An appeal for nuance: Five challenges to the argument that ‘all educationally relevant knowledge acquired during instruction is, and only is, domain-specific’

Here I will present five philosophical challenges to the argument presented by Tricot and Sweller in their paper Domain-Specific Knowledge and why Teaching Generic Skills does not work.[i]

(NB: Whilst I have many concerns about their use and discussion of Geary’s biologically primary and secondary knowledge, I will not be discussing that here. Suffice to say that I have a great deal of sympathy with @mpershan’s description of it as a ‘just so story’.

The main focus of this post is the logic of the arguments, rather than the evidence for the truth of the premises.)

A summary of the logical form of their argument

I shall begin by summarising their argument as coherently as I can. From the abstract, we can reconstruct the main steps as follows:

  • P1. The data is unintelligible with the assumption that domain-general knowledge should be emphasised over domain-specific knowledge
  • P2. The data is explained by an assumption of the primacy of domain-specific knowledge
  • C1. The data is unintelligible with the assumption that domain-general knowledge should be emphasised over domain-specific knowledge andthe data is explained by an assumption of the primacy of domain-specific knowledge
  • P3. If (C1) is true, then an emphasis on domain-general knowledge may be misplaced
  • C2. An emphasis on domain-general knowledge is misplaced

Much of the paper is then devoted to describing examples in support of P1 and P2 (and therefore C1). Tricot and Sweller use examples from Binet, Cahan and Cohen, Miller, Piaget, Chi, and Cognitive Load Theory. I do not wish to dispute any of these examples per se, and I find many of the papers cited to be convincing and very informative for teachers.

Each of the examples that Tricot and Sweller use to support P1 is connected to the main argument using a similar logical form:

  • 1a. The assumption that domain-general knowledge should be emphasised over domain-specific knowledge is correct, only if X had occurred
  • 1b. X did not occur
  • P1. The data is unintelligible with the assumption that domain-general knowledge should be emphasised over domain-specific knowledge

The converse argument (P2) in favour of the assumption of the primacy of domain-specific knowledge superficially appears equally robust:

  • 2a. If X did not occur, then the data is explained by an assumption of the primacy of domain-specific knowledge
  • 2b. X did not occur
  • P2. The data is explained by an assumption of the primacy of domain-specific knowledge

Having provided evidence for these two steps, it is not unreasonable to reach the conclusion that an emphasis on domain-general knowledge is misplaced. I would thus support the paper, were this to be their conclusion. The evidence provided also seems to suggest that it is extremely useful to remember that skills do not transfer easily from one domain to another.

This is where the authors should, in my view, have stopped. It is a heuristic, a rule-of-thumb. The argument cannot be extended beyond that.

Challenge one: The main bulk of the paper does not support the claim that ‘all educationally relevant knowledge acquired during instruction is, and only is, domain-specific’

However, they do go further than this – in the introduction, they make a much bolder claim: ‘all educationally relevant knowledge acquired during instruction is, and only is, domain-specific’.[ii]

They appear to think that they are showing that since educationally relevant knowledge is not domain-general, it must be domain-specific. Reconstructed more formally, we could write this alternative argument like so (I’ve labelled these alternative premises as AP..to distinguish them).

  • AP1. All educationally relevant knowledge acquired during instruction is, and only is either domain-specific or domain-general
  • AP2. No educationally relevant knowledge acquired during instruction is domain-general
  • AC. All educationally relevant knowledge acquired during instruction is, and only is, domain-specific

This alternative argument is clearly not the same as what they have actually argued in their paper.

My first challenge is a simple one. From the summary of the article above, we saw that the bulk of the content went into proving that:

  • C2. An emphasis on domain-general knowledge is misplaced

However, their alternative argument relies on the much stronger claim:

  • AC. All educationally relevant knowledge acquired during instruction is, and only is, domain-specific

Neither the alternative conclusion, nor either of the alternative premises follows from what they actually argue in the main bulk of the text.

Challenge two: They have no grounds for suggesting that ‘domain-specific knowledge is the primary factor driving acquired intellectual skills’

Here I want to dig a little deeper into their argument to try to extract why they believe the above leap is acceptable. How they believe they can jump from this weaker (but reasonable) conclusion to this stronger one is hinted at in the abstract where they state, ‘An emphasis on domain-general knowledge may be misplaced if domain-specific knowledge is the primary factor driving acquired intellectual skills.’

