A matter of principles

Children don’t need to learn their sums off by heart to make good progress in maths.

That’s according to a study presented yesterday at the British Educational Research Association annual conference. Whilst the National Curriculum expects to know their “addition and subtraction facts up to 20” by the time they finish Y3, academics at the Institute of Education, London discovered that of 259 Y4 pupils, studying at ‘outstanding’ schools and assessed as having above average maths skills, none knew all of their number facts.

Led by Professor Richard Cowan, the study used two tasks to assess the children’s knowledge. The first credited children with knowing the sum if they answered correctly within three seconds, with results appearing to show that although 61 per cent knew more than half, only one per cent knew all of them. The second asked children what strategy they used to solve each problem, and revealed that only 10 per cent relied on their knowledge of sums on most problems and that none did on all of them.

This demonstrates, the study explains, that ‘task one’ may overestimate fact knowledge because on ‘task two’ the children showed that they could calculate many sums in less than three seconds using their knowledge of principles – i.e., a child might use their knowledge that 6+6=12 to calculate that 12-6=6.

“The current national curriculum suggests children develop their knowledge of facts initially through counting, then by using principles until the facts are well established,” Professor Cowan said. “It is a compromise between a traditional emphasis on knowledge of facts as a basis for success in maths and a progressive emphasis on understanding principles.

“Many people agree with the traditional view and think children should spend more time learning facts to become competent in arithmetic and progress in mathematics. This study does not support the traditional view.

“We are not saying that fact knowledge is irrelevant, just that it develops more slowly than the current National Curriculum allows and that this does not jeopardize children’s mathematics progress,” he concluded. “Facts help children grasp principles, and applying principles helps children learn facts.”

The study consequently advises parents that in order to help their children’s mathematical skills they should encourage them to employ their knowledge of principles rather than merely to memorise the answers to problems.