, who have deep awareness of their material can help – can be a useful scaffold – can model the confidence to move away from just handling “established truths or algorithms”; the willingness to ponder, to wonder, to slow down and be in a state of “not knowing”, not being sure. (Having worked for a while in R&D labs, I would say that by no means do all “scientists” like this state either – my first role was to support the engineer with whom all the intractable problems always ended up – i watched while we spent 9 months on one problem, which was a good introduction to uncertainty; a sense that was respected by some, studiously avoided by others, who liked neater problems.)

(5)  many scientists and mathematicians have felt that the workings of the unconcious have something of the character of revelation , as Koestler's investigation into scientfiic and mathematical creativity demonstrated  

(6) Papert’s and Turkle’s investigations into computer programming, left them with a sense of the diversity of ways that people approached the task (eg some liked to open up all the inner workings of the library routines etc; others were happy to black box them and move on). So the world of programming has its own varieties of knowledge construction and representation. Which is obvious enough to programmers – but education needs to know that –the programming class will want to structure this material in different ways.

(6) and the OLPC, potentially any computer … is all this (explorative space) via software, by being all the other things that software can be; simulating literally every other system – including a collaborative tool .

What boils down out of all this?

what degree and types of scaffolds; what character of knowledge; or learning can be planned?

Well, nothing too radical
(1) Give training wheels : Give structure; give clarity; give scaffolds; give tutorials

(2) Give hills : invitations to enquire; examples (living and written) of this; give the whole story and context, not just disembodied facts, give tools to explore with; tools that can build other tools, be constructed, broken down, rebuilt.

(3) cannot proscribe how the first two will interact – not so much scaffold that we lose the hills
(like being invited to a restaurant and then being fed the menu, as Papert says of school maths)

so ... when all is said and done, both modes are needed - the last rules of thumb are already familiar intuitions, i think, for teachers - who are still needed to instruct, in my view of things, no matter how commonplace devices may become - and the moments of insight are worth cultivating, but resist being scheduled