Here we have another argument! (which I will label BP..):

  • BP1. If domain-specific knowledge is the primary factor driving acquired intellectual skills, then an emphasis on domain-general knowledge is misplaced.
  • BP2. Domain-specific knowledge is the primary factor driving acquired intellectual skills
  • BC. An emphasis on domain-general knowledge is misplaced

The problem here is that, whilst they provide solid evidence for this conclusion (BC) elsewhere, they at no point provide any evidence for the premise (BP2)!

What they do provide evidence for is:

  • C1. The data is unintelligible with the assumption that domain-general knowledge should be emphasised over domain-specific knowledge and the data is explained by an assumption of the primacy of domain-specific knowledge

There is a subtle, but very important distinction here between C1 and BP2. C1 is discussing the explanatory power of assuming the primacy of domain-specific knowledge, whereas BP2 is clearly hinting at some kind of causal description.

There is a demonstration of a dangerous ambiguity in the word explain, of which I believe that cognitive-scientists should be particularly aware. It is not uncommon to read a description where the author slips imperceptibly from (i) b explains a to (ii) a happens because of b to (iii) b causes a. An explanation in the first sense amounts to a correlation, a congruence between what has been observed and what one’s theory or assumptions would predict. By the final sense, we have mechanised and reified the situation such that we are now tempted to begin looking for the exact and fixed definitions of the words we use. The difference is in the direction of fit. In the first sense, the theory is subservient to the observations, and by the end, the observations have become subservient to theory; the purpose of the first is to satisfy our expectations, whereas the purpose of the second is to claim the existence of a necessary relation.

This is a necessary move for Tricot and Sweller if they are to prove their strong conclusion. To support the stronger conclusion, they need to argue that, not only is an emphasis on domain-general knowledge is wrong but that the assumptions concerning domain-specific knowledge are definitely right.

I can see three possible strategies to shore up this argument:

Firstly, assume that a disjunction of the following kind is true:

  • The primary factor driving acquired intellectual skills is either domain-specific knowledge or domain-general knowledge

However, it is clearly not the case that either one or the other of the sets of assumptions are true; it is entirely possible that a completely different third primary factor.

Secondly, they could replace the terms used to defend P2 in the original. As a reminder, the sub-argument that they actually do present can be summarised as follows:

  • 2a. If X did not occur, then the data is explained by an assumption of the primacy of domain-specific knowledge
  • 2b. X did not occur
  • P2. The data is explained by an assumption of the primacy of domain-specific knowledge

With the relevant swapping of terms, it would be

  • 2a. If X did not occur, then domain-specific knowledge is the primary factor driving acquired intellectual skills
  • 2b. X did not occur
  • BP2. Domain-specific knowledge is the primary factor driving acquired intellectual skills

But it is quite clear that no amount of empirical observation is sufficient to prove a particular theory to be true! This is the nub of Popper’s argument that scientific theories must be falsifiable. Which leads us to our third option, which is to suggest that, rather than being a necessary condition of the evidence, domain-specific knowledge being the primary factor driving acquired intellectual skills, is a sufficient condition. This gives us:

  • 2a. If domain-specific knowledge is the primary factor driving acquired intellectual skills, then X will not occur
  • 2b. X did not occur
  • BP2. Domain-specific knowledge is the primary factor driving acquired intellectual skills

Unfortunately for the authors, this strategy will not work either, given that the argument is now affirming the consequent and therefore invalid.

So, none of these three strategies can result in anything like a strong enough conclusion to show that Domain-specific knowledge is the primary factor driving acquired intellectual skills.

Challenge three: The definition of ‘domain’ results in the conclusion being an empty truism

According to the alternative conclusion:

  • AC. All educationally relevant knowledge acquired during instruction is, and only is, domain-specific

My third challenge is that there is a confusion in the paper as to whether the authors believe this statement to be analytically true, or empirically true.

