Don’t mind the gap

How many digits of pi can you remember, Layla?

Only twenty, Miss.

Layla sees nothing extraordinary about the fact she remembers four times more digits of pi than her maths teacher. Not when her classmates can remember 40, 50, 60… hundreds digits of pi*. Not that she’s upset about it, mind. She knows that a fortnight ago, the most anyone in her class knew was three digits. She knows that the reason for the difference now is sheer hard work.

How is it possible for a 12-year-old child in an inner-city comprehensive to see knowing 20 digits of pi as unremarkable? By not minding the gap. In fact, we encouraged the gap through competition. Two weeks ago, the gap between the best and worst in the school at reciting pi was three: between those who had no clue, and those who knew 3.14. Now, the gap is in the hundreds.

In absolute terms, the achievement and progress has been excellent. Pupils, including the weakest, reel off scores of digits. In relative terms, it’s a disaster. Layla can say twenty, but Aliyah can recite 160: an eight-fold difference. In relative terms, we were better off a fortnight ago, when the difference was a mere handful of digits.

“Closing the gap”: a well intentioned policy, but one that worries me. I worry about its effect on our Aliyahs; that it encourages us to rein in their potential artificially. But I also worry about our Laylas.

When we focus on closing the gap, our implicit messages are toxic. We imply that there’s only so much we can expect; that there’s a cap on what’s reasonable to achieve. Our monitoring and scrutiny doesn’t leave room for pupils to go off and propel themselves, independently, beyond what our limited imaginations can fathom for them. Round-the-clock interventions for those struggling, while the top end go off and revise on their own, induces a learned helplessness; a sense that work can’t be done without a teacher holding their hand. The intensity of the teachers’ attention implies to the children that their teachers are responsible for their grades, not them. Pupils may even come to recognise that the less they do, the more the teachers worry, and the more the teachers do for them. Pupils are not allowed to fail, and thus gain no experience of the link between laziness and failure; the link between hard work and success.

In fact, I’d posit that if your gap is narrowing, you’re doing something wrong. The Matthew effect states that with the same inputs, the knowledge-rich will get richer more quickly. My experience is that the top end will accumulate knowledge more quickly even if given a fraction of the input of the bottom end.

We should not be concentrating on “closing the gap”. An obsession with relative under-performance doesn’t just harm the top, but also the weakest we are trying to help.

Encourage competition. Encourage every pupil to do their best. It won’t close the gap. It will widen it. In relative terms, it will be a disaster. In absolute terms, it will be a triumph.


*A note on pi: this was an optional competition, a bit of fun for pi day; pupils learnt pi of their own accord outside of maths lessons. I don’t think learning pi is maths, but it was great at creating a buzz!

9 thoughts on “Don’t mind the gap

  1. julietgreen

    Whether or not it’s valid to extrapolate from pi (it’s not an extrapolation, its an analogy), I’ve also argued strongly against what you describe as the ‘toxic’ message of closing the gap. There is no gap, there are only humans with a multiplicity of challenges and strengths. It’s the nasty rhetoric of expected attainment with all its preconceptions and limitations that is the inherent stick with which to beat teachers. We can only close the gap if we stop those who are further on from moving forward. My view is that we need to return to thinking about education and not attainment.

  2. joiningthedebate

    It is in (any) government’s interest to tell the public they are raising standards while simultaneously dumbing things down. Closing the gap is just rhetoric and doesn’t really mean anything anyway

  3. Robert Craigen

    There can only be one explanation for the knowledge gap between Aliyah and Layla: Between them they have 180 digits, so 90 digits each. It is obvious that Aliyah has used her privilege and power to rob Layla of 70 of the digits to which she is entitled! Aliyah should be penalized or at minimum investigated for a violation of academic standards. And her digits should be taken away and redistributed to Layla.

  4. inco14

    As long as each student is making progress from their personal starting point, surely there will always – and acceptably – be an attainment gap? This isn’t the gap that ‘closing the gap’ refers to. The gaps that we aim to close are the ones between socio-economically disadvantaged students and their not disadvantaged peers, between certain ethnic groups, between girls and boys… there are groups that shouldn’t be lower attaining simply by virtue of being identified in a certain group.
    Even with that in mind, however, I agree that the accelerated progress of historically lower attaining groups shouldn’t be at the expense of higher attaining students. And I agree that all students should be encouraged and supported to make the most progress that they can (I’m not sure anyone was suggesting otherwise).
    There can be a gap.. as long as the lowest attaining are making better than expected progress from their own starting points and as long as the division between highest and lowest, or fastest and slowest, isn’t also the division between two ethnic groups, between girls and boys, or between richer and poorer students.
    Closing the gap can’t be allowed to be disadvantageous to our most able (but I’ve never encountered a situation where a school or teacher is actively holding an able student back to close a gap!!!), but equally we can’t allow the possibility of closing the gap disadvantaging the most able to excuse leaving our lower attainers to fall behind. Just see all kids as kids, give each what they individually need, and give it 100% without excuse.

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  6. Kelly L

    Spot on! Just adopted a group of challenging students in year 9. Mixed ability ranging from set 2 to set 5. Teaching to the top with all of them and throwing in some healthy competition for good measure! Excellent response from them so far. They are not only loving bearings but enjoying the incorporation of Pythagoras and a little bit of trig along the way. The less able know they’ve got to raise their game and work harder. Support when needed but the art of struggle is championed. The more able are pushing to know more because the rest of the class are hot on their heels! Teach to the top, no glass ceilings, create an environment that encourages this in a nurturing way. Seems like this is what happens at Michaela.


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