The top news items surrounding this year's primary school league tables mention again the fact that progress in mathematics and English seems to have stalled.

One theory is that some authorities have already reached as high as they can go

With the government's targets for the tests at age 11 still a tantalising 4 - 5% away, there is understandable concern that the recent improvement in results has run out of steam.

However, the great value of the league tables is that they can tell us much more than this: They also give some clues as to which bit of the standards motor is misfiring and which bit is still ticking over well.

The scores achieved by individual school are, of course, fascinating to parents, who can compare the performances of those in their neighbourhood.

Focus on LEAs

But individual school results, based on a small sample of pupils, will inevitably fluctuate year by year.

The real key to interpreting these tables is the average figure for each local education authority. These indicate where progress is stalling and perhaps offer a clue why this is happening.

How education authorities performed

Overall, three quarters of education authorities improved their scores, making it all the more important to find out what might be going wrong in the other quarter.

Interestingly, a large proportion of these fallers are authorities which get relatively good scores.

One theory is that some authorities have already reached as high as they can go. After all, to get 80% or more of 11 year olds to the "expected levels" (not average levels) is a good achievement in most areas.

Shire problem

So could this "reached the ceiling" theory could explain the falls in high-scoring authorities such as Kensington and Chelsea, Surrey, Rutland, Trafford and Harrow? All of these are still achieving good overall scores which put them in the top quarter of the national league table.

But what about that big bulge of fallers amongst middle-scoring authorities? These include councils such as Shropshire, Hampshire, South Gloucestershire, Bath, East Riding of Yorkshire, Warwickshire, Dorset, Cambridgeshire, Bournemouth and Wiltshire.

Although they may have pockets of social deprivation, these are mostly not inner-city, high-unemployment communities. Indeed they are relatively affluent shire counties or towns, mostly in the fringe areas of the South East where house-building, and house prices, are on the rise.

A theory emerges

And what about the fallers amongst the low-scoring councils? These include Swindon, Brighton, Milton Keynes, Medway, Newcastle upon Tyne, Leicester City and Bristol.

Across all three categories of fallers there is a large number of councils from areas where housing costs are high . . .

Now there will, of course, be particular reasons and excuses in each of these areas.

But one pattern is striking: Across all three categories of fallers there is a large number of councils from areas where housing costs are high and teacher recruitment is difficult.

The areas of England with the highest primary school teacher vacancies are: London and the South East, the East of England, and the East and West Midlands. Parts of the South West also have recruitment problems.

Look back at the list of councils in the paragraphs above and you will see that a very large proportion of them fall into these areas of high teacher vacancies.

In short, the statistics do seem to confirm the fears of Ofsted, whose recent report on the numeracy and literacy strategies suggested that the biggest obstacle to further improvements in test scores was the high turnover of staff and the difficulties of recruitment.

And the good news

This apart, there is another feature of the tables which offers more encouraging news: The biggest risers are predominantly amongst the lower-scoring councils.

Of the top 10 most-improved councils - excluding the City of London which has only one school - just one is in the top 50 councils, three are in the middle 50 and 6 are in the bottom 50 councils.

Amongst these improvers are some of the most deprived areas - Nottingham, Haringey, Kingston upon Hull, Derby, Tower Hamlets and Middlesbrough.

Improvement in these areas is particularly encouraging at a time when the latest big international study - the Programme for International Student Assessment from the Organisation for Economic Co-operation and Development - shows that the UK has a very inequitable education system, with one of the world's largest gaps between the achievements of rich and poor children.

If, as these tables suggest, that gap between top and bottom areas is closing, this is very good news.

Mike Baker and the education team welcome your comments at educationnews@bbc.co.uk although cannot always answer individual e-mails.

The table below shows the relative performance of England's local education authorities in their schools' Key Stage 2 national curriculum test results.

The columns show the average point score (APS), the aggregate score of the tests in English, maths and science (AGG), the change in this from last year, and the rate of unauthorised absence.

Click on the name of any individual authority for a full list of its schools' results.

(FM) indicates results significantly affected by the foot and mouth outbreak.

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