How many is too many?

How many friends do you have? No, not the huge number that Facebook suggests and which we can increase through the mere click of a button. Not the list of people you send Christmas cards to, either. Nor, at the other extreme, the number of people who we would call 'close friends' or, to use an old word, 'confidantes' - the select few we trust to keep our secrets and to whom we are prepared to open up our hearts. I'm talking about people who we see regularly and know by name, whether at home, at work, or in the pursuit of our hobbies and interests. Chances are there are roughly 150 of them. Maybe when you've got a moment, you could list them all?

There were about 150 boys at my Prep School, Aysgarth School in North Yorkshire. There were slightly more at my daughters' Primary School, Byfleet County Primary School. 150 is also about my limit when it comes to learning the names of those I teach in any given year. With as many as twelve classes of up to 30 students on my books, that leaves 210 pupils who pass the year in total anonymity. Despite my best efforts, they are only a line of grades and codes in my markbook. Who are you? Ah, yes. Here you are - "HA, G&T, 87% Pred 7 PP Asthmatic". It sounds more like an excerpt from the Shipping Forecast, which is a pity because she's called Sophie (not really, I made the grades up - she's cleverer than that).

The communities where both myself and my children started out in life worked because they were the right size.

What's that then?

Well, there's a theory, proposed by a guy called Dunbar, which says that "the tightest circle has just five people – loved ones [and that] that’s followed by successive layers of 15 (good friends), 50 (friends), 150 (meaningful contacts), 500 (acquaintances) and 1500 (people you can recognize)." He even goes on to suggest that people move in and out of these groups. So if you and your wife/husband opt for more than four children, one of them (or, possibly, your spouse) will cease to be a 'loved one' and become a 'good friend'.

"What's this got to do with education, though?", you ask. Well, it's one way of explaining why many schools are, to a lesser or greater extent, dysfunctional. My own school was a boarding school made up of 1200 boys not far from the River Thames. You may have heard of it. Boris Johnson was actually Captain of the School when I started out there. 1200 was a small enough number for us all to recognise one another, so it would be hard for someone to sneak across the M4 from Slough, nick a tailcoat, waistcoat and pin-striped trousers from the school tailors and start coming to my Latin lessons. What is more, we were divided into about 25 houses, each with fifty boys in them, which was a small enough number for us all to be friends and for our housemaster, Dr Harrison, to keep tabs on us all. My own year group in my own house consisted of nine boys, which was where it fell down slightly as five got into the smallest group - 'loved ones' - while the other three didn't make the grade.

Now I work in the largest secondary school in Warwickshire. I can't name half my students or half of my colleagues for that matter. I can only cope with 150 meaningful contacts in my life. Once my wife, my two daughters and their partners have taken the 'top' slots, and my three work colleagues, my elderly father, my brothers and their families take up my 'good friends' slots, I'm left with 130 vacancies ... just over four classes, who can be meaningful contacts. The rest are doomed to be acquaintances or, at worst, people I can just about recognise.

Classes of 5? Maybe not, but it does explain why tutorials at university can be so productive, or even the little 'break out' groups that are designed to support struggling students. Classes of 15 would work as they could all be 'good friends'. I'd even suggest that classes of fifty might be more manageable with support from a colleague or a Teaching Assistant than classes of thirty. But thirty? It's not that it's too many. It's just a 'wrong' number. Like a football team with twenty players. It wouldn't function well as the game is designed to be played by two teams of eleven.

We need to shrink our schools. Or at least have fewer people trying to cram their way into the narrow corridors at the same time. You've got two buildings? Put just one year group in each of them for two days each week and you'll see everyone in classes of no more than 15 over the course of five days.

There's a story in the Bible about Peter, a fisherman, spending the whole night out on the Sea of Galilee looking for a catch. When he brings the empty boat ashore at first light, Jesus encourages him to have another go. And the Bible says that they caught so many fish that their nets began to break.

How many fish is too many fish?

It turns out to be one hundred and fifty-three.

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