If it is analytically true, then they are merely saying that ‘educationally relevant’ is synonymous with (or contains within it) ‘domain-specific’. If this is the case, then, given their own definitions of domain, an empty truism. Tricot and Sweller define ‘domain’ as the ‘various problems to which the theorem can be applied’. If there was a skill that could be applied to any problem, then presumably the domain of that skill would be all problems. Thus, by this definition, even if there were a domain-general skill, it would also be a domain-specific skill.

Challenge four: there is a confusion as to the role of ‘domain-transferable’ knowledge

Given the length of the article, one would assume that they wish to do more than simply offer an empty truism – they wish to add some new information, make an empirical statement. By saying that all educationally relevant knowledge is only domain-specific, they are trying to say that it is not something else, i.e. not domain-general.

The authors write that ‘Domain-general skills, by definition, can be used to solve any problem in any area.’ Charitably, then, we can assume a dichotomy between those skills that can be used in any area (domain-general) and those that cannot (domain-specific) and we can then interpret their conclusion as:

  • There is no knowledge which can be used to solve all problems in any area

This again appears to be a reasonable, but weak conclusion. I’m not sure that there are many who think that there is a piece of knowledge that is applicable to everything or all problems. Even those who are attempting to look for or describe universal laws of either logic or science are fully aware that we don’t have such knowledge. I would suggest that Tricot and Sweller want to make a stronger point than this. Some people would, however, argue that there is plenty of educationally relevant knowledge acquired during instruction that is domain-transferable. I think that the authors would like to de-emphasise the possibility of this also.

However, Tricot and Sweller’s description of the cashiers who were better at mental arithmetic questions than someone who was thought to be generally ‘intelligent’, is a clear demonstration of a skill being transferred from one domain to another. We would not call them domain-general but we certainly can call them domain-transferable. Or are the authors claiming that doing sums is a domain all of its own? Are some domains not made up of, or part of other domains? Do domains not overlap?

Earlier, I suggested that the alternative argument required the following assumed premise:

  • AP1. All educationally relevant knowledge acquired during instruction is either domain-specific or domain-general

…but here we appear to have a third option of domain-transferable.

The authors do seem quite set on eliminating this third option also. They write:‘We are unable to find a domain-general, cognitive strategy that has been described and tested for effectiveness using randomized, controlled trials varying one factor at a time with far transfer test tasks to eliminate the effects of domain-specific knowledge.’

However, if we follow the logic of this statement through, we return to the patent nonsense of the truism above.

If a skill is effective at solving a problem, then, by the author’s definition, that problem would be in the skill’s domain. Their definition of ‘far-transfer’ appears to be somewhere which eliminates the effects of domain-specificity. But if you eliminate the effects of domain-specificity, then you, by definition, remove a skill from any context in which it might be useful!

Similarly, I suspect that the authors would attempt to define any usable domain-transferable skill as being a domain-specific skill. But this dissolves the distinction between domain-transfer and domain-specificity into nonsense. If there were a usable domain-transferable skill that was transferable and usable with all problems, that too, would be defined as being domain-specific, so they cannot simply absorb domain-transferability into domain-specificity.

I would repeat my caveat that I am not against using the term domain-specific but not to the exclusion of the idea of domain-transferable. These terms are clearly vague, organic concepts, blunt tools, and one would presumably assume that its meaning might change and vary (as with all words) depending upon the domain in which it is used. I would argue that the term domain is most elucidatory when it is seen as something equivalent to ‘language game’ in Wittgenstein’s Philosophical Investigations[iii]or ‘sphere of actualization’ in Aristotle’s Nichomachean ethics[iv]. In both cases, the terms are used in an organic (some might say emergent) fashion, a multiplicity of uses is recognised. I would argue that the term is more meaningful if one accepts that ‘domain-specificity’ should be applied to the various uses of the term ‘domain-specific’. The irony being that Tricot and Sweller appear to be using the term in a very ‘domain-general’ way.

This is not, I believe, a minor complaint. Firstly, the concept of ‘domain-specificity’ is infinitely more useful to teachers if it is used in the more organic fashion. Secondly, it is simply empirically incorrect to suggest that separate domains exist in silos, immune from outside influence. One only has to look at the many advances in technology made by garden-shed tinkerers, or to recognise the often-haphazard nature of scientific progress to see that domains or language-games or spheres of actualisation or disciplines and sub-disciplines are constantly interacting with each other in a chaotic fashion. Thirdly, it is an epistemologically and dare-I-say-it, ethically unsound position. This will be the subject of my final challenge.

