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John Radford's responses to the criticism of his earlier letter (Letters, THES, December 15) simply reiterate that males happen to do better on the most commonly used tests of mathematics than females. This does not constitute an argument that mathematical ability is sex-linked.

First, male superiority in the subject depends on the definition of mathematics adopted. Females outperform males in tests in Kansas in the US, where students not only are asked to make choices but to give reasons for their choices.

Second, girls find the kinds of teaching in mathematics lessons in the UK inimical to their preferred "ways of knowing". There is little time to reflect on the meaning of the mathematics being learnt, nor to make connections to existing knowledge. Such a mature approach to learning would be an advantage at university level, but at school level, a desire to understand what one is learning is a handicap.

Third, many females who do succeed in mathematics drop the subject as soon as they can. Their quest for understanding is more important than the utility of an A level in a "hard" subject.

Therefore, while males do better than females for a particular definition of mathematics, we cannot attribute this to genetics, and we should not accept that such imbalances are in some way "natural".

Dylan Wiliam
Professor of educational assessment, King's College London