boys using a sum checking machine
OK computer: a unique table method helped pupils learn maths in the UK in 1960 © Getty

Maths lessons have changed since Tom Ding was at school. Recalling his favourite subject, Ding remembers: “A big pile of textbooks, the teacher taking you through an example, giving you a bit of context and then telling you what page to open the book at.”

So he was surprised to enter a classroom as a trainee maths teacher to find the textbooks on a shelf while pupils grappled with questions such as: “Does speaking a different language mean you count differently?” In another lesson, students debated the best way to represent a number – was it as a fraction, a decimal or a percentage?

Ding, who gave up a career in advertising to train as a teacher with the UK state school chain Ark, says that such questions are a way for students to move beyond rote learning. “If something is learned too much by rote, there’s a chance those broader concepts are lost.”

Education is under pressure to respond to a changing world. As repetitive tasks are eroded by technology and outsourcing, the ability to solve novel problems has become increasingly vital.

The origin of the word computer is an indication of the shift. The first computers were not machines but groups of people, each working on part of a complex calculation.

As computers have grown more powerful, humans are no longer needed to crunch the numbers. Instead the role of people is to work out which mathematical model approximates best to a real life situation – whether that is the fastest way to deliver Christmas shopping, or organising relief in a disaster zone.

As the rise of tech companies shows, there are high salaries for those most able to organise the world’s messy information. The challenge for schools is to combine the teaching of knowledge with the ability to marshal those facts in unfamiliar situations. How well are they doing it? And can they do better?

The first of those questions was answered in April this year, when the OECD published an assessment of the problem-solving skills of teenagers around the world.

About 85,000 teenagers in 44 countries and regions took the tests for the OECD’s Programme for International Student Assessment study. The tests expected them to devise strategies for tackling unfamiliar problems. In one, they were shown a map of routes linking the suburbs of a fictional city and asked to suggest a place where three people could meet but no one would have to travel for more than 15 minutes.

They faced situations where the information was incomplete, such as dealing with a new digital device: “You have no instructions for your new air conditioner. You need to work out how to use it.”

And they had to cope with surprises. In another problem, students were told to buy a number of tickets at a concession fare from a ticket machine, only to discover that the concession was not available.

Pupils at Williamwood High School attend a math class
Something doesn’t add up: rote learning alone leaves pupils less able to solve problems © Getty

Schools in Europe are frequently criticised by business leaders as “exam factories” that churn out students unable to cope with life beyond the classroom. But the lesson to be drawn from international comparison is that Europe’s schools are far better at teaching creative thought than this criticism implies.

Students from the main western European countries – England, France, Germany, Italy, the Netherlands and Belgium – all performed above the average, as did pupils from the Czech Republic and Estonia. In the rest of the rich world, the US, Canada and Australia also performed above average. But the laurels were taken by east Asian territories; Singapore and South Korea performed best, followed by Japan, and the Chinese regions of Macau and Hong Kong.

That result poses a challenge to schools in the west. Critics of east Asian education systems attribute their success at maths and science to rote learning.

But the OECD’s assessment suggests that schools in east Asia are developing thinking skills as well as providing a solid grounding in core subjects.

Across the world, the OECD study found a strong and positive correlation between performance in problem solving and performance in maths, reading and science.

In general, the high-performing students were also the ones best able to cope with unfamiliar situations.

But there were interesting exceptions to the rule. When Japanese students were compared with children in other countries of similar performance in maths, science and reading, the Japanese teenagers showed better problem-solving abilities.

This, the OECD suggested, might be explained by Japan’s focus on developing problem- solving skills through cross-curricular, student-led projects.

While there is agreement about the goal, there is a divide over how best to teach children the skill of critical thinking.

Daisy Christodoulou, an educationalist and the author of Seven Myths about Education, argues that such skills are domain specific – they cannot be transferred to an area where our knowledge is limited.

“Trying to teach abstract strategies that can apply across domains, there isn’t much evidence for that,” she says.

“The farther away from the original domain you are, the weaker the transfer is. In our lives this does ring true. We all know people who are good at thinking critically about a historical problem, and not very good at thinking critically about a mathematical problem.”

Critical thinking is a skill that is impossible to teach directly but must be intertwined with content, Christodoulou argues. Shakespeare, lauded for breaking rules, was the product of a rigidly traditional education.

“We have a good idea of what Shakespeare’s education was like,” she says. “He would have learned figures of speech by heart, in Latin.” And the rhetorical devices that he learned as a schoolboy are deployed with increasing confidence in his plays.

“In his early plays, it is quite mechanical, and as he goes on he is playing with these figures of speech and using them in a creative way. Learning by rote, far from stifling creativity, enabled it,” Christodoulou says.

Some argue that placing too strong an emphasis on children acquiring knowledge alone leaves them struggling when faced with more complex problems.

Tim Taylor, a former primary school teacher who now trains teachers, says: “If you front-load knowledge and leave all the thinking and critical questioning until later, children don’t develop as effective learners.”

There are some generic tools that transfer across disciplines, Taylor argues. “What is reading if not a cognitive tool? And that is clearly ‘transferable’.”

The style of teaching that he coaches, called Mantle of the Expert, encourages children to pose as experts faced with an imaginary scenario; aiming to engage their imaginations and help them figure out how they would get access to the information they need.

In a class studying the Great Fire of London, for example, pupils will play the parts of experts helping a museum create an exhibition about the fire. “It’s a way of making content more meaningful,” Taylor says.

The way to teach generic skills is to be “mindful of it as a teacher”, Taylor suggests. “You create opportunities to keep that in the forefront of what you are doing – how is this helping us? How can we use this in another context? That is the point of education, to develop a ‘growth mindset’,” he states.

It is hard to know how much of the advantage east Asian pupils have in international comparisons comes from the academic rigour of their schools, and how much is derived from recent reforms in the countries that have sought to give students a more holistic education.

The OECD suggests that those countries where students do best at problem solving, are not only good at teaching the core subjects, but are good at providing learning opportunities that prepare students well for complex, real-life problems.

Ding, the trainee maths teacher, says the school where he works in north London attempts to sidestep the debate between facts and skills by pursuing both with equal relish.

“On the one hand, our maths lessons begin with times table drills,” says Ding. “We put a lot of emphasis on repetition, and frequent testing means students are regularly rehearsing and assessing what they know.”

“On the other hand, we also try to use rich, open questions to structure the units of work, making them more enjoyable and memorable for students, and allowing us to avoid shallow rote learning and discuss higher-order concepts along the way.”

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