Just after school drop-off time there is a knock at the head’s door. A teacher enters clutching a piece of paper. “I think you need to see what was pinned to the school gate,” she says.

It is a print out from the “find and compare schools” section of the DfE website, showing the school’s latest KS2 results alongside those of other local schools. This school’s results are the lowest in the group. For good measure, the mysterious source has also circled the highest-performing school and added “WELL DONE” in red pen.

I was shocked when the head in question told me this story. It transpired that the printout had been left by a parent who was angry that other schools in the area had higher results.

In his speech to the NAHT heads’ union conference in May, education secretary Damian Hinds made a number of welcome announcements intended to tackle the “spectre of our accountability system [that] can loom large over schools”.

First is the intention “to replace the current confusing system” of floor standards and coasting measures with a “single, transparent data trigger” to identify schools in need of support. What this new system will look like remains to be seen, but this is a hugely significant shift in policy away from high-stakes accountability measures and towards a more collaborative system.

Next came clarification on inspection: “Ofsted inspectors are the only people who should be inspecting schools” and regional schools commissioners (RSCs) will be stopped from “performing visits that can feel a lot like inspections”.

This is all great news for schools under the cosh of accountability, but so much more needs to be done.

It is not just RSCs getting in on the inspection game. Numerous bodies are carrying out “mocksteds”, increasing stress and workload and distracting teachers from doing their job.

And it’s not just coasting measures and floor standards piling on the pressure. Local authorities rank schools and send out “red letters” to the lowest performing; consultants and advisers make undue demands for data that has little or no impact on learning; and local newspapers print their own league tables. All of these factors are exacerbating the problems of an education system that is teetering on the edge.

But if the government really wants to tackle that spectre of accountability, they need to go to the root of the problem. That means taking a long hard look at the pernicious impact of their own league tables. These are what encourage competition among schools, do little to foster collaboration and even provoke angry parents to pin letters of protest to the school gates.

James Pembroke is the founder of Sig+, an independent school data consultancy (www.sigplus.co.uk)