He says many teachers are making genuine improvements in their pupils’ performance. However, I believe this genuine improvement is more about teachers’ abilities to coach pupils to do tests. Given that the test scores are used as a measure of schools’ standing in the league tables, it is hardly surprising that teaching to the test has become the pre-occupation of many teachers.

A child’s “ability” to answer a question in a test does not imply real learning or deep understanding of a concept, neither does it indicate that a child can recognise how to apply the required skill and transfer it to a different context outside the confines of the examination room. The information collected is limited, spurious, misleading and, at best, a futile attempt to provide a temporary measure.

As a teacher of mathematics, I believe the tests cannot measure the important aims of teaching mathematics, as listed in HMI, Mathematics from 5 to 16, pp 2-6: Mathematics as an essential element of communication; Mathematics as a powerful tool; Appreciation of relationships within mathematics; Awareness of the fascination of mathematics; Imagination, initiative and flexibility of mind in mathematics; Working in a systematic way; Working co-operatively; Pupils’ in-depth study in mathematics; Pupils’ confidence in their mathematical ability.

Indeed, with reference to the final point, I argue that those students whose measured achievement must fall below the “national average”, as a consequence of them being entered for a tier which automatically limits them to a certain below-average level, are not going to feel confident about their mathematical abilities.

All too frequently, I hear teachers tell me that they cannot allow time in their lessons for practical or investigative work because this takes too long and they feel they must use the time to focus pupils’ attention on narrow skill acquisition in order to pass the tests; the consequence of this is that much learning is exercise driven, with textbooks as the prime resource.

The tests were originally designed by the previous government to fulfil politically-motivated dogma; to provide benchmarks in support of a free-market ideology. Sadly the new Government is continuing to use the tests in the name of standards and excellence, as a way of being seen by the general public to “get it right”.

This is different to engaging with the complexities involved in raising the standards of children’s learning of mathematics. These tests do not improve children’s learning opportunities nor do they encourage a wider range of teaching strategies. Instead, they trivialise children’s learning and divert teachers’ energies away from curriculum development initiatives.

I have been encouraged recently to read of the proposed demise of terminal examinations at 16 and a move towards a more flexible structure of assessment. I think this means coursework-type assessment, where teachers will be trusted more and testing, as the main method of measuring achievement, will be marginalised. This would improve children’s learning opportunities.

MIKE OLLERTON

Greenbank Crook Kendal, Cumbria