Is this places like China, Singapore and Korea, or Finland and Australia?? How does this fit in with the current governmental love of Shanghai Maths?
Top of the PISA tables are Shanghai, Hong Kong, Singapore, Japan, Taiwan, Finland, Switzerland, Canada, Australia, New Zealand and others. Shanghai came top in all areas in the last 2 rounds of tests and was a considerable distance ahead of everyone else in maths.
Does China operate an academy school system? I got the impression it had pretty fixed expectations when it comes to curriculum?
China does not operate academies as such but its schools have considerable autonomy over matters such as curriculum. Some standards are set centrally but there is a lot of local autonomy.
And you do know, don't you, that competition in state education will only ever work up to a point, because our state is never going to be willing to fund the excess places necessary for parents to be able to exercise the choices necessary for competition to work
That is a point of view. Other countries have managed to create competition without increasing funding. Places that aren't taken up don't cost very much.
And because children need a continuous education, not one regularly interrupted by turf wars, space constraints, school closure, building works, expansion, etc?
And yet somehow the countries that allow competition see the best results. Strange that. I prefer to rely on solid data about what does happen rather than speculation as to what might happen.
Are the countries where academies are successful under the same amount of pressure on school places?
If you mean the countries that offer schools the freedoms which, in the UK, are associated with academy status the answer is yes.
And are their schools free at the point of use, or do people pay?
In most of the countries concerned schools are free at the point of use.
And do they have the same physical space constraints and demographics?
Some of them do, yes.
And what is the success being measured by PISA and the OECD? And how do they measure it?
I believe I have already answered that question. But I have answered it again in the last paragraph of this post.
And what makes them so credible as an authority on this?
PISA is the largest international study of the performance of various education systems. There are plenty of other academic studies I could point to which arrive at the same conclusion.
Do they not have a political agenda, rather than a purely academic one?
No, OECD does not have a political agenda beyond stimulating economic progress and world trade. OECD members have a wide range of political outlooks. The top few places on the PISA tables are not occupied by OECD members. The OECD members near the bottom of the PISA tables do not offer their schools the freedoms I have mentioned - Mexico and Chile for example. Note that the OECD did not itself conduct the analysis as to what factors are associated with success. They commissioned academic research that came up with these findings.
I'm confused as to what is supposed to be taken for granted as a good outcome
PISA tests performance of 15 year old students in maths, science and reading. In general good outcomes for education are expressed in terms of how much students learn. If you want to measure schools another way you are free to do so, but this is known to be by far the most reliable measure of how well schools improve the life chances of their pupils.