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.
Knowledge accrued by the discipline.
e.g. History: knowledge of the past. Science: Newton’s three laws of motion. Mathematics: Pythagoras’ theorem.
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.