Traditionalists will warm to the maths report. Whole-class teaching is commended. Numerical skills must be securely embedded. Agility at mental arithmetic is a plus. Posters displaying multiplication tables should be removed when pupils are doing their sums. As for calculators, the Japanese and Koreans don’t let youngsters loose on them and (QED?) maths performance is highest in east Asia.

Achievement for All, a paper from the last government, set the scene for HMIs’ ideas on maths. Advocates of mixed-ability teaching criticised the emphasis on setting by ability, but it is clear that they have made no impact on either the inspectors or their new political masters. True, there has to be nimble footwork in drawing lessons from Japan and Korea, where mixed-ability classes are the rule. It is hardly a counter-argument for HMIs to say that pupils resort to privately run evening classes to keep up.

The debate about class organisation should not cloud other messages in the report. Prime among these is the need for teachers to stretch pupils. The 5-14 programme encourages teachers to meet minimum targets rather aspire to have most pupils aiming for the next level. Secondary maths departments are rightly rapped over the knuckles for discouraging primary colleagues from embarking on level E work and subjecting S1 to a mind-numbing “fresh start”. It is clear what the thrust of the forthcoming report on the full S1 and S2 curriculum is likely to be.

High attainment comes from high expectations. That is the lesson from high-achieving countries. There is no suggestion that some nationalities are innately or culturally better at maths. But the assumption that most pupils will become skilled in computation and will be introduced to algebra at a young age affects performance. The next step is to look at teaching approaches, and that is where there is bound to be a striking of attitudes, or, put crudely, another outburst of squabbling between liberals and traditionalists.

Mathematicians, like modern linguists, say that their subject demands good grounding. Shortcomings at an early age - lack of numerical facility or ignorance of grammar - are bound to depress later achievement and probably deter pupils from continuing with a subject they have come to perceive as difficult. Therefore skill with the basic tools is essential and if that involves hard graft, like learning your tables, so be it. But improving competence does not mean sacrificing what we have learnt about pedagogy: involving pupils in their own learning and sharing ideas with classmates is stressed. Re-emphasising traditional skills does not mean returning to learning by rote. We do not want to borrow that from anybody.