Tom Sherrington wrote an interesting blog in which he expressed his frustration about people criticising the model of learning he uses – specifically the concept of schema – on the grounds that ‘there is more to learning than that’ or that it ‘reduces learning to memorisation’. He wrote that he was annoyed that people criticise the model without offering an alternative.
Various definitions of the concept of schema have been given over the years, but there are some common elements to the notion that seems popular at the moment: A schema is a mental structure that is involved in organising knowledge. Sherrington uses this diagram (by Oliver Caviglioli) to explain his version of the model and schema:
Firstly, I shall outline four criticisms of this model that an alternative would need to overcome, and then I shall provide an outline of an alternative view. I will say at the outset, that I have a great deal of respect for Tom Sherrington’s work, and I in no way intend to disparage it. Nor do I think that his own approach to teaching is necessarily guilty of these criticisms. The criticisms that I raise here are perhaps more generally aimed at some of the assumptions prevalent in cognitive science. And I’m definitely not against the use of models to help teachers understand, prepare and plan for teaching. My concerns are that when such a view, with its figurative language, becomes embedded in our discussions of education, what follows from it might be quite unpleasant. However, I think that the concept of Schema is an important one that could easily be maintained with some slight adjustment.
Four problems with the model adopted by Sherrington
1. The concept of a ‘mental structure’ is nonsensical
The conception of a schema that Sherrington has adopted conceives of a causal relationship between a mental entity (such as the schema) and the physical world. As Peter Hacker has argued, this doesn’t make any sense. If we are to hypothesise a causal relationship between two entities, we should be able to establish correlations between such a mental structure and the physical world, but this presupposes that we are able to correctly identify the mental structure. However, any criterion of correctness for identifying a mental structure would have to be public, but mental structures (thus conceived) are metaphysically private – that is, no one is privy to your mental structures but you. Therefore, here we can’t talk about a correct use or an incorrect use – whatever you think is right is right. Thinking that this is a best hypothesis is no more sensible. A ‘mental structure’ cannot be hypothesised in the same was as ‘water on Mars’ can be, since there can be no way in which we could establish its existence.
As a result, what looks like an explanation of how the cognitive system functions is merely a redescription of the problem – it is tantamount to saying, ‘the student hears stuff, then some magic happens, and then they remember it’. (I know that Sherrington fleshes out the model with techniques and theories that do not solely rely on such mental entities – so I am not attributing this view to him!)
2. Human beings have ‘two-way’ powers of communication
According to this article, trees communicate with each other via ‘underground fungal networks’; they support each other and help each other grow by sending chemical and electrical signals to each other. Whilst there’s something wonderful about the idea of envisaging trees in this way, it is quite clear that the sense in which trees talk to each other is quite different to the sense in which humans talk to each other. The tree is not sending signals intentionally. It would not make sense for me to berate a tree for not having warned me of the change of seasons. (Although Jesus did weirdly have a go at a tree for not bearing fruit – but that’s a topic for another post.) The tree, or rather the leaf has no choice but to change colour. Peter Hacker calls this a one-way power. If the conditions are right for the leaf to turn brown, it will turn brown. There is no such thing as a leaf refraining from turning brown. My wife, on the other hand, has a two-way power to send me a signal – she has a choice. And because she has a choice, it makes sense to say that she acts intentionally, voluntarily.
If the causal relationship described by the model were correct, the powers of cognition would be one-way powers. That is, if the conditions were right, we would have no choice but to think and respond in the way in which a perfect model predicts. The mind is reduced to a passive receptacle. What is interesting is that Sherrington’s discussions of Generative Learning, other methods and the way in which he talks about education generally don’t suggest that he conceives of the mind like this, but I worry about what some may believe follows from a conception of a mind with only one-way powers – namely, that education is reduced to the transmission of information.
