Ted Wragg joins in a steamy debate. It is not often that an official paper contains a misprint that explains things better than the correct version. A description of a paper on scores in national tests from Her Majesty's Stationery Office referred to Achievements in Mathermatics.
I doubt it was a misprint - any discussion of maths goes thermal, generating more heat than light. However, relatively small changes in primary maths teaching would improve things.
If you listen to criticisms of education on radio or television you will soon hear "British pupils are bottom of the international league tables. Take maths, for example". Rarely does anyone say "take science, for example" and never "take information technology, for example".
The assertion that Britain's schools are at the bottom of the heap usually goes unchallenged. The public assumes it must be derived from some massive bank of international league tables while in fact they are based on a small number surveys.
It is particularly in the field of number that we are really poor. British pupils often do better in the league tables in topics such as shape and space, or probability and statistics.
There is a high price to pay for being at or near the bottom of the league in number. Number lies at the heart of mathematics, so arithmetical errors can spoil the accuracy of other branches in which a child might otherwise be proficient.
Number is also a very public matter. "He can't even do Pythagoras's Theorem, and as for Euclid" is not the kind of complaint heard from employers, parents or fellow citizens. It is usually: "In the shop she tried to charge me Pounds 22 instead of Pounds 2.20."
In the recent Kassel Project, an international maths comparison of several countries, 44 per cent of British 13-year-olds were unable to divide 900 by 30, compared with only 7 per cent in Germany, while 80 per cent could not multiply 12 x 45, compared with 28 per cent of German pupils.
In the past we may have tackled too wide a syllabus. When the national curriculum maths programme was first assembled, the working group had 354 topics, which were eventually reduced to 14, still more than in many countries.
I do not think the solution is as drastic as some propose. The answer is not the mindless chanting of tables, the abandonment of everything other than a small list of basics, or aiming for a fixed amount of whole-class teaching. It is largely a matter of balance and the opportunity for practice.
It is important for pupils to understand the mathematics they use, so primary teachers try to ensure they realise that 4 x 3 is the same as 3 x 4, and 3 + 3 + 3 + 3, and 4 + 4 + 4. In adult life, however, much of the relatively small amount of maths that people use is based on the need for immediate and accurate responses to simple use of multiplication, addition and so on.
I see much more rapid oral mental arithmetic in German classes than in English primaries. It is often done in an enjoyable way, and it mimics the situations in which children will find themselves.
British schools are much better than they are made out to be, but we are doing very badly in number. More oral practice would reduce the attacks on maths in particular and education in general. It is a small price to pay.