One of my favourite storylines in series 4 of The Wire followed the initially calamitous attempts of Prez, the recently disgraced cop turned high-school teacher, to get his maths classes learning anything (it’s tragic that in a drama about drug gangs I still find the bits set in a school the most interesting, but I can’t help myself). Prez’s breakthrough comes when he realises that the probability theories his students are failing to absorb in class are the same ones required for success in the sidewalk dice games that they often play after hours. He begins to present the problems in the context of the dice games, and sees their understanding take a leap forward. The implication (though from memory it is never explicitly stated in the series) is that once the students have executed the strategies in this relevant real-world context, they will also be able to demonstrate that understanding back on the paper and textbook tasks on which they were originally so stuck. This storyline is a great dramatisation of the problem of transfer, the ability to apply knowledge learned in one context into another.
As David Didau pointed out in an excellent recent blog post, transfer is pretty much the point of education itself. Despite this, learning can often remain defiantly, and surprisingly, context-specific. Didau recounts a number of studies which clearly demonstrate that the transfer of knowledge is actually much more complicated and less efficient than we expect it to be, including an example very similar to that fictionalised in The Wire, involving children working in Brazilian markets being able to demonstrate mathematical strategies on their stalls that they could not do in the classroom.
Although there is lots of excellent coverage (both academically and in blogs, e.g. here, here, here and here) on what the problem is and where it occurs, I realised that I hadn’t ever read much on why it occurs. I thought it might be interesting for those interested in these problems to provide some small insight into the neuroscience of transfer, to explain why it is about the way that the brain operates which means that transfer is so difficult to produce.
One of the reasons why we expect knowledge to transfer between contexts lies in our natural intuition that information in our brains is stored in a way that is fairly stable, so that it can be called up as often and whenever it is needed. Unfortunately this is an illusion. In actual fact, the development of our brains and the storage of information in them is hugely context-dependent, so that even in maturity we are still only ever dealing with ‘partial representations’; representations of the world which capture some, but not all of it. Partial representations are, by their very nature, completely context-dependent; that is they reflect of the features of the world (and of the brain) which were the case when the information was originally stored. What follows, taking the theory of ‘Neuroconstructivism’ by Mareschal et al (2007) as my guide, are four different levels on which the activity of the brain is constrained by the context in which it occurs, and why this context-dependence is relevant to the transfer problem.
- Neural context – ‘encellment’
The cellular neighbours of a neuron exert a large influence over its eventual function as a processor of information. The characteristics of its response and the way in which it connects and influences other neurons is in turn dependent on the type and amount of activity that the neuron itself receives. On a simple level this can be demonstrated by the foundational principle of neuroscience, paraphrasing Donald Hebb, that “cells that wire together fire together”. The more that cells communicate with each other, the more that their connections are strengthened, and the greater influence that a preceding cell exerts over the activity of subsequent cell. However, the context-dependence of neural activity is not limited to the simple co-operative strengthening of connections. They can also compete. Many areas of the brain show competition between different neurons within the same region. Competition between cells is thought to be crucial to creating specialisation (such as cells which respond only to particular orientations in visual cortex), but it can also have more drastic effects. A famous example comes from Hubel and Wiesel’s Nobel Prize-winning work on the cat visual cortex. They found that newborn cats who had one eye occluded for a time (and then reopened) showed reduced space dedicated to processing information from the occluded eye and increased space processing that from the uncovered eye. As other structures earlier in the visual system still functioned normally after the re-opening (e.g. retinal ganglion cells and the lateral geniculate nucleus – the relay station to the visual cortex), the conclusion was that these changes were the result of activity-based competition between neurons; with the diminished input from the eye at a competitive disadvantage to input from other sources. This disadvantage eventually leads to visual processing being outcompeted, and other functions expanding to occupy the territory.
What does this mean for transfer?
How any neuron responds to an input is constrained by a number of different factors: the ever-changing strengths of connections to potentially thousands of other inputs (both excitatory and inhibitory), competition (or co-operation) between neighbouring cells, or a progressive specialisation of the cell’s function. This means that a signal from a neuron can only be interpreted as representing that cell’s response to a particular set of circumstances at that specific time; the neural context, if you will.
Another consequence of the reliance of each neuron’s activity on so many of its neighbours is that this means that any information that is encoded by the neuron is likely to be done so in a distributed fashion, across large groups of neurons. Such ‘distributed representations’, whilst more robust on the face of damage and brain changes, are also far more likely to be ‘partial representations’, relying as they do on numerous small contributions from different neural sources. They will never capture a concept or an idea in its entirety. Instead, they record a blurred snapshot of some of the key details approximating the concept, a partial representation.
2. Network context – ‘embrainment’
Just as individual neurons can be affected by the context in which they find themselves, so entire brain areas can co-operate, compete and change function as a result of their context within the brain as a whole. On a larger scale than that noticed by Hubel and Wiesel, Cohen et al (1997) found that in people who have been blind from an early age, visual cortex begins to take over other functions entirely, such as touch when reading braille. Similarly, if you re-route visual information into a ferret auditory cortex, the area will begin to respond to different orientation patterns from the visual scene outside (Sur and Leamey, 2001), as normally happens in visual cortex. In less drastic fashion, maturation in the brain involves the progressive specialisation of many different brain areas, which gradually take over sole control of functions which initially call upon wider networks of regions. Again this process can be categorised by competition, with one area gradually coming to exert a dominant influence over a particular kind of processing. Good examples of these sorts of processes have been found in the pre-frontal cortex (PFC) during adolescence, such as the inferior frontal gyrus for response inhibition or the rostrolateral PFC for relational reasoning (see Dumontheil, 2016 for a review of these and others).
What does this mean for transfer?
