And now, as a result of meeting John Edwards, I know that the CASE project undertaken at King’s College, London, was not a freak result.

This brilliant and snappily-titled research project (CASE stands for Cognitive Acceleration through Science Education) demonstrated that where secondary school pupils were taught not only science but how to think about science (and indeed how to think about how they were thinking), they did dramatically better in Science GCSE. Not only that, they did better in the other core subjects, too.

Yet the Government never invested a penny in promoting the teaching of thinking skills. It never even paid to repeat the experiment to double-check the findings, as would certainly have happened with medical research of the same significance.

It wasn’t a fluke. John Edwards produced a bibliography as long as a list of Michael Howard’s excuses to show that where young people are explicitly taught how to think, they do much better in school. The same bibliography shows, incidentally, that governments elsewhere ignore the findings too. It is not only ours that is remiss.

Some individual schools have made use of the findings. Some always do. But most don’t. In this respect, most are still as I was when I was teaching. We imagine that if we teach “stuff”, children will learn how to think automatically, much as if we slap them at birth they begin to breathe. My favourite classroom conversation went like this.

Teacher to boy sitting at the back of the room staring out of the window: “What are you doing?” Boy: “Thinking”.

Teacher: “Well, stop it and get on with your work.”

If John Edwards is to be believed, this conversation is going on daily across the globe. We are so obsessed with getting knowledge across that we miss the importance of the ability to use it. In case anyone thinks this is a re-run of the depressing “knowledge versus skills” debate, think again. This, like most of the fiercest debates in education, is a false dichotomy: skills without knowledge is as absurd as knowledge without skills.

John Edwards’ point is different. It is that the knowledge will be more readily absorbed, better understood and more effectively applied if children are actively taught how to think about it.

His other point is that a concentration on knowledge alone is a task as thankless as the one the gods designed to punish Sisyphus. Often in education we sub-consciously (ie without thinking!) promote the view that there is this body of knowledge which people learn some of at school, and some more of at university (if they are lucky enough to get a place). Thus as you get older your knowledge increases and your ignorance correspondingly decreases. When Beveridge urged “a war on ignorance”, this must have been what he had in mind.

But the reality of ignorance is different. The collective knowledge of the human race is expanding exponentially. The knowledge of even the best-informed individual is no more than a grain of sand on a Queensland beach. The more we know, the more ignorant each of us becomes.

Again this doesn’t mean that knowledge doesn’t matter: but it does mean that the ability to absorb new knowledge and make use of it is fundamentally important for everyone. It also means that people engaged professionally in the knowledge game should be humble enough to acknowledge the extent of their ignorance.

Being Australian, John Edwards is ahead of this game too. He has found out what they are doing at - of all places - the University of Arizona Medical School. Amazingly, they have established there a centre which researches medical ignorance.

Out there in the Arizona desert, they have even drawn a map of ignorance. They describe four types of ignorance. What you know you don’t know (for instance, I know I don’t know Ancient Greek); what you don’t know you don’t know (such as everyone on earth not knowing they did not know about penicillin before 1900): what you think you know but you don’t (a type of ignorance which politicians specialise in) and what you think you don’t know but you do (often intuitive learning). This implies that at least some education, instead of being about pouring knowledge into a vacuum of ignorance, should be about challenging misconceptions and about revealing among learners the things they know but think they don’t.

Good teachers do precisely this from time to time, with a question so perfectly pitched that a pupil gives an answer she didn’t know she was capable of a moment earlier.

Surprising though it may seem, the University of Arizona is on to humility too. Every medical student attends a compulsory course of lectures on medical ignorance. Leading medical researchers from all over the world are invited to give lectures about what they don’t know. No one turns down the invitation: it has become a mark of respect, an honour, like being mentioned in Private Eye.

There is a great deal of talk these days about schools becoming learning organisations, in which staff as well as pupils consider themselves to be learners.

This is a welcome, exciting trend but I am sure that we have not yet realised its full implications. One is that the first step on the road to becoming a learner is admitting one doesn’t know, thus if a school is to be a community of learners, then teachers as well as pupils need to own up to ignorance.

Another is that if we are to have a learning society - another welcome modern cliche - then every citizen will have to own up, too. Even politicians will sometimes have to admit they don’t know.

Imagine it. Paxman to Howard: “Was it a policy issue or an operational matter?’

Howard to Paxman: “I am not really sure, and by the way how do you spell ‘operational’?”

As half-term draws to a close, why not raise our glasses to ignorance? Then we can start the second half of term with the thought that ignorance and learning, far from being in opposition, actually go hand in hand.

Think about it.