Roy Williams

Scott and Jenny and Deirdre ...

Receptivity to emergence can, in the first instance be lost (as children are 'socialised' into conventional schooling) - I think it's innate in young children, as in your great example, Deirdre.  

Once children become settled and successful at school, they probably have to re-learn what they prevously knew (how to trust their creative, curious instincts), but this it requires a move on their part back into a more uncertain and risky learning environment, away from the 'comfort' and 'certainty' of schooling. That's a big ask, and must be quite confusing. 

Does this make sense? 

Deirdre, agreed. When we first formulated our framework on emergence, and developed the footprints visualisation tools, we deliberately tested our ideas against open learning - as broadly as we could, and Montessori preschools were one of the key examples (alongside higher education, etc). 

Our generic footprint of Montessori preschools is here: http://footprints-of-emergence.wikispaces.com/Montessori+pre-school

And we used Montessori (as well as the interactive space, MEDIATE) as key examples in a further paper (forthcoming, 2014, in Leonardo) on synaesthesia and embodied learning - this is the abstract: 

ABSTRACT: In an integrated view of perception and action, learning involves all the senses, the interaction between them, and cross-modality rather than just multi-modality. In short: synesthetic enactive perception, which then forms the basis for more abstract, modality-free knowledge.  This can underpin innovative learning design, and is explored in two case studies: children in Montessori preschools, and in the MEDIATE interactive space (for children on the autistic spectrum) in a ‘whole body’ engagement with the world. The challenge is to explore the rich opportunities offered by these modes of learning, and understand the transcriptions and transformations between them.  

The Footprints of Emergence provides a method, and a toolkit, to describe and communicate the complexity of learner experience in the new 'open-courses'. 

It's not a simple matter, particularly if we want to track the dynamics of changes in learner experience over time.  

So, here is one way to describe the four 'clusters' or 'quadrants' that form the basis for the way we make sense of the 25 emergent factors.  This might make it easier to get a sense of what the footprints are all about ... 

Open/Courses

What is the balance between Openness and Structure?

Interaction

How are you able to interact with/ in the learning space?

Independent Initiative

Do you develop your own capacity for action, or just compliance with fixed roles?

Presence

What traces (and connections) do you make and leave behind  you?

 The five or six 'factors' for each quadrant are, then, the next layer of description of the details of what is critical for emergence and emergent learning. 

By learning to live on (and love) the edge of chaos.  

No, that's too easy. Avoiding jumping to conclusions is a prerequisite for learning, and for many unusual diagnoses, no?  

A favourite of mine: in my (brief) days as a medical student, I worked in a rural hospital, including a Leprosy unit - in which 'feeling no pain' is the key evidence for the disease (nerve degeneration leads to loss of sensation), which is why it is missed so often by doctors who don't normally see cases of Leprosy, and 'can't imagine' why NOT feeling pain would ever be a key symptom for disease.  

So ... the rarer it is, the more difficult it is to diagnose. 

Elegant analysis, thanks. 

So, mathematics is an infitite set of transformational metaphor processes /structures /tools, sometimes linked to other (less abstract, bu possibly equally complex) practices?

My first insight into metaphor was from my philosophy lecturer, who said they are 'deliberate category mistakes' - precisely a near-boundary / edge of chaos tools, and his favourite metaphor (and one of mine too) is a fruity one, see here ...