Most formal education is taking place during periods of rapid brain development and maturation. Brain areas are progressively specialising and refining their functions, dependent on their relationship to other brain areas and input from the outside world. In this context, the distributed and partial representations that we build of the world are likely to be highly context-dependent, not only on the particular pattern of inputs, but also on the time and stage of development in which the information was learned.
3. Bodily context – ‘embodiment’
The brain does not sit in glorious isolation from the rest of the body. Some hard-wired nervous behaviours, such as reflexes, can in fact form the basis for the beginnings of brain development. Infants make spontaneous reaching movements from an early age and even new-born infants will move their limbs to block a light beam (Van der Meer et al, 1995). These kinds of behaviour initiate the beginnings of feedback mechanisms between the visual and motor areas of the brain and eventually allow for the development of complex visually-guided behaviour. Of equal importance, the design of some parts of the body can constrain brain development by ensuring that it does not need to develop certain skills; cricket ears are designed to respond preferentially to male phonotaxis (a sound made by rubbing one wing against the other). The cricket brain has no such specialisation for making this distinction, because the job has already been done (Thelen et al., 1996). In human cognition, examples of ‘embodiment’ might include state-dependent memory; the finding that we recall information more successfully in a similar ‘state’ to when we learned it, for example after exercise (Miles and Hardman, 1984) or even when drunk (Goodwin et al., 1969).
What does this mean for transfer?
The development of our brains is constrained and uniquely differentiated by our nervous systems and by the body in which we find ourselves. Again, this is not just the case between individuals but also within individuals as they develop over time, and as they pass through the myriad different internal states which characterise our existence. The representations that we have of the world will reflect these changing embodiments, and will be ‘partial representations’ in that they are formed, and linked to, this embodied context. This therefore provides further scope for learning to be constrained by the situation (in the widest possible sense) in which the information was initially encountered. The Goodwin et al. paper is particularly relevant here, as it tested two outcomes; recognition and transfer. They found that, whilst recognition memory was not significantly affected by the a change in states between learning and recall, the ability to transfer the information was. Transfer, as a more complicated cognitive procedure than simple recall, is as a result even more susceptible to being restricted by the context in which it occurs.
4. Social context – ‘ensocialment’
The concept of ensocialment, the idea that the social context for any act of learning is crucial to shaping the learning that takes place, will be the most familiar of these four levels of analysis to educators. Vygotsky’s social constructivist theories are probably the most famous educational application of this sort of idea. People learn from others with more skills than them; with the more knowledgeable mentors using language and guidance to ‘scaffold’ the learner’s interactions with the world in the most productive manner. The concept of scaffolding; a supportive structure which is gradually removed as the learner gains in ability, is used to one degree or another by almost every major educational approach.
What does this mean for transfer?
The type of scaffolding that is used may become inextricably linked to the solution that is produced, to the point where the ‘partial representation’ that we have of the solution is not accessed when the problem is framed differently. Think of Prez’s dice-rollers on the street corner or the Brazilian market-children, still struggling when trying to solve the same problems back in the classroom.
It might be a problem… but it shouldn’t be a surprise
It seems eminently sensible that if we know how to do something, we should be able to reproduce that skill regardless of the changing context. No doubt it seemed obvious to the writers of The Wire that the dice-rolling students would be able to solve the probability exam questions in their next test. What I have tried to show here is that actually there is good reason for suspecting that this natural intuition is flawed. Context-specificity is built into even the most basic levels of our brain function, and it operates right through from the cellular level to the societal. It is therefore hardly surprising that we also see it occurring at the higher levels of cognition focused on by education, given that it occurs pretty much everywhere else. Even the most seemingly simplistic acts such as learning a sequence of movements does not transfer into improved learning of a sequence of the same movements in a different order (Karni et al., 1995), so the idea that we might be able to teach a problem solving technique in Geography and expect it to be used in Biology suddenly looks very optimistic indeed. Even strategies normally taken to be clearly domain general, such as some kinds of study skills, may actually be quite context-dependent (although there is evidence that some other skills, such as metacognition, may improve performance across domains). In fact the potential scale of this problem is something that I think many in education are simply in denial of, as to consider just how ‘partial’ are our representations of the world can seem to be the first step on a slippery slope into educational nihilism.
What the transfer problem means for education
Not that I think such pessimism is justified. None of this is to say that transfer is not possible or does not happen. Barnett and Ceci (2002) provide examples of how transfer can be made more likely. Indeed, as Didau points out, if the conditions are right then transfer could indeed become the norm. This would be especially true if we focus on problems of ‘near’ transfer with more modest goals, such as transferring strategies between different exam questions, or different classrooms etc. I agree with Didau’s prescription that explicit teaching of knowledge plus practice in applying the knowledge to different contexts is the approach most likely to bear fruit in educational terms. From the perspective of ‘partial representations’ this strategy is likely to lead to multiple, overlapping partial representations which are strengthened through repeated access, increasing the likelihood of them being more easily accessed subsequently. To take a contrasting educational perspective, such as discovery learning, this would only lead to the (time-consuming) creation of a single partial representation, which would be far more susceptible to context-dependency. From this perspective, it is not the discovery of the strategy which is important for subsequent success, but the practice of accessing the strategy multiple times and in multiple different ways. Perhaps ironically, then, the theory of neuroconstructivism can shine a light on why many ‘constructivist’ approaches in education fail. Constructivist learning theories tend to emphasise the importance of the construction of knowledge and the placement of knowledge into a concrete context from the very start. However, this prioritises the discovery of the strategy in a single context over the practice of a strategy in multiple contexts. It argues for the formation of a single representation over multiple representations. What I have tried to show above is that our representations of the world, by their very nature, are only ever ‘partial’ representations. Given that, it makes sense for educators to work to create as many of them, and to strengthen them, wherever possible.
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