The power to communicate is essentially, necessarily a two-way power: Communication is concerned with meaning and to be able to mean something with our utterances or behaviour is to have a two-way power. To mean something is to intend to convey something, to do so voluntarily. If we don’t have the ability to not utter something or behave in a particular way (i.e. if we only have a one-way power) then we cannot mean anything with what we do. (This confusion is knotty, however. We can even see this one/two-way power distinction with the verb mean: compare ‘the heavy blizzard meant there would be no school’ with ‘I didn’t mean to upset you’. The former sense merely means to have as a consequence, whereas the latter sense means to intend to convey. My harsh words might mean that he left, but that doesn’t mean that I meant to make him to leave.)
In a great deal of education research, we see the power to communicate reduced to a one-way power. John and Susan Sweller, for example, argue that Human Cognition is a Natural Information Processing System. They compare the human mind with evolution. Evolution (as conceived by Sweller et al.) will only possess one-way powers. Evolution cannot intend to do anything, and as a result it makes no sense to blame, be angry with or punish evolution (except perhaps poetically). As a result, concepts like communication, language, information and knowledge, come to mean something quite different to what we refer to in ordinary language. All the meaningis removed from their account and replaced with mere consequences. (It is not difficult to see how this might have grave consequences for how we conceive of education.)
3. We do not have a clear view of the nature of the ‘inputs’ for this mental structure
Any alternative conception of a schema would also have to avoid the problems concerned with what might constitute an inputinto this information processing system. Like Sweller’s conception, Sherrington’s model conceives of information or data going ‘into’ the mind. But what is this data? Although we might now imagine a series of 1s and 0s or statistical data, that doesn’t really clear anything up. Without the sense of intention, we still have no means of distinguishing between data/information and mere noise.
In his paper, A Mathematical Theory of Communication, Claude Shannon came up with an ingenious distinction between noise an information in terms of how likely the signal was to occur, so the amount of information contained within a signal is inversely proportional to the probability that it occurred. The less likely it was to occur, the more information it contained. Mathematically, he expressed this as I(x)=-log2p(x), where x is a discrete random variable, and I(x) is the amount of information contained in x and p(x) is the probability of x occurring. Shannon’s sense of information became ubiquitous with the rise of computers, and is clearly the ancestor of the sense of information that Sweller et al have in mind (although I’ve never seen them say anything like, ‘the amount of -log2p(x) in the long-term memory’, so I am still unsure as to whether even this clarification would make their view coherent).
It’s fairly obvious that Shannon’s definition of information bears little relation to the everyday concept that we are referring to when we say, ‘all the information that you need is on the sheet’, for example. Shannon had set out to find a way to solve engineering problems involving communication over a noisy channel. He did not set out to deal with questions of meaning or interpretation, which his theory, in his words, ‘can’t and wasn’t intended to address’. The power to transmit or receive Shannon-information is always a one-way power; the power to communicate or receive information (in an ordinary sense) can be a two-way power – it can be done so with intention and meaning. The Logico-Linguistic model avoids this problem because it does not posit the existence of any kind of system.
4. The role of emotions
A final problem for the usual cognitive psychological model of a schema is that it has no place for the emotions. If the human being is conceived of as a natural information processing system, then emotional responses merely become another form of processing, perhaps even a glitch in the system. But emotions play a central role in learning, and in human nature more generally. There is a critical failure in cognitive psychology to recognise the distinction between explanations for action in terms of reasons, hopes, purposes, desires, and explanations in terms of a very narrow view of causation. Reasons, purposes, desires, and meaning are the hallmarks of our humanity and our dignity. They must be returned to their rightful place in our schemas of explanation.
An alternative conception of a schema: a Logico-Linguistic view
(The following conception of schema is built upon the philosophy of Wittgenstein and particularly influenced by the interpretation of his work by Danièlle Moyal-Sharrock.)
The origin and the primitive form of the language game is a reaction; only from this can more complicated forms develop.(Wittgenstein, Culture and Value p. 31)
Language – I want to say – is a refinement. “In the beginning was the deed.”
There is a tendency to think that the basic form of an utterance is a declarative sentence, a description. However, children don’t tend to utter declarative sentences until they’re about 3 years old. All things being well, when we are first born, we don’t describe our surroundings, we cry – we exclaim. There is a sense in which human communication is inherently emotional. Whilst the initial cries of a baby are instinctive, through interaction with caregivers, they soon become purposeful and seemingly laden with preferences and evaluations.
