In reading, the CEM has conducted independent studies using its Performance Indicators in Primary Schools (PIPS) examination and found a meaningless one-point increase in reading scores between 1997 and 2002, the same five years when the Government's Key Stage 2 showed a large increase in the percentage of primary school students reaching Level 4 or above. The Progress in International Reading Literacy Study (Pirls), a sophisticated and rigorous testing survey covering large samples from 40 countries, showed a statistically significant decline in reading scores among English nine-year-olds (Year 4) from 2001 to 2006, years when the Key Stage 2 continued to show improvement.

In maths, the Trends in International Mathematics and Science Study (TIMSS), conducted by the same organisation that administers Pirls, tested English 13-year-olds (Year 8) in 1995, 1999 and 2000. During that period the Government's Key Stage 3 test shows the percentage of students scoring at Level 5 or above as rising impressively from 58 to 71 per cent. The TIMSS results? The scores for 1995 and 2003 were identical (498, on a test with a mean of 500). In 1999, the score had dipped trivially to 496.

To sum up, I have been unable to find an independent assessment of the achievement of students leaving secondary school that shows the increases in test scores since 1997 that the government figures show. Once again, I hope this article will unearth evidence to the contrary that we can all examine carefully.

There is some good news in the TIMSS maths scores: English nine-year-olds showed a large and statistically significant increase. And therein lies a story that has also bedevilled attempts to raise maths scores in the United States. Maths in the early years is based on simple concepts (how many sides to a triangle) and on arithmetic - rudimentary skills that almost all children should be able to learn. When the schools begin to put more emphasis on drill in arithmetic, and make sure that the curriculum does indeed teach children about the shape of triangles, test scores can show large improvements. But when mathematics moves beyond the simplest concepts and arithmetic to the abstractions of algebra and the logic of geometry, large numbers of children fall by the wayside - they are just not clever enough in logical-mathematical intelligence to keep up. That's the reason why a test at the age of nine (Year 4) can show improvement while a test at 13 (Year 8) does not.