Challenge five: the nature of value-judgements in a domain-specific world

Hidden amongst the many examples used by Tricot and Sweller are a great many value-judgements. This is based on the very reasonable assumption that a teacher should aim to lead students towards expertise, that is, they should aim to make students better. I have no issue with that and accept that such value-judgements are part-and-parcel of teaching.

However, in order to make a meaningful judgement about something, one must have some form of criteria for making such judgements. If ‘all educationally relevant knowledge acquired during instruction is, and only is, domain-specific’, then it would stand to reason that the criteria for making judgements upon performances in a domain are also domain-specific. Now, whilst I accept that the standards of what makes good historical writing are generally best decided by historians, and what makes good physics is generally best described by physicists, this cannot be the whole story. It cannot be the case that the only authority over disciplines and domains lies within the discipline and domains themselves. There must be some criteria that lie outside the domains, or that are at least shared with others – indeed this is the case: if one wishes to get the go-ahead to conduct some research, for example, most research institutions require that some kind of ethics clearance is granted.

If we are to exclude the relevance of domain-transferable or domain-general knowledge for education, then we are also accepting a bizarre form of self-legislation from within the domains. Is such self-legislation a problem? Well, Kant, for instance, did not seem to think so, his entire ethical system was built upon it – but there is one important caveat here. For Kant’s ethical system self-legislation was only logically viable because there was a further force to which human beings were answerable: reason itself (and God). If we do away with such an external force altogether, then self-legislation amounts to no legislation at all. I don’t know whether the correlation is particularly strong, but in my experience those on edu-twitter who fiercely defend Tricot and Sweller, are also frequently the same people who bemoan the relativism of postmodernism. I am not overly worried about postmodernism, but if such relativism is a concern, then the self-legislation of domains would also be something to fear.

Tricot and Sweller state that, ‘Our acquired ability to reason logically is due to biologically secondary, domain-specific knowledge. A person who is able to reason logically in science may show no such ability in his or her personal life or in any areas outside of his or her areas of science.’[v]It is unclear from these sentences whether the authors believe that there is something in common to logical reasoning from one domain to the next. Nor are they clear about the relationship between logic and knowledge. If they do believe that there is nothing universal about logic, then I, personally, would have sympathy with that position. I would repeat my concern, however, that domains not be treated as being in any way fixed or inorganic. I would argue that what appear to be the ‘laws’ of logic are merely norms that have developed from shared practices – yes, perhaps domain-specific practices, – but a complex web of overlapping, constantly interacting domains. The ‘laws’ of logic lay very firmly in the domain-transferable camp. These overlaps and interactions are our common understanding, our shared practice, our form of life, our transferable (if not general) domain.

If we deny the existence of any external mark scheme, then domains do become silos, separated off from our shared forms-of-life. In his paper, Education and Human Being, J K Elliot discusses Hursserl’s thesis that Physics, from the Galileo to the present day, has been undergoing a gradual but massive change, with the result that it ‘no longer provides an understanding of the reality with which it was originally concerned; and that its own practitioners proceed for the most part technically and have only a technical understanding of what they are doing’.[vi]I quote this, not because I agree with Husserl’s account of Physics, but because if we believe that domains legislate for themselves then we will inevitably reach such a situation where we are merely educating students to be ‘technicians’, players of idiosyncratic games that have little bearing on life outside their rules. Of course, this is part of the role of a teacher, but to become educated is more than simply to become some form of calculating machine – it is to participate in our shared humanity.

[i]André Tricot and John Sweller, ‘Domain-Specific Knowledge and Why Teaching Generic Skills Does Not Work’, Educational Psychology Review, 26.2 (2014), 265–83

[ii]Ibid. p.3

[iii]Ludwig Wittgenstein, Philosophical Investigations.(Oxford: Blackwell, 1967)

[iv]Aristotle, The Nichomachean Ethics, Oxford Wor (Oxford: Oxford University Press, 2009).

[v]Ibid. P.15

[vi]K R Elliott, ‘Education and Human Being I.’, in Philosophers Discuss Education., ed. by Brown S.C. (London: Palgrave Macmillan, 1975), pp. 45–72.p.60

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