I’ll stray into areas where I know what I know is limited… but I’ve found what follows to be a very useful model, even if it’s not quite right. Where I have it ‘not quite right,’ hopefully someone can fill in the blanks for me.
Substantive Knowledge
Knowledge accrued by the discipline.
e.g. History: knowledge of the past. Science: Newton’s three laws of motion. Mathematics: Pythagoras’ theorem.
Disciplinary Knowledge
How the academic discipline accrues said knowledge.
e.g. Source analysis. Empirical experimentation. Conjecture and proof.
I feel like there’s more to disciplinary knowledge that I’m not fully getting… Michael Fordham suggested that there is a ‘know-that’ component to disciplinary knowledge, as well as a ‘know-how.’ I wonder whether concepts such as ‘measurement error’ and ‘inductive reasoning’ would be ‘know-that’ disciplinary knowledge for science. They’re certainly not knowledge accrued by science, while they are necessary as a part of its processes for accruing knowledge. Interestingly, I then would note that ‘measurement error’ is possibly part of the substantive knowledge of mathematics, while ‘inductive reasoning’ is part of the substantive knowledge of philosophy…
Anyway, all this makes me feel I may miss out some complexities here, but the overall theme holds up, I think.
What’s interesting is that once you start to view a school ‘subject’ in terms of disciplines like this, we can keenly observe how we distribute time between the two kinds of knowledge. What’s most interesting is that the distribution varies quite dramatically from one subject to another.
Where’s your subject on the axes?
My thinking on this has been sparked recently by a couple of pupils who asked ‘What do mathematicians actually do…?’ One of these is an exceptionally high-achieving Further Mathematician; a possible candidate for mathematics at Cambridge and the like, who may genuinely need to make the choice between studying mathematics, and studying engineering. It’s much easier to see and understand what engineers do; they build stuff!
Why is it so difficult to understand what mathematicians do? To what extent do I understand this myself, not being a trained mathematician?
Over the next few posts I’m going take a look at the distributions of substantive and disciplinary knowledge communicated in the different academic subjects of a typical school curriculum. I’ll be making plenty of assumptions along the way, having only taught mathematics myself. Any assumptions I make that are far off the mark, please let me know.
...to the real. 
Many thanks for this post Kris. I hope other subjects do take up your call to show where the ‘school subject’ version of their discipline sits on these axes. Michael Fordham and I, and the Cambridge history mentors, have often had this discussion; and in particular: i) how do subjects necessarily differ in the incidence, sequence, patterning and blending of these two types of knowledge? ii) why is this? i.e. How do the distinctions between (say) university maths and school maths *differ from* the distinctions between university history and school history? The bigger question still, is, (iii) what should senior school leaders know about this and how should it affect their leadership of curriculum and staff development/debate on curriculum? In other words, what is curricular knowledge for school leaders?
Clarity about some of these questions would have obviated some of the catastrophes of the last 20 years, namely, forcing blanket assessment structures on all subjects (such as LDs, which, where applied as the main means of identifying ‘progression’ have been so damaging for systematic growth of substantive knowledge in history); and talking at cross purposes in schools over a huge range of issues, from assessment to the madness of insisting that Blooms Taxonomy shapes all lesson objectives. Blooms plays havoc with both our substantive and our disciplinary knowledge in history. So how was it possible, for so many years, for some school leaders to imagine that it was a good model for formulating a lesson, let alone for assessment?
My tentative answer to that question is that if there is a vacuum in curriculum knowledge at senior level (i.e. if there is no premium on senior leaders finding a language for adequate discussion about the nature of the disciplines that form the curriculum, their convergences and and their necessary differences), then into that vacuum will flow generic principles about pedagogy, assessment (or even curriculum!) that ride roughshod over rigour.
Your axes seem to me a very good place to start in all our efforts to theorise that absent tier of leadership knowledge. Bernstein wrote of the ‘recontextualisation’ of disciplines as school subjects. Recontextualising is central to what a school does (if it cares about knowledge, that is! – the specialised knowledge that pupils would otherwise not get).
Thanks for this comment Christine, really interesting to read.
What were LDs?
I agree with all of the points you made. In my experience, I don’t even think teachers know what disciplines are; I’ve only started to piece it together very recently, thanks to sufficient fragments from chance conversations, and I’m not even sure I have it 100% on the money! I’ve never heard anyone in a school talk about disciplines rather than just subjects. I heard Sir Ken state boldly in a video once “…and remember, these are *disciplines*, they’re not subjects.” and I couldn’t figure out what he meant by that.
