In the debate about attainment in Scottish and English schools, my main point has been that there is an unexplained - and, for Scotland, startling - set of facts. According to several measures, England has been getting better faster than the other parts of the UK.

In my TESS contribution on July 17, I offered some speculative explanations (relating to policies in England encouraging diversity, competititon and emulation) that have attracted a surprising amount of ire and assent. But neither side has offered a refutation of the facts, an alternative explanation, or an empirical confirmation of the speculation. So we do need more research.

In response to David Raffe’s interesting rejoinder (August 21), let me make four points. First, I did not say examination standards could not have diverged between the two countries. I suggested it was implausible that any divergence might have been large enough to explain the different trajectories of attainment in public examinations, and that no such divergence of standards could explain the comparison of England with Wales or Northern Ireland or the comparative performance in wider international studies.

There is, as he says, a “widespread perception” of a fall in standards in England, but one could cite similar views in Scotland (including critics in the universities).

Second, the careful research by Professor Raffe and Linda Croxford on divergence between the systems relates to a previous period (ending just after Labour came to power). Policy has become more different between the systems, precisely at the time when attainment has diverged more sharply.

Third, it may well be that setting performance targets encourages a concentration on the targets, since that’s presumably their whole point. But teaching to the test is undesirable only if the test is invalid. Encouraging borderline candidates invalidates nothing if what they are being encouraged to do is pass a meaningful threshold.

Fourth, there is fairly good evidence that specialist schools do lead to small rises in attainment, but my main speculation was not about them at all. It was about a more general ethos. So my question remains: if not the difference in general policy, then what else might explain England’s distinctive trajectory?

Lindsay Paterson, School of Education, University of Edinburgh.