Maths – 19.03.2016 – Don’t mind the gap21 Mar 2016, Posted by Michaela's Blog in
Posted on March 19, 2016 by Bodil Isaksen
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!