There's often a lot of controversy surrounding how history is taught. Maybe educationists would say I'm wrong but it seems to get discussed much more than, say, maths or geography. Politicians and hacks don't argue about how there's too much emphasis on the numbers five and seven while 11 is sadly neglected. At parties, no one moans about the modern obsession with the oxbow lake at the expense of the names of Asian capital cities.

But, when it comes to history, everyone's got a sob story: how they were taught a meaningless series of dates in an atmosphere of chalk dust and looming corporal punishment which sedated an interest in the subject only reawakened decades later by a visit to the Ellis Island museum. How their daughter is finding the GCSE syllabus terribly unchallenging, focusing as it does on empathising for deceased proletarians rather than learning of the triumphs of kings. How we ignore African history, or teach it to the exclusion of anything else. How we're obsessed with battles and nationalistic glory, or can't stop banging on about social history and what people's wives were doing. "Kids need to know dates!" "We mustn't bore them with dates!" everyone alternately shouts.

Last week Professor David Abulafia of Gonville and Caius College, Cambridge, was of the former opinion. In a proposed curriculum for the think-tank Politeia, he's come up with 31 events that every schoolchild should know. This comes only a few days after the Department for Education announced that it was giving £2.7m to English Heritage to compose a list of historically interesting sites to encourage schoolchildren to visit. "We have a rich island story, which can be brought to life by seeing our historical and heritage sites," said Michael Gove. Yes, a rich island story, all about a rich island.

I hate the expression "island story". People who talk about our island story are often trying to reduce history to the level of a Pride and Prejudice box-set or a marketing strategy for scones. The things that happened on this island before what's happening now are, in many cases, interesting. But they're not a simple narrative to which we're the happy, sad or ambiguous ending – or a shaggy-dog story with the Cameron administration as the disappointing punchline. They're a confused series of events. Or rather our best guess at a confused series of events constructed from studying a random hotchpotch of surviving artefacts.

For example, we don't absolutely know that the Tudors didn't have CDs. I mean, obviously we completely do know that, but only because of the absence of the objects themselves or related technology dating from that period. We only know it because any other inference from the available evidence would be insane, not because there's a trustworthy place where such obvious facts are stated. We're only ever one discovery of an album of Henry VIII covers in a priest hole away from a major re-evaluation of what all the nooks and crannies in castle walls might have been used for. (Surround sound?)

But I must admit that "Some things happened but we're not sure what" is a confusing message to give schoolchildren. The emphasis on teaching the past through understanding sources has led to several generations entering adult life with a pointless grasp of 1% of the skills needed to be a professional historian, but no clear idea who Richard III was. They have a right to be told that he was the hunchbacked guy who said "My kingdom for a horse". Only those doing A-level need find out that, actually, he wasn't and didn't.

Society doesn't function well unless we have shared references. When turning up at a new job, university, or party, we all rely on mentioning TV characters like Spock, Bagpuss or Hitler in the confidence that others will know what we're talking about. In the last 50 years, television has supplanted history, culture and mythology as what we have in common. We're much more likely to have fond pub chats about Blake's 7 than Gog and Magog.

Now TV channels are proliferating even faster than obscure GCSE social history modules, this cosy community of viewers is dispersing. Just as jokes about Napoleon are obscure to those who only studied the history of cutlery, or disability under the Plantagenets, so the number of TV references that we all get is being drastically reduced by the bewildering quantity of viewing options.

This gives the Gove-Abulafia approach to history a real chance of success. If everyone has learned the same 31 dates and trudged round the same 12 castles, our history (or rather what a government-written curriculum has chosen to define as our history) could become a major national shared experience. Stand-up comedians wouldn't do jokes about Grange Hill any more, but about the visitor centre at Sutton Hoo.

It wouldn't much matter what dates and facts were picked. Pupils, until degree level at least, would have no way of checking the importance or even veracity of what they'd been told. It would just be an exercise in learning, like Latin or remembering what objects were on a tray before a cloth was put over it: press-ups for the brain.

But this could present problems. Leaving aside the terrifying question of what right any central authority has to decide which are the most important historical dates and facts, this shared "island story" lacks generational demarcation. We feel ownership of "our" generation of kids' shows, be they Battle of the Planets or whatever crap you watched if you're not my age. But history is the same for the children as it was for the parents, just marginally longer. The history syllabus couldn't replace popular culture as what defines our various age-groups' tribal identities unless it was deliberately changed each generation. So kids now could learn about the Jarrow crusade but, come 2020, it would need to be replaced by the suffragette movement, while the unification of Italy gets benched in favour of the war of Austrian succession.

Advertisers would love this as it would help them to reach particular demographics. If you want to appeal to the under-25s, they'd know, you could exploit their understanding of the Crimean war, while you can always touch the over-40s with Industrial Revolution-, interregnum- or Danelaw-themed stuff. Being aware of which island story each generation has been told would be the perfect complement to accessing our Google search histories. Corporations wouldn't just know what each of us wants, they'd also know what we know.