Thursday, 26 July 2018

Freire and the Arbitrariness Problem in Learning Conversations: insight from music, maths and physics

If the cyberneticians were completely right about learning conversations, then conversations would have the form of a kind of Brownian motion: utterances would respond to utterances, learners and teachers may adapt to the utterances they hear, but the whole thing would be a kind of wandering in search of a point of resolution. This is why I think Pask believed that "Teach-back" was critical to the learning conversation - because without it, how could the learning conversation have any closure? So closure comes from a logical judgement as to whether the student has "taught back" what the teacher taught to them.

I don't think this is quite right, and more critically, it isn't what we see in aesthetic phenomena like music. The critical point is that utterances are not arbitrary. Learning conversations take a form which is found in their originating material. In music the originating material is in the initial musical ideas, the instruments, etc. In learning, the originating material is in the whole constitution of learners and teachers, and the subject domain. There is no originating point of a learning conversation which isn't bathed in personal biography, and histories and social structures which extend far beyond any individual life.

What appears to happen in music is that completion arises from the overlaying of multiple descriptions which unfold some originating idea. Eventually there is some kind of coordination between descriptions which means that a return to some originating state (silence) becomes a natural progression. This would suggest that those physicists who believe that everything comes from nothing (like Peter Rowlands) are right. Quantum mechanics holds some important messages for constructivists.

Composers say what they say by finding ways of generating multiple descriptions (redundancy) and layering redundancies over one another. But redundancies are not chosen arbitrarily. They emerge through a kind of symmetry-breaking process, where the originating principle of this symmetry breaking is implicit in the first instance.

Learning conversations are much like this I think. But what is the originating material of a symmetry breaking process in a learning conversation? It is the root of oppression within the individuals talking. Freire was right.

Closure does not arrive through teach-back - although this may be seen to be an epiphenomenon of closure. Closure arrives through the articulation of multiple descriptions of oppression. This may be what it is for something to "make sense" (c.f. Weick on sensemaking: "the ongoing retrospective development of plausible images that rationalize what people are doing").

What this means, most simply, is that the model of perturbation and response needs a historical dimension. The reflexive selection of utterances depends on the dynamic interplay between three dimensions:

  1. prediction based on what has just happened
  2. prediction based on a model of what is happening
  3. speculation on possible models of what might be happening, and what might be possible. 

Daniel Dubois's mathematical work on anticipatory systems identifies these three dimensions as "recursive", "incursive" and "hyperincursive". They are coexisting processes. Between them they produce elaborate fractal patterns like this:

When I first saw patterns like this, I thought it looked rather deterministic, too neat. But now I think that is not what the picture is showing. It is showing in an idealised way that the interaction between history, the present and future produces moments of symmetry breaking, from which new descriptions of the same thing can emerge. There are moments when multiple descriptions come together and produce moments of closure because the combination of past, present and future produce distinct moments of "resolution" (perhaps this might be in the big diamonds of the picture). 

More importantly, the stratification of this diagram suggests that utterances are not arbitrary. They exist in, and articulate a structure. Emancipation is the revealing of the structure through very careful articulation of levels of description: the production of redundancy. This is very similar to what composers do. It is also worth comparing to the stratification articulated in the quantum mechanical twin-slit experiment:

Stratification is not arbitrary. Learning conversations are not Brownian motion. They are layered accretions of redundant patterns - like music. 

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