Multiplication, the name of the game?…but, with apologies to Bobby Darin, each generation is not playing it the same. Across the country, many, and I think probably most, primary schools are teaching children to count in multiples rather than to learn tables, and this is causing huge knock-on problems for mathematics. Ask a child to say his or her two times table, and you are likely to hear 2,4,6,8. Readers who are school governors or who have children in school might like to try it.
So what? The answer comes from brain research. Whenever we learn something, we build connections between brain cells that run on tiny voltages of electricity. The Royal Institution Christmas lectures this year showed how this happens, and how connections are strengthened with practice. Set up the right connections with the two times table, teaching it carefully, and if necessary slowly, so that children do not lose their place, and you form a mental template into which all of the other tables fit. Have them count in multiples, and there is no such template, so that each table or set of multiples appears on its own.
I offer free help to people with literacy and maths problems – see my blog for details. I regularly introduce tables to children aged from 10 to 14 who do not know their two times table, either because the school does not believe in teaching tables, or because it has been misled into thinking that multiples are as good. They are also easier to teach, at least at the start. The snag is that teaching multiples does not allow the quick, accurate manipulation of numbers that is needed for multiplication and division. “Progressive” maths specialists have tried to tackle this issue by establishing overly complicated templates for multiplication – involving more work and not less – and by not teaching long division at all.
The most popular textbook for primary teachers, Derek Haylock’s Mathematics Explained, prefers to teach multiple subtractions for short division and says this of long division:
I do not intend…to explain long division. In my view it is a method that could well be laid to rest in the twenty-first century. To be honest, this is mainly because I have been singularly unsuccessful myself when I have attempted to teach the method. (3rd edition, P101)
Well, I can teach long division, and have just done so successfully with a twelve year old who has a statement of special educational needs pronouncing him to be dyslexic. The key to it is knowing tables well enough to be able to apply them quickly, and then keeping track of doing the small calculations in the right order, for which I use a small crib on a card that sets out the steps. As with tables, the problem is not in the maths, but in co-ordination, and not losing one’s place. Mr Haylock is not opposed to tables, but does not explain how to teach them. His book is predominant in teacher-training, with a whole shelf-full of copies in the library of Cambridge Department of Education. The devastation of base-10 arithmetic in our system owes much to his well-intentioned errors, and to their acceptance by his colleagues. This is no excuse for his failure even to describe long division to teachers in training, who may not have been taught the method in school. If I can teach it, so can other people.
The government’s decision to make learning tables compulsory by nine is derived partly from Singapore, where base-10 arithmetic is taught carefully and effectively, using methods that are being adopted around the world. In the meantime, our teachers are still being led into a labyrinth by regressive maths specialists who are leaving children to their fingers and thumbs.