Roy Williams

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 ... 

Love the anatomy of Babel fish - and yes, we do need universal translators, and yes, no need to ostracise the strange language of academics. 

Jutta (in Austria) will be running her next workshop using some of the images in the new mapping sheet - although I dont know in detail how she want to use them - it'll be interesting to see, and interesting to find out if the images 'travel' or not.  

Scott, your question about emergence and diagnosis ...

Might it be that although the process of intervention - in mechanics - might be very specific, with little room for the luxuries of 'emergent thinking', the process of arriving at a diagnosis (and even tentative prognosis) might be of a different nature, and might involve tacit, fuzzy, decisions about not what specific interventions to employ, but what metaphors or homologies to employ in thinking about the diagnosis.  

This reminds me (I hope this is pertinent) of a piece of research into mis-apprehensions in problem solving in science, in which the root of the mis-apprehensions was in the misapplication to either a calorific or a Brownian conceptualisation of heat, which led to 'bugs' in thinking through the problem, and that in turn led to an inability to think through a strategy to achieve the solution. It was only when the two frameworks were made explicit, and discussed openly, that both students and the teacher realised that the two frameworks / metaphors / models were appropriate to different kinds of context. 

Maria ... 

The JRR Tolkien piece on the 'degrees of freedom'/ agency in applications (high) and allegories (tends to zero) is very instructive. And from the footprints that we and many others have created so far, and taken into a range of conversations, its clear that learners have a keen, instinctual feel for pedagogy (or heutagogy - if you must), and a keen, instinctual aversion to the abstractions of pedagogical discourse.  

In the Nested Narratives project (which overlaps with footprints to some extent - see the link to the BJELT paper, here, for details) we got students to engage in complex layers of reflective practice (using prompted narratives), which they loved, but only because they learnt reflective practice by doing, not by instruction.  All we told them was that we wanted them to tell us stories about something they had learnt which was important to them - no mention of pedagogy, and we deliberately did not mention 'reflection', as they had told us they would tell us stories only on condition that it would involve no reflection, and no critical thinking - both of which they found deadly boring. 

So ... why are we constructing a footprints tool that is immersed in abstract pedagogical discourse? - a good question. (Best answer I have, and its a poor one, is that we started off this developmental process as researchers, exploring the wonders of pedagogical, psychological, neurological, ecological, sociological, etc discourses  -  particularly me - I love the stuff!).

However ... tools of 'mapping and consent' (involving real choice) must ensure that there are some clear entry points into 'doing' footprints that are unencumbered by the requirement to first learn pedagogical abstraction - alongside entry points for the specialists who want to engage through (and with) pedagogical abstraction too, no? 

Barb - if you are folllowing this thread, this might resonate with the concerns you raised about course designers who demand that participants 'learn (the technical, software skills) by doing' alongside learning the content and conceptual tools of the course itself. Food for thought.