When something surprising happens - be it some kind of accident, a transformation, a joke - we can rationalise it and identify the causes for the surprise. Accidents are a classic example: we look for the 'factors' which caused the accident - learning about the causal factors like a slippery floor or a blind bend in the road, might avoid similar accidents in future. Nice surprises like a joke's punchline, or the climax in a play or in music, can also be analysed for the factors which produce them.
However many factors we identify, we cannot enumerate all the 'factors' or angles which lead to a surprise. I think that's another way of saying that there are many possible stories that might be told about it. In music, for example, there is the story about the harmony, melody, rhythm, dynamics, structure, tempo, and so on. In drama, there is the back story of the characters, the situations they find themselves in, the material environment, their possessions and artefacts (like a murder weapon) which they have access to, objects of their affection, and so on. This also applies to the classroom - which is the scene of a kind of drama. Each dimension viewed in its own terms will produce its own pattern of surprises - of course what "on its own terms" needs unpacking. The surprising event will occur at a point of coordination between many different factors, some of which we only become aware of after the event.
In discussion with one of my Phd students the other day, we talked about layers of clouds overlapping one another, where the surprise is the sun breaking through (in Manchester it is a surprise!). I like the metaphor, but it makes the business of identifying the different layers easy - the different stratification of clouds.
In drama, music or the classroom there are different descriptions, and the different descriptions have different structures. There are also layers of descriptions. In a Schenkerian analysis of a piece of music, for example, there are descriptions of a large-scale structure of 'prolongation' of a fundamental tonality; there is a description of key melodic features (and to some extent rhythm - although this is not Schenker's strong point), and there is a description of the surface with more of the detail exposed. The climax occurs at the point of coordination or overlap between the layers.
There is much less "information" or "uncertainty" conveyed at a deep level than at the surface level. The difference between the deep structure and the surface is an increase in constraint. The deep level points to clear moments of structural articulation which, even if one didn't accept the terms of the analysis, one would still be able to hear. The middle layer has less constraint, but exhibit some attenuation in stripping-out superfluous features. The foreground layer exhibits the least constraint and is closest to the actual music taken in totality, without any specific distinctions being made. The meaningfulness of the Schenker graph is a dynamic of oscillation between high and low constraint.
This brings me on to these diagrams by Gordon Pask in his research into teaching machines. These graphs demonstrate the different strategies different learners take in negotiating new concepts. The Y-axis of each is labelled according to the different variables A, B, C, D (which can be taken to be different concepts), and their different combinations. Single concepts (A, B, C, D) are at the top - these represent high constraint and relatively low information in terms of focus on individual concepts of the topic. At the bottom is the label ABCD (no commas) which represents the integration of the concepts A,B,C,D. This represents lower constraint and higher information: a master of a subject is able to produce a variety of interpretations, representations and performances of a subject.
But what of surprise here? I think the point here is that as one journey into concepts takes place, there is an interaction with another journey into concepts: There is a conversation. Surprises occur between people when one person does something that the other doesn't expect. The behaviour of the other person does not fit the model that is held by the person who is surprised.
Pask is interesting in his analysis because he codified the levels of description as degrees of complex interactions. He created a situation (and technology) where the combinations of specific concepts could be monitored - this is what we should be doing with learning analytics!
When we look at drama, is it possible to analyse the 'concepts' that each character has, and to consider the dynamics of the conversations they have with one another and see where they have to adjust their models of each other? When each character has to change their conceptual model, they have learnt something, and the result of the learning is to change the dynamics of the conversation. This is the moment of surprise.
In music, we "learn something" in the moment of climax, or some other event that surprises us. We can describe the rhythm, melody, dynamics, etc, and surprise will be some kind of "coming together" of different descriptions. What if each description is like Pask's A, B, C and D? In music though, we start at ABCD (at the bottom). At different moments, we focus on different 'concepts' or aspects. As the thing progresses, the aspects change, and indeed, what might be called "A" or "B" changes. What we learn at the moment of surprise is something about the composer, and maybe something about the performer.