As we grow, we develop new abilities, e.g. the ability to follow an object with our eyes; grasp at an object; move it around in our hands. Each new ability provides the baby with a new way of ordering their experience. E.g. when we follow an object, it is distinguishable from its surroundings; there are things which move and things which don’t etc… It is useful to think of these abilities as organising tools. (The root of many words relating to knowledge [ascertain, certain, concern, criterion, discern, discriminate] have their root in the Proto-Indo-European *krei, meaning sieve. To be able to do something new (e.g. shake an object) is to have a new criterion, a new sieve which we can apply to our experiences – i.e. these objects make a noise when we shake them, these don’t.)
Eventually, toddlers learn to play games using those abilities – that is, they learn to use these abilities to follow rules. Language is an extension of these rule-bound techniques. Since language is rule-bound, conventional there is simply no need to posit the existence of a new ‘mental’ structure that organises knowledge, since linguistically expressed knowledge already is structured. When we successfully communicate with someone else it is because, for the duration of that interaction, we are following a shared set of rules. The rule-bound nature of communication is captured in Wittgenstein’s description of these interactions as language-games.
The logico-linguistic rules and conventions constitute and explain the structure of knowledge. As we learn to speak, we learn new kinds of tools: words and concepts. To understand a word or concept is to have mastered its various rule-governed uses: the various ‘language-games’ of which the concept forms a part. We demonstrate our knowledge when we use the concept correctly, can correct other’s use of it, and can explain what the concept means. What is important, for our purposes is that we tend not to master concepts immediately, but instead gradually build up mastery of its various rule-bound uses. Thus, we can conceive of a schema as the collection of rule-bound techniques that we have mastered.
Neither is there any need to posit the existence of a ‘short’ or ‘long-term’ memory as mental entities. There are some rule-bound techniques which we have practiced sufficiently such that they have become habitual and automatic. (We may now be tempted to ask where this collection of rule-bound techniques is located but that is obviously a nonsensical question – as if someone who has been asked, ‘where did you learn Spanish?’ were to reply, ‘in my head’.)
This whole process is essentially emotional. The baby’s cry is emotional, and the development of new abilities is driven and motivated by desires and interactions with other people, until eventually we learn to replace that cry with ‘I’m hungry’, or ‘I’m upset about the incompetence of the current government in dealing with both Brexit and the Coronavirus pandemic.’
The Logico-Linguistic model enables us to get a much clearer view of the nature of logic – in terms of games – and the multiplicity and messiness of ideas, without becoming over-complicated. We can still ask, what are the tools (concepts) that I want the children to learn? What are the rules for the uses of those concepts? How will they be able to practice using those tools?
(There are many aspects of this upon which I could expand – but I’ve tried to keep it as short as possible give that this blog post is already very long!)
The effects of this version of the model may not be much different for teachers, but it avoids the many pitfalls of the conventional version. I’m no Oliver Caviglioli, but I’ve attempted to make a little diagram of it using a bit of word art:
 P. M. S. Hacker, ‘The Relevance of Wittgenstein’s Philosophy to the Psychogical Sciences’, in Proceedings of the Leipzig Conference on Wittgenstein and Science, 2007, pp. 1–23.
 P. M. S. Hacker, Human Nature: The Categorical Framework (Oxford: Wiley-Blackwell, 2010). p.95
 One could argue that I am indulging in a mereological confusion here – the leaf may have no choice to turn brown, just as my finger may have no choice to extend, but perhaps the tree has a choice as to whether it sends me a signal, just as I have a choice as to whether I point. All that this shows, however, is that the prototype of sending a signal is human and intentional, and that it has at some point been applied to trees metaphorically.
 C. E. Shannon, ‘A Mathematical Theory of Communication’, Bell System Technical Journal, 27.4 (1948), 623–56 <https://doi.org/10.1002/j.1538-7305.1948.tb00917.x>. See also M. R. Bennett and P. M. S. Hacker, ‘On Explaining and Understanding Cognitive Behaviour’, Australian Journal of Psychology, 67.4 (2015), 241–50 <https://doi.org/10.1111/ajpy.12080>.