It could be unsettling for a teacher to be unsure of the nature of knowledge, yet questions relating to the concept appear frequently on Twitter. Here, using David Didau’s proposition: ‘Knowledge is what we think with and about’ as my starting point, I hope to provide some clarity on the issues and put forward a conception of knowledge that I believe could make a contribution to the philosophy of psychology, and thus to cognitive science.
Addendum (20/07/2017): To be clear, this is not a critique of Didau’s post, nor an attempt to undermine it. On the whole I agree with the above proposition. The aim of this post is to attempt to expand upon it by answering the questions: where do we go from here? how should a teacher make use of this proposition?
I shall take David Didau’s proposition as the trunk of this essay, and in the spirit of a philosopher-gardener, I shall attempt to prune three branches that I think unhealthy, and tend to a fourth which I believe will yield more fruit.
My question is this: what can ‘knowledge is what we think with and about’ actually mean, and how can we teachers make use of it?
1. A propositionalist conception: Knowledge as propositions
One difficulty with Didau’s statement is that one could argue that I might think with and about my brain but my brain is not synonymous with knowledge, i.e. my brain is not knowledge, it is my brain. Whilst this may appear to be mere sophistry, it does raise an important point about distinctions between objects in the world, and facts about the world. One possible move at this point would be to refine Didau’s original proposition thus:
- Knowledge is the collection of propositions which we think with and about.
Such a view is manifest in education in the form of the now-popular knowledge organisers. These are straight-forward collections of the propositions which the teacher would like the students to remember, so that they can think with and about them. The problem we now have, however, (as Chrysippus first pointed out in the third century BC) is that there is a distinction between the words that make up a proposition, and its meaning. A student could diligently learn to recite a proposition without having the first clue what it meant.
One option is to create yet more propositions that enumerate the connections between propositions. This is certainly reasonable in many situations, but not in all. If we were to apply this to all situations it appears to reduce all knowledge to the merely explicit, and clearly not all knowledge is explicit. It may be implicit, awaiting someone to make it explicit, or it may simply be inexpressible. Take the following example, I once taught a student who could count perfectly well, though it was fair to say she had no real idea what the numbers meant. Whilst she was learning her times-tables I had to explicitly tell her the answer to each question (NB: this was in an unusual educational setting). I could say to her: 2×2=4, 2×3=6, 2×4=8… but she had no idea how to go on; she did not know the rules. Wittgenstein described such rules appearing to lay in front of us like train tracks. —So then can we not just teach her the rules? With this student, no! I was unable to find any expression of the rules that she could understand. (An expression of a rule is no more a rule, than the words ‘my brain’ are my brain.) As Wittgenstein points out, this train-track analogy is misleading precisely because the rules do not exist without the content and context in which they are embedded – rules are embedded in practices. Not noticing this will lead one down a logical positivist path…
2. A logical positivist conception: knowledge as the capability to perform
Last week on Twitter, I had an exchange with @crispinweston who was putting forward a logical positivist stance. His argument was that, in practical terms, we can only meaningfully define knowledge in terms of the way in which it is demonstrated, i.e. the capability to perform. @ChrisMWParsons then suggested that were Stephen Hawking no longer able to communicate, we could still meaningfully say that he knew things. @crispinweston rejected this saying that without demonstration, no one could meaningfully say that ‘Stephen knows X’. I responded to this by saying that by the same token, if there were no way of demonstrating it, neither could anyone meaningfully say that ‘Stephen loves…’
According to the logical positivist approach, all meaningful statements must be verifiable, and all ordinary sentences are reducible to an ideal logical expression. Thus, a logical positivist would respond to my argument by saying that what I really meant was that ‘were he able to demonstrate knowledge/love, he would’. I outright reject this approach, and the assumption that all utterances can be reduced to unifying logical rules for the following reasons:
- Different domains have different rules – compare the rules governing the writing of a police report with those of writing poetry.