The 'model' of music we create on listening is very much like the model we create of other people in conversation. What this is, fundamentally, is a kind of pattern of constraint relations which present a map of the relations between aspects which are highly focused (for example, the rhythm in Bolero), to the unconstrained totality, and can take us from the unconstrained totality back to details.
However many factors we identify, we cannot enumerate all the 'factors' or angles which lead to a surprise. I think that's another way of saying that there are many possible stories that might be told about it. In music, for example, there is the story about the harmony, melody, rhythm, dynamics, structure, tempo, and so on. In drama, there is the back story of the characters, the situations they find themselves in, the material environment, their possessions and artefacts (like a murder weapon) which they have access to, objects of their affection, and so on. This also applies to the classroom - which is the scene of a kind of drama. Each dimension viewed in its own terms will produce its own pattern of surprises - of course what "on its own terms" needs unpacking. The surprising event will occur at a point of coordination between many different factors, some of which we only become aware of after the event.
In discussion with one of my Phd students the other day, we talked about layers of clouds overlapping one another, where the surprise is the sun breaking through (in Manchester it is a surprise!). I like the metaphor, but it makes the business of identifying the different layers easy - the different stratification of clouds.
In drama, music or the classroom there are different descriptions, and the different descriptions have different structures. There are also layers of descriptions. In a Schenkerian analysis of a piece of music, for example, there are descriptions of a large-scale structure of 'prolongation' of a fundamental tonality; there is a description of key melodic features (and to some extent rhythm - although this is not Schenker's strong point), and there is a description of the surface with more of the detail exposed. The climax occurs at the point of coordination or overlap between the layers.
There is much less "information" or "uncertainty" conveyed at a deep level than at the surface level. The difference between the deep structure and the surface is an increase in constraint. The deep level points to clear moments of structural articulation which, even if one didn't accept the terms of the analysis, one would still be able to hear. The middle layer has less constraint, but exhibit some attenuation in stripping-out superfluous features. The foreground layer exhibits the least constraint and is closest to the actual music taken in totality, without any specific distinctions being made. The meaningfulness of the Schenker graph is a dynamic of oscillation between high and low constraint.
This brings me on to these diagrams by Gordon Pask in his research into teaching machines. These graphs demonstrate the different strategies different learners take in negotiating new concepts. The Y-axis of each is labelled according to the different variables A, B, C, D (which can be taken to be different concepts), and their different combinations. Single concepts (A, B, C, D) are at the top - these represent high constraint and relatively low information in terms of focus on individual concepts of the topic. At the bottom is the label ABCD (no commas) which represents the integration of the concepts A,B,C,D. This represents lower constraint and higher information: a master of a subject is able to produce a variety of interpretations, representations and performances of a subject.
But what of surprise here? I think the point here is that as one journey into concepts takes place, there is an interaction with another journey into concepts: There is a conversation. Surprises occur between people when one person does something that the other doesn't expect. The behaviour of the other person does not fit the model that is held by the person who is surprised.
Pask is interesting in his analysis because he codified the levels of description as degrees of complex interactions. He created a situation (and technology) where the combinations of specific concepts could be monitored - this is what we should be doing with learning analytics!
When we look at drama, is it possible to analyse the 'concepts' that each character has, and to consider the dynamics of the conversations they have with one another and see where they have to adjust their models of each other? When each character has to change their conceptual model, they have learnt something, and the result of the learning is to change the dynamics of the conversation. This is the moment of surprise.
In music, we "learn something" in the moment of climax, or some other event that surprises us. We can describe the rhythm, melody, dynamics, etc, and surprise will be some kind of "coming together" of different descriptions. What if each description is like Pask's A, B, C and D? In music though, we start at ABCD (at the bottom). At different moments, we focus on different 'concepts' or aspects. As the thing progresses, the aspects change, and indeed, what might be called "A" or "B" changes. What we learn at the moment of surprise is something about the composer, and maybe something about the performer.
The 'model' of music we create on listening is very much like the model we create of other people in conversation. What this is, fundamentally, is a kind of pattern of constraint relations which present a map of the relations between aspects which are highly focused (for example, the rhythm in Bolero), to the unconstrained totality, and can take us from the unconstrained totality back to details.
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