Jeremy Hodgen, professor of mathematics education at the University of Nottingham, writes: 

In the only international survey of primary mathematics, the Trends in International Mathematics and Science Study (Timss), England compares well to most countries: in 2011, it scored well above the international mean. 

In fact, only six educational systems have scores that are statistically above that of England, and England has made the greatest increase of any country at primary level since Timss started in 1995. 

Although there is certainly room for improvement in primary maths, the international evidence indicates that England’s relatively high performance at that stage is not sustained at age 14. This suggests that the focus for reform should be at key stage 3 rather than primary.  

There is no evidence to suggest that long division is important to children’s mathematical development in today’s world. What the evidence does suggest is that a good understanding of multiplication and division is crucial. However, some two-thirds of 14-year-olds in England struggle to grasp even the simplest ratio problems. 

Rather than focusing on long division, then, we should teach the application and interpretation of multiplication and division alongside mental arithmetic and estimation: these are the skills that children will need for work and further study.

Children should learn their times tables. But there is much more to understanding multiplication than knowing these facts. In my research surveying a nationally representative sample, only 17 per cent of 14-year-olds knew which calculation to use to work out the cost of a litre of petrol if 6.22 litres of petrol cost £4.86. (It’s 4.86 divided by 6.22, but some students are tempted to divide the larger number by the smaller one.)

I am concerned that education secretary Nicky Morgan’s announcement mentions a focus on long division. Certainly kids should see long division and figure out how it works. But I think it is just as important - if not more so - to be able to figure out that the answer to 816 divided by 24 is going to be about 30, and can be worked out by dividing first by 8 and then by 3 (because 24 is 8 x 3).

I share the government’s aims to raise attainment for all, but I worry that making headteachers’ jobs dependent on these tests will encourage gaming of the system in which our lowest attainers will lose out.