Roy Williams

Kathleen, OK, I'll give it a try, to unpack the basic drive (health warning, I love semiotics - see here, for example - it's an analysis of two pictures of "The Pope sat on the chair") ... 

I would say

• we all want to be in touch with each other (figuratively and literally) 
• so, we use touch, glances, movement .. 
• we move on to sounds, to language
• all of which leave impressions - on the mind, the imagination, the subconscious ...
• then on to physical inscriptions - in the air (dance, music), on the ground (sandcastles, castles, highways), on the body (ours and the bodies of others)  
• and in the process we become part of communities ...(like this online one) 

Kathleen, I have been working in the Mathematics Dept. for some years (as an elearing and e-assessment designer, and my Head of Dept's inaugural lecture was on "the unreasonable beauty of mathematics" - I can understand the beauty, but (also) not always the formulae.  

But I have dabbled in programming (via LOGO) and do know what an 'elegant' solution to a programming problem looks like, and it does bring satisfaction and joy to the learner (me in this case). 

Ila, agreed.  The best advice we ever got about "what should we read to our children / give them to read? (from an owner of a bookseller), was simple: something that will make them love reading.  

Barb, spot on: the factors and the clusters do "seem to move together and independently".  Jutta, I think, reminded us that the footprints are literally holistic - they are an integrated whole, in the  learning event, on the drawing surface, and on the mind.

An oil droplet is what comes to mind, which is pulled and pushed in different dimensions and directions, and settles (for a while) temporarily, sometimes in a stable state, sometimes unstable, at one point or another in the course of a learning event.

But it's the way the oil droplet is re/configured, as a whole, that embodies what's happening in the learning experience at that point, the detail of particular factor is in a sense is secondary, no?. 

Scott, I love the idea of chimps creating learning objects which they place strategically for their young to explore - just like a Montessori environment.

Looks to me like we need to distinguish something like '[open] learning objects with intentionality', and [closed] 'learning objects with instruction' (corresponding to emergent and prescribed learning, perhaps?) - the point being that the learner can accept and explore the intentionality and internalise it in some way, but the instruction only allows for complicance, and there is no need (or motivation?) for internalisation.

This certainly applies to Montessori materials, and would be a useful tool to discriminate between 'well designed' Montessori materials, and (mere) 'learning objects'.  I can think of many examples, from the 'scubbing table' throught to complex mathematics. 

And ... I will have to set aside some time to visit Emily Cross at academia ... thanks ...