Yet… as a distinction, it’s very useful. Suddenly you have a language for talking about ‘skills’ and ‘knowledge’ and appreciating a little bit more about from where the divide arises. You start to see how different school subjects are distributing their times differently between the two, and you even start to appreciate exactly how and why some subjects subjects really *aren’t* academic disciplines at all. From that, you grow to appreciate why some subjects are considered ‘academic’ and others not, beyond a simple gut feeling that some are ‘harder’ or require ‘book smarts’!
So… in response to your question, I think that every teacher should be aware of this, not just the Heads, but certainly them included.
Reblogged this on The Echo Chamber.
I’m sort of left wondering whether “disciplinary knowledge” is meaningful or helpful. We often seem to give a lot of weight to how new knowledge is created in a discipline, as this is how those who have mastered an academic discipline tend to spend their time. But just because “disciplinary knowledge” sets the boundaries of a discipline, it does not mean it is at the heart of the discipline or provides the definition of the discipline. And then we have the question of how “disciplinary knowledge” changes with time too, as new techniques for exploring a subject are developed. It makes sense to say we find out new ways of finding out new things about a discipline. Does it make sense to say we have disciplinary knowledge of the disciplinary knowledge of a discipline?
I think this doesn’t have just to be about the creation of new knowledge: it’s also about learning how the knowledge we have today was delivered to us. For example, I would consider teaching pupils the basic idea of the ‘Whig’ interpretation of history a worthwhile exercise. I guess in science there might be some worth in teaching a bit of history of science? Generally though most people currently interpret ‘disciplinary’ knowledge as ‘learning how to do history’ or ‘learning how to do biology’, when really this is only one part of what might be understood as disciplinary knowledge. All of this notwithstanding, the overriding focus in schools should be substantive knowledge: if I had to put a figure on it I might be tempted to go 90:10 substantive to disciplinary. And on the final point, I think the discipline that thinks about disciplines is philosophy, and I wouldn’t teach that until they had a good grounding in the other disciplines: Sixth Form or university realistically.
I do get the sense that there is something a bit more to disciplinary knowledge, as you say. I’m not sure I appreciate your point yet about ‘how the knowledge we have today is delivered to us.’ On history of science, maths: personally, I am *massively* in favour of this. I do it a lot, but not as structure as I would like, and I don’t build it into assessment enough. I think it helps to create a sense that maths and science didn’t pop into being, fully formed, the day before we started school, as well as providing a human narrative for the subjects, and helping us to appreciate the problems manifest at the time that led to the creation of new ideas. Often there are key moments where we can point to maths and science having the chance to go one way or the other: Descartes hypothesised that light was made up of rotating particles whose angular velocity was modified by a prism. White was the purest form of light. Newton hypothesised prism didn’t modify light, but filter them. White was the impure amalgamation of the pure colours green, red and blue. Why did Newton’s ideas become the theory of light we have today? On the other hand, Fermat created a coordinate system at the same time as Descartes. Why now do we use a Cartesian coordinate system, rather than a Fermatian one? And there, we’ve seen the same character now, Descartes, in both our science lessons and our maths lessons – it’s a very natural blending of the two, rather than some arbitrary cross-curricular project.
Re: philosophy – would you teach anything at all about it? For example, I do think everyone should at least know that Socrates, Plato and Aristotle existed, that they were students of one another, roughly when they lived, and that they made philosophical and mathematical contributions that today underpin all Western intellectual thought. They’ve cropped up several times in maths lessons, but I’ve never gone into any depth about their actual ideas.
Essentially I’m arguing for teaching a bit of the history of philosophy lower down school, but not a hardcore course in metaphysics until end of school.
I find it useful (see my comment to Christine, and future posts…) It’s just a language for describing a part of a discipline that sort of *is* the discipline but *isn’t* the stuff the discipline creates/invents/discovers. That it can change over time doesn’t seem to harm the language in any way, no more than a revisionist history means the previous telling was not the substantive knowledge of history in its time. It also provides something useful to understand in a discipline beyond the fairly obtuse definition of ‘skill.’ Finally, I find it makes it much easier to appreciate exactly why it doesn’t make much sense to overly focus disciplinary knowledge during school years.
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This information is so important n helpful
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