The new term seems to have encouraged a greater-than-usual tsunami of junk emails from firms offering educational services. Occasionally, taking control of my inbox, I click on the “unsubscribe” link. Some respond courteously: “You are now unsubscribed from Education.”

I often feel like that: more than ever nowadays. Last week I wrote about times-tables: my point was that children should learn them and schools should test them but we don’t need government adding heavy-handed tests. Twitter indicated support, though one Tweet accused me of whining, on the grounds that such tests are essential, so government knows what’s going on.

It’s the accountability argument: the older I get, the more it irritates me.

No school is perfect: desperately proud as I am of mine and what it achieves with its students, we sometimes get things wrong. I try to be honest and open with parents, and I have little difficulty in admitting errors: yet knowing we’ve hurt or disappointed a child tears me up.

That is true accountability: the responsibility to every individual child (and parent) for giving them the best we can in terms of opportunities and support.

We heads also feel a powerful responsibility (you can see I prefer that word) for, and duty to, the institution as a whole and for the staff whom we employ and with whom we love to work. We understand and empathise with the difficulties and challenges of teaching, as well as its satisfactions: we need to.

We also acknowledge that we are answerable to our communities and to society as a whole. No school (or academy) is an island. It has a context, however it might labelled as “independent”. Truly independent (by which I mean fee-paying and free from government control) schools are nonetheless conscious of their settings. Notwithstanding Corbynite mutterings to the contrary last week, private schools are keenly aware of their situation, of the needs of their neighbours and communities, and of their moral duty: but I don’t have space to expand on that here.

Academies, when a new idea, were described as “independent” by government, which quickly found that total independence is unhelpful. Just as private schools form alliances and associations, so academies increasingly cluster and form chains. Yet it is not to trusts or government that schools/academies or heads owe their first allegiance: it is to people. In a difficult or deprived setting, that responsibility, that true accountability can appear crushing: sometimes the challenges are just so enormous.

The great myth peddled by policymakers and by hawkish observers and commentators is that government benchmarks, targets and tests (which always measure the institution, never the child) are essential to rendering schools and heads accountable. If only such people spent enough time within schools to see where the true accountability lies, they might talk and write less tosh about the need to “hold school leaders to account”. We already are so held - by the children, parents and communities we serve.

I’m not writing this to share my pain. I’m in my 26th year of headship, and run a school in a privileged position. But, when I try to stand up for my fellow heads and speak out against absurdly onerous accountability regimes, I grow weary of being accused of being soft, seeking to create some kind of secret garden, or being plain pathetic and ducking responsibility. I know where my responsibility lies - and it’s with the community and children my school serves.

Dr Bernard Trafford is headteacher of the Royal Grammar School in Newcastle upon Tyne and a former chairman of the Headmasters’ and Headmistresses’ Conference. He tweets at @bernardtrafford

Want to keep up with the latest education news and opinion? Follow TES on Twitter and like TES on Facebook