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A moment of realisation occurred when I first read Dan Willingham’s 2002 article in American Educator on the topic of inflexible knowledge. Willingham presented the useful distinction between surface structure and deep structure. As with all models, it is probably something of an oversimplification but, as with all good models, it offers explanatory power and in this case, practical implications for teaching.
Willingham contends that initial learning tends to become locked to the surface structure of a domain and this contention is supported by considerable experimental evidence. For instance, Willingham describes how a strategy for solving the problem of defeating an evil dictator who is holed-up in a fortress is structurally identical to a strategy for solving the problem of giving a brain tumour the correct dose of radiation. However, subjects who had successfully solved one of the problems generally failed to apply the same strategy to the other one.
We may have a bias for attending to surface structure. After all, deep structure is a layer of abstraction. Such a bias may account for the stories people tell about how they were only ever taught procedures in maths or names and dates in history when at school. Once we are aware of this as teachers, we can build programmes that carefully cycle students through surface structure and deep structure, perhaps by presenting different examples that have the same deep structure and drawing attention to this.
However, there is a danger in this discussion that we start to see surface structure as bad and deep structure as good or, alternatively, that we see surface structure as straightforward and deep structure as more complex or profound.
Deep structure often encompasses a simple principle or set of principles that it would be quite straightforward to memorise and reproduce. For instance, the principle of the conservation of momentum in physics can be stated as something like, “The total momentum before any collision or explosion is always equal to the total momentum afterwards.” Stick that on a knowledge organiser and pretty soon kids will be able to repeat it back to you. The sophistication is in recognising when this principle applies and then applying this principle to different examples with different surface structure. And this surface structure can become really complicated. That’s why it is effective to use worked examples to minimise cognitive load when first trying to apply such principles.
So expert performance requires expert manipulation of both deep structure and surface structure, rather than one or the other.
This is similar to the issues that arise from the dichotomy between conceptual and procedural knowledge in mathematics. In many ways, we can consider conceptual knowledge to map onto deep structure and procedural knowledge to surface structure. It is certainly a good thing if a student can give some accurate definition of what the equals sign in an equation represents (i.e. that the two sides have the same value rather than ‘write your answer here’), but if the student cannot actually make use of this to solve 4 + 7 = ? +2, either because they do not recognise that it applies or because they lack the ability to apply it, then it has little value on its own.
Mathematics also gives us an example where the ideas of deep structure and surface structure perhaps become iterative. Once internalised, the principle of equivalence as embodied by the equals sign is central to all algebra. Yet different algebraic worked examples could in turn represent the surface structure of some other deep structure such as the fact that circular functions are periodic.
The distinction between surface and deep structure can also be applied to educational concepts. Consider Response to Intervention, for instance. This was developed as a means to systematically address literacy and numeracy difficulties, but it has spread to other domains such as behaviour management – School-Wide Positive Behaviour Support (SWPBS) is a Response to Intervention model that applies to social, emotional and behavioural development.
The deep structure of Response to Intervention consists of three tiers. The first tier applies to all students and manifests as high quality explicit teaching coupled with systematic screening. The second tier represents targeted interventions aimed at those who have not made sufficient progress as identified through screening. The third tier involves intensive, individualised intervention for those who make insufficient progress in tier 2. If you are unfamiliar with Response to Intervention then your first question is likely to be, “Can you give me an example of exactly what this looks like?” In other words, to increase your understanding, you would request a description of some surface structure. Without these worked examples, the concept remains in the abstract and far less useful.
I have started to wonder whether we have a problem in education with pseudo-deep structure. I am going to define this as abstract principles and ideas that are uncoupled from surface structure. The utility of pseudo-deep structure is that it allows a person to adopt the abstract language of the expert without having to test these ideas against messy reality. The concepts of ‘rich tasks’ and ‘deep learning’ seem like good candidates to me. I admit that there may be people out there who can clearly define each of these terms and link them to specific, concrete examples, but this has not been my experience.
Once we view pseudo-deep structure in this way, it implies an approach to identify and battle it. The next time someone presents some principle that raises your suspicions, you may ask, “Can you give me an example of exactly what that looks like, please?”