When I was in Year 7, my maths teacher got us to calculate the number of possible unique handshakes in a group of people. We learnt that the number of handshakes in a group could be modelled by the formula h = n/2 * (n-1) where h is the number of handshakes and n the number of people. Two people can have one handshake; 30 people can have 435 handshakes; 68 people can have 2278 handshakes. I remember the latter as that was what we were expected to work out!

In my mind, this is how knowledge works in classrooms.

Imagine Jon Snow. He knows nothing, and there are therefore no possible links between the things he knows. And if he knows just one thing, then there are still no links. Once he knows two things, there can be one link, but for that link to mean very much, the two things he learnt would probably have to be already fairly closely connected. Jon Snow might learn fifty things, but there are still only around 1000 possible links, and many of those might not be immediately obvious. But what happens when Jon Snow knows 1000 things? Well, there are now potentially half a million possible ways in which he could join up the things that he knows.

We can usually see this as history teachers (and I suspect the same is true in other essay-based subjects) where a pupil who knows little produces a highly formulaic response to a question, falling back on generic structures and stock phrases to make up for the fact that he does not have a sufficiently powerful network of knowledge to activate in answering a question. A pupil who knows a great deal, who has layer upon layer of knowledge, has no need to fall back on such clumsy phrasing, for she has such an extensive knowledge base that she can confidently respond to the question being asked of her.

This is kind of the point I was trying to get at in an opening paragraph in a chapter I contributed to a recent book. I wrote that

When I read words such as ‘middle class’ I think not of dictionary definitions, but rather of London coffee houses, Viennese concert halls and Parisian tennis courts. I call upon a lifetime of textual encounters in imagining the middle classes: Lucy Pevensie, Phileas Fogg and Marius Pontmercy are as much a part of this as Charles Darwin, Emmeline Pankhurst and George Mallory. These images furnish the words ‘middle class’ for me, endowing them with a lingering residue that I call on in subsequent encounters with the term. Language and knowledge in this way stand in mutual support of one another, and, as I build fluency in one, I gain mastery over the other.

A single definition of ‘middle class’ will probably serve a pupil better than no definition at all, but, I would argue, one can only begin to use the term confidently once one has learnt a wide variety of instantiations of the idea.

This is why breadth of knowledge matters. For me, Lucy Pevensie, Phileas Fogg, Marius Pontmercy, Charles Darwin, Emmeline Pankhurst, George Mallory, and many, many others, are all shaking hands at a party in my head that has been summoned under the auspices of the term ‘middle class’. I have similar parties in my head for concepts such as ‘revolution’, ‘noble gas’, ‘glaciation’ and ‘tragedy’. Each new instance is not just one additional thing I know. It also creates an ever-growing possible network of links to other things that I know.

And this is why we need to over-emphasise the value of breadth in curriculum design. It is not enough to teach a single definition of ‘middle class’, and nor is it sufficient to teach one example of ‘middle class’. We rather need to create knowledge parties in the minds of our pupils.