Professor David Reynolds of Newcastle University said he believed teaching methodology could be pinpointed for Taiwan’s better maths performance, even though there were many other differences between the two countries. Chief Inspector Chris Woodhead authoritatively plucked the figure of 60 per cent as a suitable proportion of time for whole-class teaching in maths in English primary schools.

What was the research basis for these conclusions? Professor Reynolds’ review of the international literature on achievement, commissioned by the Office for Standards in Education and used as the peg for Panorama’s focus on primary schools, is not to be published before the end of the month.

International comparisons are fraught with difficulties because there are so many cultural factors to take into account. But the most important questions are those to which international comparisons cannot provide final answers. How do we raise standards in maths in primary schools? They may not be as bad as sometimes painted, but we need to do better, particularly in junior classes. Britain often comes out ahead in problem-solving, but behind in number. But are all aspects of maths equal? Number is surely at the core.

It is easy to poke holes in the arguments presented in favour of more whole-class teaching. So many factors could contribute to Taiwan’s success. Children have a longer school day, more homework, many also attend crammers. There is more parental pressure to achieve. The society as a whole is more obedient and conformist. The achievements of the Gatsby Project in Barking and Dagenham, where German and Swiss methods of interactive whole-class teaching have boosted performance and enthusiasm, could also be attributed to other factors. Any enterprise involving so much training, interest and attention might achieve good results.

But David Reynolds’ main point remains valid. We should pick and choose methods used elsewhere which look good to us and experiment with them. Complacency is the biggest obstacle to improvement.

What, exactly is “whole-class teaching”? It need not imply a return to the bad old days of bored youngsters sitting in rows chanting tables. It can be engaging and lively, as Panorama showed. It need not be seen as the opposite of learning which is “child-centred”. The buzz-phrase which emerged from the 1992 Three Wise Men report was “fitness for purpose”, the idea of using whatever style, seating arrangement, or approach would be most effective for the task at hand. It seems pointless to propose percentages of time for any one method. As David Blunkett, the Labour spokesman, said in his speech to headteachers last week, “Teachers must use teaching methods which work and are not just the latest fashion. We must have faith in their professionalism and they must have faith in themselves.”

One of the biggest problems not touched on by the Panorama programme is teachers’ own lack of knowledge in maths. How can a generalist teacher who just scraped through her O-level or GCSE answer the tough questions of precocious 10-year-olds? The case for specialised teaching in the top juniors has not gone away. This does not appear to be a problem for the Taiwanese - or Swiss - teachers, who work from manuals, and follow a set syllabus. The brightest children’s questions may well be saved for the teacher at the crammer. Is this what we want here?

The issue of bright children was brushed away by some of the pundits on Panorama. Under the Taiwanese system, the higher-achievers helped the slower ones to catch up, and the class did not move on until everyone understood. This is less complicated than using individual assessment and then providing appropriate work, but its effect on the top pupils is unclear. The question of differentiation is interesting. OFSTED has been criticising schools for not doing enough of it. But does too much “setting by ability” actually “set” children into lower expectations? The Eastern view sees intelligence as more fluid.

Fluidity, flexibility: these are the thoughts we should take away with us. Primary schools have moved on since The Three Wise Men criticised some for hanging on to outdated dogma. But there is still an ethos in much of the primary sector favouring the busy, discovery-based classroom with the teacher as facilitator, and which cannot believe that whole-class learning in core subjects can be exciting. Schools and teacher-trainers say they use whole-class teaching, but how often is it just in music and PE? In order to raise creative, questioning children, we need creative, questioning schools.