At a conference earlier this year for "leaders of education", almost every issue under the sun was discussed apart from the most important one for schools today. When I tried raising it on several occasions, the 40 or so attendees thought I was, well, weird, and didn't really understand what they were talking about (there was an awful lot about the "middle tier" ...).
The elephant in the room was the problem that Labour failed to solve in its 13 years in power and that is now the coalition government's primary education concern - and fault-line. It is the continuing existence of an immensely strong private sector in schools that, despite all the money and energy that Labour pumped into the state sector, is outperforming it now by a wider margin than it did when Tony Blair came to power in May 1997.
Had Blair addressed the issue as he and Gordon Brown intended, we would not be having the debates today over the appointment of Les Ebdon as director of the Office for Fair Access, which has sent a cold shudder throughout Middle England. The aim of the appointment is to try to redress the ill-balanced performance of state and private schools.
In the 20th century, both sectors operated substantially separately, with suspicion and mutual incomprehension being the dominant factors. The Conservatives were happy to leave this as it was: most of their members had been educated in private schools, they sent their children to them and they were not unduly troubled, the opposite in fact, by the products of the independent sector dominating the elite positions in public life. Labour growled menacingly while in opposition, but when in office strangely found that they had other preoccupations.
Many today would like to maintain the status quo. The education establishment has little interest in seeing the sectors working much more closely together. It worries not that the 21st century may continue with an Iron Curtain between both sectors, as in the last century.
It does not have to be like this. Providing bursaries for children from non-privileged backgrounds to attend independent schools is one solution. This provides excellent routes for children from low-income families to excel. But it is not a systemic solution to bridging the divide and it may even deepen it. Partnerships between both sectors, where the students and teachers participate in joint activities and share facilities, is another option. But in these financially straitened times, it will require more government funding to capitalise on the goodwill for such partnerships.
Independent schools funding academies has been my favoured way. The prime minister's backing for this initiative has not gone down well with leaders of the independent sector, who dislike being "bullied" into forming such relationships. Parents at their schools, they say, are already paying through their taxes for other children to attend state school. They worry that they lack the expertise to start academies and that it would be a distraction for them.
A solution is at hand in the form of the peak bodies that oversee the independent sector: the Headmasters' and Headmistresses' Conference; the Girls' Schools Association; the Independent Association of Prep Schools; and the Independent Schools Council. They could provide the "back office" expertise to set up academies and even to oversee them once they are running, which would then allow independent schools to form bilateral relationships with academies.
Academy sponsorship is surely the right way. To have an independent and state school as one family - with pupils befriending each other, teachers sharing expertise and everyone participating in joint activities - is the intelligent response to Britain still being the most socially divided country in the developed world.
Anthony Seldon is Master of Wellington College.