IN ANNIE HALL, the Alvy Singer character, played by Woody Allen, is intensely irritated by the opinions of a man standing behind him in a cinema queue. Moving through the work of Fellini and Beckett, the stranger ultimately invokes the work of media philosopher Marshall McLuhan, at which point Allen cracks. A heated discussion follows; the man announces he is a lecturer in media at Columbia University and Allen triumphantly produces McLuhan from behind a poster display board.

“I heard what you were saying,” McLuhan tells the lecturer. “You know nothing of my work. How you ever got to teach a course in anything it totally amazing.” Allen looks wishfully into the camera. “Boy, if life were only like this,” he says.

And wouldn’t it be great? A little machine that enabled one to press a button and recall the perfect person from history to settle any argument. No more of those interminable debates about who was the greatest footballer, George Best or Pelé? Hold on, one might say after several hours of verbal ping-pong, I’ve got it — we’ll send for Bobby Moore. Bobby pops back from beyond. “Actually, I always found it harder to mark George.” Thanks, Bob. Fancy a drink before you go?

The best, the most useful tool, though, would be Summon-A-Politician. Tap in a code and the minister of your choice appears, enabling you to ask, in the face of irrefutable evidence, how exactly government policy on, say, NHS waiting lists can be said to be working when you are now entering your fifth hour in A&E. We had one of those moments last week. Had we known the right code, we would have mustered Tony Blair or Ruth Kelly at the Tate. We were at the Turner Prize exhibition, just the two of us, and a party of young teenage schoolchildren. No idea which school, but clearly local. It is no great shakes, the Turner Prize this year, four exhibits, one dull, one depressing, one disappointing, one borderline fraudulent, but that is hardly the point. The kids were meant to be making notes, expressing opinions, being the challenging vessels of independent thought and enthusiasm that appear in those government adverts imploring hard-up graduates to teach. You know the ones: funky music, bright-eyed smiling faces, lots of laughter and voice-over guff about the inspirational benefits of the job. And those cheeky, cheerful, children: “They tend to think what they think, not what they’re meant to think.”

Want to know what they thought at the Tate? They thought let’s make shadow penis puppets using the light of this installation, let’s shout, let’s swear, let’s charge about, let’s make no attempt to engage with anything in this room, including other members of society. Meanwhile, their teachers trod the sad route of many inner-city educators by sticking with the handful of pupils open-minded enough to want to learn, while letting the rest dig an intellectual grave. And then we came to the final room, the one in which visitors are asked for comments. The one in which I wanted Tony and Ruth to magically appear.

It was a work of art in its own way. Dumb Britain, 2005, by its citizens. Shit, said the first comment card. Very shit, said the next. And that was it, all the way along. Shit. Very shit. Very shit. Shit. Someone thought James Lambie was tripping. Which he is (although in the world of faeces-for-brains that deviation from the herd might later have earned a playground beating). And at that moment, surrounded by the deepest thoughts of our future generation, would it not have been wonderful to make the Prime Minister read the writing on the wall. What was that you said, Tony? Education, education, education. One word for you, old chum, and you are surrounded by it. The exam results lie. We are not producing wave upon wave of geniuses. A discarded notesheet told its semi-literate story, the basic rules of spelling entirely absent (“healthyer”, “rideing”), the work itself abandoned less than halfway through.

A card came through my letterbox the other day from a fledgeling “bilding” company. They do “extenshun, roofin, pavin, plasterin, decoretin and fencin”. I’m not makin this up. To produce one school-leaver with the literacy standards of an under-ten is unfortunate, to produce almost an entire class that cannot express itself beyond the rudimentary graffiti stage is shameful. Nobody has to like art, certainly nobody has to like the Turner Prize; but being able to encapsulate that opinion in something more than an abusive text message is important. Maybe these children were an unfortunate sample: a Village of the Damned Thick.

Yet the work of Professor David Jesson suggests that disproportionate stupidity does not happen. He tracked from the age of 11 to 16, the 37,500 brightest children in the country, of which 30,000 were in state schools. At 16, all 7,500 private school pupils had five GCSE grades A or A*, compared to 20,000 at state schools. Ten thousand children had gone missing academically. The old argument that a clever clogs will succeed anywhere is no longer true. Take 30 random children and there will be 30 random intellects, from mediocre to startling. That class at the Tate should have had a few bright sparks, a few right little bleeders and the bulk who might not know much about art, but knew enough to respect their environment.

In New York recently, at the Museum of Modern Art, a class of very young Americans joined the room gazing at Jackson Pollock’s Lavender Mist. They did so without running riot or making the place inhabitable. Only one was sharp enough to spot that the artist must have laid the canvas down and walked around it, but the rest were attentive enough to be taught, and receptive enough to want to learn. They looked like the idealised pupils in those teacher recruitment campaigns. So what does that say about standards in our schools? Shit? Very shit? Maybe you just had to be there.