- No two phrases are entirely synonymous in terms of their meaning; to treat them as such is to lose much of what is important. If we ‘translate’ the utterances of a toddler into this ideal language, we will lose all the cuteness. This cuteness is part of the meaning of the sentence. In more extreme cases, such a belief in ideal logical rules is simplistic to the point of parody: If my wife lay dying, unable to speak and I said, ‘I know loves me’, I would not be too impressed if someone were to say, ‘no, what you mean is that if she could demonstrate her love for you she would.’
- The manner in which a logical positivist appears to require verification or falsification is very limited, and results in us believing that we cannot know something without an explicit test. There does, however, exist imponderable knowledge, which we may be unable to make explicit. We can tell whether someone is annoyed with us without necessarily being able to pin down why. Of course, I accept that in most cases this imponderable knowledge may be made ponderable, – it may be pointed out to me that the other person’s lips were curled when they spoke to me – but in such a situation I recognise the truth of this description after the fact, but may not be able to say before that ‘if their lips curl when they talk to me, then I will know that they are annoyed with me’.
There are various purposes of measuring things in schools, but often, it comes down to holding people accountable: the teachers, the students. Another way of looking at it is to try to get people to be better, to improve: to achieve an A* or an ‘outstanding’. But this presupposes that one knows what ‘improvement’ looks like. (If we know what improvement looks like, then surely we need to simply tell people what to do and then get them to do it.) However, the level of complication expands with the number of possible answers that could be judged passable. If the question was merely ‘2+2=?’ Then we can clearly state that 4 is a better answer than anything else. With, for example, an essay, there are more possible answers than there are people who answer it, multiplied by the number of occasions on which each person answers it. This level of complication then tempts people into creating generalised algorithms for marking and levels, but as one realises the poverty of one’s first attempt, such a positivist approach will soon get out of hand as one develops more and more strands to one’s algorithms; strands that flit in and out of the core levels in ever more complicated arrangements. These strands are often what are referred to as ‘skills’ but these are at best heuristics, rules of thumb. There is nothing wrong with heuristics, and I am very much in favour of them. They are tools that can be taught and that can be very helpful, but to view them as being mechanical elements of a working mind is probably fallacious. All this was summed up very neatly by Dylan Wiliam: ‘the more neatly we specify what we want, the more likely we are to get it, but the less likely it is to mean anything.’ Humanity is present in the subtle inflexions of life, not dull-footed scientism.
3. An idealist conception: knowledge as that about which one thinks
A further route open is to treat David Didau’s proposition as an expression of idealism (similar in ways to George Berkeley’s Master Argument). If this were the case, which I don’t think it is, then Didau would simply be arguing that ‘we cannot think about that which we do not know’. Again, I have a great deal of sympathy with this interpretation; the problem with this is that it gets us nowhere: every object of thought becomes knowledge and we are offered no means of connecting it to the world outside our minds. If we cannot connect it to the world outside our own minds, this is not that useful for teachers: a. the minds of the children appear to be entirely hidden from the teacher, and so we are again unable to know what they know, and b. we have no way of distinguishing between a truth and a falsehood and thus we will end up in a post-modern mess.
4. A nomological conception: knowledge as expectations embedded in ‘cases’
I propose that we can make most sense of Didau’s proposition, if we see it through, what I shall call a nomological conception of knowledge in education.
NB: I am not legislating for language here! I am simply offering a way of looking at ‘knowledge’ within the context of education that avoids the difficulties above. I fully accept and understand that the word ‘know’ can be used in a huge variety of different senses!
If we accept that there is a. a difference between the words that constitute a sentence (declarative knowledge) and its meaning, and b. that a sentence might have different meanings in different contexts, then the difficult task is to achieve some clarity regarding the meaning of a sentence as opposed to merely the words. Wittgenstein described the meaning of a sentence (in most cases) as its use. This seems appropriate for any item that may find its way into a knowledge-organiser: We do not simply want the students to be able to repeat that ‘the battle of Hastings occurred in 1066’, we also want them to understand how this sentence might be used. It might be used (to employ a silly example) to explain why Harold did not use guns. These possible uses are defined and limited by rules.
