Children’s “intuitive” feel for maths – a skill that once helped Stone Age hunter-gatherers to find food – is undermined by teaching that encourages rigid application of set techniques, the head of maths at an independent school has claimed.
Everyone is born with a genetic predisposition to work with concepts of quantity, Stuart Welsh told a Holyrood Events conference on literacy and numeracy in Edinburgh.
“It’s a survival instinct that we developed because of evolution and prehistoric needs, whether it was looking at the quantity of wild boar and knowing straight away that one is a meal and 10 is a stampede, or judging quickly that a bush is full of berries. Counting isn’t necessarily required, but an understanding of quantity is,” he told TESS after the event.
Everyone has this innate ability, he added, “but, more or less, we kill it off in school”.
An over-reliance on strict techniques, such as times tables and chimney sums, obscured what children already knew, explained the High School of Glasgow teacher. Many children did not respond well to such techniques, he said, and switched off from maths, sometimes in the early stages of primary school.
“As maths goes on and on, it really does seem to be a never-ending stream of procedures that need to be memorised and practised,” he said. “Somewhere along the line the intuition is completely eroded and they just become almost slaves to the written method.” He added: “Reliance on a calculator is one of the most dangerous things I see – [pupils] clutch it like a security blanket.”
Fostering qualities such as determination, creativity, character, and resilience was more important than the ability to “rattle through a quadratic equation”, he insisted.
Mr Welsh’s comments come after Jo Boaler, a maths professor at Stanford University in California, told TESS that maths teaching in many schools was “narrow and impoverished” (Insight, 11 December).
It was a miscomprehension, she said, to think that maths was a subject where the answers were always either right or wrong, and pupils needed to shake off their fear of making mistakes.
Education academic John MacBeath also used a recent interview with TESS to restate his doubts about the strong emphasis on maths in the curriculum, saying that it did not deserve its “sacred” place in schools (Insight, 29 January). Professor MacBeath – who was one of the contributors to the book Why Learn Maths? – questioned why, after mastering basic numeracy and multiplication, students were obligated to study maths until the age of 16.
The ‘blah’ effect
Professor MacBeath said he “totally agreed” with Mr Welsh that school did not make the most of children’s natural feel for the subject. He had witnessed a girl at the early-years level in a room of four people, who on seeing a plate with five cakes, immediately asked “Who’s the other one for?”
But often when presented with algebra at a later age, children “just go blah”. Drumming rigid techniques into pupils made many “hate maths and numbers” rather than seeing it as something that could be useful, he said.
The teaching of maths continued to be beset by “arcane” and old-fashioned approaches, Professor MacBeath argued. The UK, for example, continued to teach times tables up to 12 despite the fact that other countries did not do so – a legacy of predecimal currency.
Delegates at last week’s conference also heard how Scotland’s upper secondary pupils were being swamped by “gallons and gallons” of tests that did little to improve education.
‘Overburdened’ by assessment
Ernest Spencer, a former schools inspector, said that the debate over the planned testing of younger children obscured the more immediate concern that older pupils were already overburdened by assessment.
The honorary senior research fellow at the University of Glasgow’s School of Education added that upper-secondary schooling often amounted to little more than training to pass exams. The system that was implemented by the Scottish Qualifications Authority (SQA) had resulted in a wide variety of external and internal tests where pupils were assessed “about every 10 minutes”, he claimed.
This emphasis meant that pupils, even those who achieved A grades at Higher English, were not experiencing in-depth learning. “They’re only writing what the teacher has identified will get them through the exam, and they are hardly reading anything in depth,” Mr Spencer said.
Teachers were adept at predicting what their pupils might be tested on, he added, so it was “very easy” for them to “coach to the test”.
Mr Spencer’s views found favour with teachers in the audience. “You end up doing better if you have a better memory,” said one delegate. Another added that Scotland’s education system “still rewards rote learning”.