Do we care enough about boys’ under-achievement to spend more on their education? That’s the question delegates were asked at a recent conference. I faltered as I pondered: do I care?

School funding normally isn’t up for discussion, so the question would be hypothetical, but the government is embarking on a serious attempt to change the way it pays schools. Instead of heads receiving funds allocated by a local body, the plan is to create a national funding formula – a sort of programmed super-cash calculator into which a school leader can plug their pupils’ details and the amount due will pop out the other side.

But what should go into this new school formula? This is the big debate. Proposals so far include extra for poorer pupils and small schools, alongside money for expensive school buildings and a few other things, all of which is then multiplied by an “area cost” factor. This almost certainly means the expensive south will get some kind of bonus on top of each pupil’s funding, whereas schools in the north will lose out because teachers there are expected to find cheaper houses.

Hidden among the plans, however, is a benign sounding “low prior achievement” factor that will give extra cash to pupils who receive low scores in their tests at primary school. Given that only 7% of pupils with low attainment at the age of 11 go on to pass five GCSEs – and we know that a lack of GCSEs is one of the highest predictors of future joblessness – this factor is a sensible attempt at doling out cash while schools can still turn things around.

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If extra cash were sloshing around then I would certainly rather it went to low attainers. But there is no extra cash. If anything, there’s less. Although school funding is notionally protected, greater wage costs mean schools will see their budgets eroded by about 8% in real terms over the next few years. When the calculator plops out its numbers, every low-attaining pupil’s financial gain will be someone else’s loss.

If more cash is on offer for lower prior attainment, the money heading into grammar schools will automatically shrink relative to that of comprehensives. But another effect of all this is that given boys’ lower achievement at primary school, schools serving only boys will gain a significant budget jump on girls’ schools. This makes me nervous.

Although it is true that girls outperform boys in tests, there are many other areas where their participation isn’t equal. Take sport. Only about 30% of school-aged girls play sport once a week, compared with 40% of boys – and that number diminishes as they get older. By age 14, it is estimated just 10% of girls are playing enough sport to stay healthy. Is there a premium for low sport participation? No, there is not.

Girls’ exam over-achievement doesn’t always translate into the highest accolades. Despite having a better A-level pass rate than boys for many years – and research last week showed they are much more likely to go to university – state school girls are still the least likely group to be accepted into Oxford. In part, this is because for the past two years boys have actually achieved more top grades than girls, but the situation persisted for many years before, when boys did worse at the top end, too. So not only did girls fail to get ahead when they were doing better, the situation now appears to be reversing.

If boys are doing worse in tests when younger, at least some are later catching up, and when it comes to society at large the continued inequalities across top jobs suggests women’s exam achievements are still apparently not enough.

All of which leaves a conundrum. Yes, it makes sense to give more funding to pupils with low prior attainment. If those pupils happen to be boys more often than they are girls, so be it. But if we bake this factor into the formula, it will mean more money is spent on boys’ education and, given everything else, this could mean we will store up worse imbalances for the future.