In order to clarify the kinds of rules with which we are concerned, I shall employ Hayek’s distinction between two different conceptions of Law, nomos and thesis: Thesis are rules that have been intentionally invented by people, whereas nomos are rules that are simply recognised as the way things are. Consider the rules of English grammar, they have not been decided by anyone, they have simply survived. Of course, they evolve and change, and of course, retrospectively we might be able to assign a reason or purpose to their being as they are, but no single individual can cause this to happen. Hayek called this way of looking at things evolutionary rationalism. It is rules in the sense of nomos and not thesis with which I am concerned here. (Hence the name nomological.)
My expansion on this is the following: the rule that a particular person is following in their use of a sentence can be described as that person’s expectations concerning that sentence -what does the person expect to occur as a result of using the sentence? I am using expectation in a particular way here:
- By expectation, I mean ‘that which is conceived as following from…’ There would appear to be some form of continuum with regards expectation that has great relevance for cognitive psychology and teaching:
- There is that which one would, without thinking, expect to follow.
- There is that which one would expect to follow, once certain facts have been brought to mind – these other facts acting as heuristics or rules of thumb.
- There is that which one would not find inconceivable, but nonetheless unexpected.
- There is that which one would find inconceivable, impossible to see how it might follow
… and many other levels in between.
- I would also distinguish between an expectation in the sense I am using it, and a belief. An expectation is seen, or embedded in the aspect of a thing that one observes. One has no choice about what one expects in this sense: I see a vase wobbling precariously on the edge of a table – I have the expectation that it will fall. (As opposed to ‘having high expectations of the class’ which I would often class as ‘belief’ in this context. See note )
- Obviously, one’s expectations can develop and change:
- I may have an expectation that I will not burn in the sun, but experience will prove me wrong. I do not mean that we need to directly experience something to develop and refine our expectations: someone who has been blind from birth might still be surprised if someone told her that the sky was green.
- A child may learn to recall, ‘the battle of Hastings occurred in 1066’ but initially have no expectations regarding it, or she may have the wrong expectations regarding it – these can then be taught and refined.
What we desire is that our expectations (the rules that we follow) and those of the students accord with what is actually the case – with nomos and not with legislation or thesis.
—How then, do we establish what is in accordance with nomos (what is an accurate expectation) and what is not? Again, I think that a most fruitful analogy is to be made with how judgements are made in law, specifically common law. In common law, the court looks to past decisions, establishes analogy with the current facts (or shows that no analogy is relevant) and synthesises and applies the past decisions. Clearly, the more cases that a lawyer knows, the better they will be able to do their job. In education, we do much the same: our past cases are the declarative knowledge that we wish the students to learn, and the judgements are the expectations embedded within those cases and examples. These cases of declarative knowledge do not say the rules (since an expression of a rule is not a rule) but the rules are shown in them; they are exemplified in them. To educate a child, therefore, is to refine their expectations through the apprenticeship with cases.
