Dear John, I read your report on the 1995 key stage 2 SAT results with interest but I must confess to being just a little puzzled.

When Gillian gave you the results to play with, did she remind you of that very detailed analysis produced by the School Curriculum and Assessment Authority some months ago? You know, the one which showed that many questions were inappropriately pitched; that 29 per cent of teachers believed that some maths questions covered material not included in the national curriculum; that the children didn’t have long enough to do the maths properly; that about 30 per cent of teachers felt that the English and maths scores were too low and 45 per cent that the science results were too high? (But then, you didn’t mention science, did you? Perhaps you didn’t have time or perhaps you didn’t think that science mattered? The results were rather good, by the way.) Maybe SCAA missed your personal pigeon-hole when that report came out? I’m sure someone will let you have one. Every school got copies and most will have finished with them by now.

I see that you based all your calculations on level 4 being the “expectation” for Year 6 children, but I seem to remember the SCAA saying that it should be “challenging” for most 11-year-olds. Of course, these children began school in 1989, didn’t they? Weren’t they the ones who had that overloaded key stage 1 with much less time given to their basics? I expect it challenged them all right.

Would I be right in thinking that you have used a two-years-per-level formula to deduce how far behind you reckon some children might be? I’m sure you didn’t realise that very few of the children given a level 3 are actually at level 3. Many of them missed level 4 by just one or two marks. They might be a few days behind your expectation but you counted them all as two years behind. Never mind, I know you’re not a mathematician. I’m sure you wouldn’t have made such an obvious and devastating mistake deliberately. After all, even if we assume that the average level 3 child is about half way towards level 4, then it would rather blow apart all of your major conclusions, wouldn’t it? (Especially as the same point applies to all the other levels too. That’s an awful lot of rounding down you did there.) I see you noticed that “only” 48 per cent achieved level 4 or above in English. (Was your pint “only” half empty when you wrote that bit? I’m sure you’d have chosen your words more thoughtfully if it had been half full instead.) When I went to school, my old-fashioned maths teacher told me that 50 per cent would be the average of a normal percentage distribution. Have I missed something, or are you so upset just because we were 2 per cent short? And in a year with such dodgy tests and even dodgier data?

Thanks for advising us that there are 1,200 schools (in English) and 2, 000 schools (in maths) who, by your “calculations”, are one year behind the national average. Aren’t there about 23,000 primary schools in England and Wales? Does that really mean that more than 20,000 of them achieved the average or better? You might have told us that too. And how many had children reaching level 5 or 6? I know most schools near me did.

I know you had a difficult job and understandably made it a little more manageable by leaving out all schools with less than 10 children taking the tests. I don’t suppose you realised that most of those smaller schools have lovely little classes and children who seem to do surprisingly well. (It must be surprising because Gillian keeps telling us that small classes don’t affect achievement and “only” 99 per cent of teachers and parents disagree with her.) Did you notice that in some local education authorities you were excluding nearly a third of their schools? I wonder if they did? Even a 0.1 per cent increase in their average would have shot somewhere like Leicestershire 30 places up your fantasy league table . . . 0.2 per cent, and they would go up more than 50.

Averages are funny. Eighty-two LEAs seem to be above your overall maths average and only 23 below. I’ll have to go back to that teacher of mine to get that one explained . . . unless you could, of course.

Chris Davis is chair of the National Association for Primary Education.