Unsurprisingly, the media interest in the recent government Green Paper was focused on the proposed increase in selection - grammar schools and secondary moderns - with some attention being given to proposed changes to faith schools’ admissions and to the appropriateness of universities and independent schools sponsoring state-maintained schools.

There was little or no coverage of the prime minister’s commitment to retain the pupil premium and consider how additional funding might be extended to schools for disadvantaged children not currently eligible for pupil premium.

In her ”grammar school speech”, Ms May said: “If you’re eligible for free school meals, and your parents earn less than £16,000 a year, then there is extra help on offer. That is good and right - and as long as I am prime minister, the pupil premium for the poorest children will remain.”

She noted that, using free school meals eligibility going back over six years, many pupils whose parents were on low incomes fell outside the pupil premium. She said: “If we are going to make the change we need and build a great meritocracy in Britain, we need to broaden our perspective and do more for the hidden disadvantaged: children whose parents are on modest incomes, who do not qualify for such benefits but who are, nevertheless, still only just getting by.”

Echoing the concerns of many school leaders and teachers to whom I have spoken, she said that the government should try to find a way of identifying such children and giving them additional support. The consultation document states that the government wants to develop a way to identify children from “just about managing” families.

As a criterion for funding, free school meals take-up is a blunt instrument. But blunt instruments have their advantages when it comes to devising funding formulae, as those who have worked for the past 20 years on a fair funding formula for all schools can testify.

‘School funding is complicated enough’

Children cannot be divided up into three or six or 12 or 24 different types, each type being eligible for a different level of funding. Children come on a continuum of infinite variety and, when it comes to funding their education, attempts to introduce granularity into funding levels create unfathomable complexity. The school funding formula is already complex enough.

School leaders often raise with me, in my role as former national pupil premium champion, the needs of disadvantaged children for whom the school does not receive pupil premium. My answer is not to recommend that they campaign for additional funding for this hard-to-identify group, or that they suggest complex ways in which funds can be allocated for children of “just about managing” families. No funding formula can possibly identify every disadvantaged child.

Instead, I suggest to them that they use the pupil premium creatively, so that it not only maximises its impact on the progress and attainment of pupil premium-eligible learners, but it also benefits other children in need.

Two examples will illustrate my suggested strategy.

First, we know from the Sutton Trust’s 2011 report that the quality of teaching disproportionately affects disadvantaged learners. Poor teaching holds them back six months more each year than their more fortunate peers, while excellent teaching benefits them more than it benefits learners from better-off families.

This evidence points to the impact that can be made on the attainment of disadvantaged students, and on closing the gap, by spending pupil premium on raising the quality of teaching. Improving teaching similarly benefits disadvantaged learners not in receipt of pupil premium.

Second, a lot of the pupil premium grant is spent by schools on one-to-one tuition for eligible learners. However, the Education Endowment Foundation’s Teaching and Learning Toolkit, which draws on thousands of research studies, shows that one-to-one tuition is only slightly more effective than small-group tuition.

Additional teaching in these small groups is more cost-effective than one-to-one - a critical consideration at a time of financial stringency.

Since every learner in these small groups does not have to be in receipt of pupil premium, this offers an opportunity to bring the benefit of pupil premium-funded small-group work to disadvantaged learners outside the pupil premium net.

Schools should consider if some of their funding spent on one-to-one tuition could more beneficially be spent on small-group work.

So, my answer to the consultation question on identifying the children of the “just about managing” families will be: “Don’t over-complicate the funding formula. Whatever the government comes up with, it won’t be fair to some learners in need. Leave it to the inventiveness of school leaders and teachers to bring the benefits of pupil premium to a wider group.”  

John Dunford is chair of Whole Education, a former secondary head, general secretary of the Association of School and College Leaders and national pupil premium champion. He tweets as @johndunford

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