Knowledge: independently necessary or collectively sufficient?

I have a little game for you to play today, and you must do as I tell you. Read each of the following sentences and, at the end of each one, either shrug your shoulders and say “this isn’t really a problem” or throw your arms in the air and say “this is just unacceptable”.

1. A child finishes school having not studied the Prologue to Romeo and Juliet.

2. A child finishes school having not studied Romeo and Juliet.

3. A child finishes school having not studied a tragedy by Shakespeare.

4. A child finishes school having not studied a play by Shakespeare.

5. A child finishes school having not studied a play written in the sixteenth or seventeenth centuries.

6. A child finishes school having not studied a play written before the twentieth century.

7. A child finishes school having not studied a play.

8. A child finishes school having studied no literature.

At what point on this scale did you throw your arms up in the air and say “this is just unacceptable”? I have created a little Twitter poll here you can complete should you so wish. The results of this poll notwithstanding, my hunch is that most people reached the point where they threw their hands in the air somewhere between Sentence 3 and Sentence 5.

What this little game reveals is an interesting curriculum problem about the specificity of the knowledge included in any given curriculum. It is always possible to be more specific, and it is always possible to be more generic. Some people lean more towards specificity, whilst others are happier to lean the other way.

So how do we resolve this problem?

In part I think we have to distinguish between things that we believe to be individually necessary and things which we believe are collectively sufficient.

Things which are individually necessary are those where one simply has to know about it in order to make further progress in the subject. Individually necessary things are more common in some subjects than others (they might incorporate what are sometimes called ‘threshold concepts’), but I would suggest they are less common than we might assume.

Let’s take a statement such as “Pupils should learn about the structure of the atom.” This sounds quite specific, and one can definitely see how knowing about the structure of atoms is necessary before one can continue in the study of physics or chemistry. But what is it about the structure of the atom we want them to study? Just how much detail ought we to go into? Protons and neutrons? Quarks? Strong nuclear force? Electron orbitals? Different energy levels? Wave-particle duality?

We see the same in a history curriculum. We might say that pupils ought to study the First World War, but what about the First World War? Do we mean the western front? If so, which part of the western front, or will any bit do? Is it necessary to study the western front in every single year of the war? Or every month? Do we need to distinguish between British and French lines? Is it enough to focus on Gallipoli? Have we taught the First World War if we have covered the role of women on the home front? Have we taught it is we haven’t covered this?

The search for things to include on a curriculum that are strictly individually necessary results in this kind of logical problem: I think it counts technically as a category problem, in the sense that it is not clear whether the thing can be understood meaningfully as anything more than the sum of its parts.

So what do we do instead?

I think the answer has to lie in changing our question in most cases from ‘what knowledge (s) is necessary?’ to ‘what knowledge (pl) is collectively sufficient?’ I’m not sure I can say with any degree of intellectual honesty that any one of the things I listed about the First World War is individually necessary, but, if you have taught all of those things I listed, I would feel happy that the First World War had been taught in a meaningful way. Importantly, however, you could select a very different list from mine, and I would still be likely to feel that, collectively, what was taught was sufficient.

The implication of this is that we cannot analyse a curriculum by analysing the specifics it contains: instead, we have to judge a curriculum as a whole. We need better concepts for talking about curricula wholes: current words such as ‘breadth’, ‘scope’, ‘coverage’, ‘spread’ and so on are woefully inadequate. Until we have a better language for talking about the collective sufficiency of curriculum, we are hamstrung in our ability to be good curriculum thinkers.