Note how, I have not stated this in terms of a purpose of education. This would be nonsensical – one could never reach a stage where one had accurate expectations about everything! Thus, this process of refinement, and education generally, has an inherently negative character. Nomos does not so much tell us what to do but rather what is wrong. This seems to me to reflect well our psychological approach to education:
In the eyes of those lovers of perfection, a work is never finished — a word that for them has no sense — but abandoned;
Hence, there can be no ‘rubric’ to follow to achieve one’s aims, since one’s aims cannot be described, and hence it would be perfectly reasonable for exams to contain unpredictable questions (see this by Michael Fordham): an exam board would merely outline the cases to be learnt, and the student, would then try to apply them to any question that might be asked. The key would be in enabling the student to properly pay attention (in the sense described by Simone Weil) to the cases being given. Imagine a student trying to complete a tessellation of some complicated shape but not realising that they could rotate the piece. To pay attention to a case is to rotate it in one’s mind, to imagine it from various angles, and in different contexts and to simply get to know it – not change it, or force it where it won’t go. (One can see a parallel here with Diderot’s Memory, Reason and Imagination delineation of knowledge, brought to my attention by Tomas White. Instead we have cases, expectations, and attention)
5. Implications for teaching
Firstly, the implications of this nomological conception for cognitive load theory, I would imagine, are obvious: those expectations that strike us most strongly as in (1) are automatic, whereas (3) requires some explanation. Secondly, one can also relate this to Hebbian learning and the way associations are brought about. However, given the frequently negative nature of expectations – i.e. one might not have an expectation about what will happen, but only what will not happen – then it is not simply a matter of mere association. Thirdly, there is also the obvious implication for marking and improvement – away from rubrics, and more towards the comparative methods championed by Daisy Christodolou. Fourthly, the tackling of misconceptions can also be seen, I would argue more fruitfully, in the light of expectations. And finally, clearly the quality of the cases matters a great deal for the nature of the expectations embedded in them. Thus, I would argue in favour of looking at the content we teach through the prism of expectations.
There are also ethical aspects running through this conception of knowledge as expectation. Of all visions of education, I find those that impute it with some form of explicit purpose, the most insidious. Someone made the comment on Twitter that: ‘there is no such thing as a neutral education’. Whilst this may be true in the sense that different forms of education will have different consequences, it is the height of hubris if someone believes that they can predict and therefore control the future and know what those consequences will be. Justice is not a state to be achieved, but an obligation to fulfil one’s own expectations of oneself. Woven throughout this nomological conception is an imperative to pay attention, to refine one’s expectations and be more aware of the expectations of others, our students in particular. (Not least because expectations have been shown to be crucial to one’s happiness!) To make this aspect more explicit, I shall finish with Simone Weil writing about the most sacred of expectations:
At the bottom of the heart of every human being, from earliest infancy until the tomb, there is something that goes on indomitably expecting, in the teeth of all experience of crimes committed, suffered, and witnessed, that good and not evil will be done to him. It is this above all that is sacred in every human being.
The good is the only source of the sacred. There is nothing sacred except the good and what pertains to it.
This profound and childlike and unchanging expectation of good in the heart is not what is involved when we agitate for our rights. The motive which prompts a little boy to watch jealously to see if his brother has a slightly larger piece of cake arises from a much more superficial level of the soul. The word justice means two very different things according to whether it refers to the one or the other level. It is only the former one that matters.
Every time that there arises from the depths of a human heart the childish cry which Christ himself could not restrain, ‘Why am I being hurt?’, then there is certainly injustice. For if, as often happens, it is only the result of a misunderstanding, then the injustice consists in the inadequacy of the explanation.
 F. A. Hayek, Law, Legislation and Liberty: A New Statement of the Liberal Principles of Justice and Political Economy (Oxford: Routledge, 2012).
 One can see here an obvious connection with the psychological concept of priming. See http://nautil.us/issue/48/chaos/shakespeares-genius-is-nonsense-rp?utm_source=pocket&utm_medium=email&utm_campaign=pockethits for an interesting article discussing psychology and Shakespeare.
 Aaron Copland, ‘Creativity in America’, Copland on Music (1944), p. 53
 I shall perhaps write a little addendum about the possible confusion between ‘beliefs’ and ‘expectations’, specifically expectations in the classroom, and the ‘Pygmalion effect’ – I’ve already written too much!
 Robb B Rutledge and others, ‘A Computational and Neural Model of Momentary Subjective Well-Being.’, in Proceedings of the National Academy of Sciences of the United States of America, 2014, cxi, 12252–57.
 Simone Weil, Simone Weil: An Anthology (London: Penguin, 2005). pp.71-72