Last Tuesday evening was also very pleasing to me because of what I did in the second hour.  In the first hour, remember, I taught Small Boy.  In the second hour, I taught Smart Boy.  Soon I will have forgotten about this myself, and I want that not to happen, so I need to write all this that follows before more teaching scrubs it from my brain.

Smart Boy had been making no secret of his desire to spend time with me, rather than with the maths teacher, Mr Vora.  The Mr Vora problem is not Mr Vora.  He is a exemplary maths teacher, and at least as companionable a person as me.  But Mr Vora teaches a batch of several children all at once, and Smart Boy really is smart, compared to some of those children.  He tends to sit at the back, oscillating between quiet resentment and rather theatrical demonstrations of lack of interest in sums that he considers somewhat beneath him.  But even more fundamentally, Smart Boy likes the undivided attention of whoever he is with, and from Mr Vora, inevitably, he does not get it.  From me, he would.  From me, last Tuesday, he did, and showed every sign of appreciating it very much. He was very happy to pay attention carefully to whatever I wanted to say him, provided I payed him the same compliment, as I was happy to do.  In other words, Smart Boy and I had a good conversation.

I began by showing off my favourite proof of Pythagoras’s Theorem.  This is the one where instead of having one right angled triangle in the middle, with squares attached to each side, you have four identical right angled triangles arranged to form a square with another square gap in the middle.  Through the magic of the internet, I am able to tell you that it is Proof number 4, here.  And moments ago, I was able to learn of an even more cunning Pythagoras proof, namely Proof number 5.  (I love the internet.)

Well, Smart Boy wasn’t that impressed by my Pythagoras-ing.  Nor was he that excited by me telling him what little I knew of pi, i.e. the ratio of the circumference of a circle to its diameter, or whatever it is, which in any case he also knew.  I told him that pi r squared is the area of a circle, but I couldn’t prove it, and that is now my homework.  I don’t know quite how that happened, but it did.

Then we got onto the subject of averages.  How would you work out the average height of all the children here?  That’s right, you add up all the heights of all the children and divide that by the number of children.

Then I took a chance, hoping merely that he would indulge me.  I found myself talking about Don Bradman’s last innings as an international cricketer, which is a story about an average.  What happened was that Bradman went out to bat, at the Oval right here in London, in 1948, to play what turned out to be his very last test match innings.  It was only the first Australian innings, but they were already heading for an almost certain innings victory by the time Bradman went in, so both Bradman and everyone else present were pretty sure that this would be Bradman’s very last innings.  At that point, his test match batting average was just over a hundred, which is about thirty or forty more than any other international cricketer then or since, which shows you just what a supreme batsman Bradman was.  This is a far more telling number, for instance, than the mere total number of runs Bradman scored, which has often been surpassed since, because in those days there were far fewer test matches per year, and there was also the small matter of World War II getting in the way of everyone’s careers, including Bradman’s.  So anyway, Bradman goes in to bat, and all he had to do to walk off the pitch and into the history books with a batting average that remained more than a hundred was to make just four runs in his final innings, and, of course, it was pretty confidently anticipated that he would do a lot better than that, perhaps making yet another hundred.  He did make a hundred in the previous game at Leeds.  173 not out, as I recall.

Guess how many runs Bradman made in that last innings of his.  If you know, you know, but if you don’t, I’ll tell you.  Zero.  He was out second ball.  For a duck.  It was the only seriously memorable thing that a certain England spin bowler by the name of Eric Hollies ever did.  Bradman bowled Hollies 0.  And Bradman’s average was forever set in the aspic of cricket statistical history at 99.94.

So, I told this story to Smart Boy, my point being that here was one average that was truly dramatic, and this time I had his attention completely.  This was the kind of thing he wanted!  I don’t know why exactly.  Perhaps he liked the arcane nature of the story, the fact that most of the people he would later tell it to (to prove to them how smart he is) wouldn’t know anything about it.  (Smart Boy’s ancestors all come from a very non-cricket country.) Pythagoras and pi and all that stuff was too routine for his purposes.  All maths teachers would know about this, and many maths pupils.  But not many would know about Don Bradman’s batting average, and how it was nearly a hundred, but not quite.  Whatever his motives were, he wrote down the name “Don Bradman” and added some notes to remind him of the key facts of the case, and declared that he would chase it up on the internet. 

Then we talked about Shakespeare.  Smart Boy is doing Macbeth at school.  I did Macbeth at school too, so we had plenty to talk about.  Miss Maxwell, the school boss came by right at the end of our “lesson”.  I said: “We’ve been talking about Shakespeare.” Would she approve?  (No mention was made of Don Bradman.) For a long moment Miss Maxwell was silently inscrutable.  Then she said: “I recommend Othello.” Phew.  Cue for me to show off my knowledge not only of Shakespeare but of Giuseppe Verdi, then pronounced with superbly Italianate relish by Smart Boy.  Verdi, I said, wrote an “opera” (cue further explanation of that) called “Otello”, that being how the Italians say Othello.

Was this teaching?  Was this education?  Should I instead have been dinning more complicated sums into Smart Boy’s head than he was used to?  Were Smart Boy’s parents getting their money’s worth?  I think that it was education, and that they were getting their money’s worth, although they might dissent.  My meta-lesson, so to speak, that I have been trying to convince Smart Boy of ever since I first talked with him, is that he doesn’t need other people to ask complicated show-offy questions to and to learn complicated show-offy answers from or for.  The world now, especially the world now, is full of stuff you can just dive into.

And if he’d rather ask me complicated questions, and gouge obscure stuff out of me, rather than out of a mere book or a mere computer, well, I love that.  The quality in a pupil that I most value when I’m teaching is that he’s driving the agenda forward.  He’s the one supplying the energy.  He’s the king and I am but the respectful counsellor.  He’s running his own life, and I’m just helping.  When I “taught”, if that’s what it was, Smart Boy, that is exactly how it was.

Or, to put it another way, my fantasies about what truly consenting education should be like - which in that Small Boy posting I oh-so-subtly implied are an impossible dream - are in fact anything but.