BaldJohn Bald writes

Last week's report on international maths standards from the London Institute of Education met with this response from Elizabeth Truss:

“This report is a damning indictment of Labour's record on education. Based on data from between 2003 and 2009 it shows that our top pupils actually lose ground as they get older, not just with their peers in the Far East, but with those in every country studied.

"This Government is clearing up Labour's mess. Our reforms – tougher discipline, more rigorous exams, more freedom for headteachers, a more demanding curriculum and higher quality teaching – will drive up standards so our pupils have a first-class education that matches the best in the world."

The headline  noted that our highest attaining children in maths at the age of 10 "almost"  match those in Taiwan and Hong Kong, but had fallen two years behind by the age of 16.  This is too bad in itself, but the report also shows both that  our ten year olds' overall scores  are well below those of the more successful countries, and that the gap between our highest and lowest achievers is sufficiently above average at both 10 and 16 to constitute a major problem in its own right.  So,  if neither the highest nor lowest achievers are achieving as much as they should, and the overall scores are also below average, we need to ask the question – "Are our current arrangements for teaching mathematics are benefiting anyone at all?"

My posting on maths last month showed substantial gaps in the calculation skills of 10-year-olds in Norfolk, whatever method they chose to complete the calculation, including no discernible method at all. The 90% success rate that we could reasonably hope for on basic calculations was achieved only for the most simple addition – with no "carrying" to the next column.

Subtraction came close in the latest study for pupils using a numberline (84%), though this is not a device for grown-ups. Only around a third of pupils in the 2010 survey successfully completed simple multiplication or division tasks. None of the theorists who berated me for drawing attention to this shambles would put up with this for their own children, and yet we have continuous complaints against the introduction of rigour, and particularly long division, into the National Curriculum.

Anne Watson, professor of maths education at the University of Oxford wrote to the Guardian that  long division was a "ping pong between the government and maths educators", most of the latter believing that specifying it in the curriculum is not the best way of preparing children for secondary education. "Why on earth is a government interfering at this level with the teaching of a subject?" she asks, adding that there appears to have been a "blatant disregard" for what is known about how children learn maths by either ministers, their advisers, or both.

The fly in the ointment, of course, is that Her Majesty's Inspectors, in the form of the national adviser for maths, have concluded that the standard methods of calculation are the most efficient. The opponent of the progressive maths establishment is not, therefore, some anonymous adviser with a bee in their bonnet, but HMI – the government, in other words, is acting on official and not unofficial advice, and to argue that long division should not be included in the National Curriculum because some children can't do it by 11 is straightforward dumbing down. Those who can, should. Those who can't yet should be given more time and skilled teaching.

If our ten-year-olds are "almost" as good as those from Taiwan and Hong Kong, that's not good enough either. Turing and Mitchell were not "almost" as good as their competitors. One thing that progressive maths advisers have not challenged is the move towards learning tables by the age of eight, although they haven't exactly taken a lead in showing how to do it – I can find no serious research on this issue anywhere.

Most of the progressives' extravagant calculation methods have been constructed to get round pupils' weak knowledge of tables, number facts, and calculation methods, and if we can teach children properly, they won't be needed. It's not much of an exaggeration to say that if their advice is not now being taken, it is because they have largely caused the problem.

The new kid on the block, in maths as in languages and, I think, in most other subjects, is our developing understanding of the brain and of the role of memory in thinking. Michael Gove's critics love to accuse him of promoting rote-learning at the expense of thinking, and miss the point that memory is as integral to human as to artificial intelligence, though it works in ways that are more subtle and not yet fully understood. It is memory of the most simple number facts that enables us to go beyond using our fingers, making notches in sticks and tying knots in pieces of string. It is memory of multiplication tables that lets us move quickly and accurately around numbers to 100, and then to smaller and larger numbers.  

These are by no means the only mental processes involved in mathematics, but they are only opposed to the development of the other forms of thinking that mathematicians rely on if they are taught in an unthinking way. Children from six onwards readily understand the idea of their brain cells forming networks that they use as they think, that these operate on tiny amounts of electricity, and that they grow. Once they know this, they practise willingly, and take satisfaction from their growing capacity to solve problems in their head rather than with their fingers.  I will return to this in future postings.

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