"The level of maths expected at school via the national curriculum is so much lower than what is obtainable by the average child."
So why does average child not get a near-perfect L5 in the standard KS2 SAT? Given the timetable slots they have for maths I think the current curriculum is roughly suitable for the majority in the middle and that's a significant part of the problem. L6 has helped mitigate this a little, but is hasn't solved it and it's quite possible that new-improved primary assessment will reverse some of the gains from L6.
It's when they get past say, one standard deviation to the right that we have trouble. Towards the end of Y4 I looked at both DD and one of those KS3 maths curriculum text-cum-comic books and my reaction was: "IS THAT IT?!?"
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DD is now in Y7 and we haven't taught her any maths outside school. Despite this being a non-selective area there has been quite a lot of "secret" tuition amongst the highers (literally living on the right side of the tracks), presumably because the secondary do set maths in Y7. So why has DD kept her shiny relative ranking?
Well there is a strong correlation between mental acuity and maths. Schools typically don't test things they haven't taught and DD is quick on the uptake, then outperforms the other children despite some of them already knowing [whatever].
I think the moral of my tale is that if you tutor a child with the hope of pushing them to a better grade in a criterion based maths exam, then that might work. However if your motive is to get them ahead of a child like DD in the class rankings (which has definitely happened here) then it probably won't work and perhaps you should also be grateful we don't have norm-referenced exams.
This inevitably sounds even smugger, but it illustrates my point: In practice DD is one of a Y7 whizzy maths trio in a bit of a league of their own in a top-set which apparently contains "loads" of children with KS2 L6 passes. DD has the top-of-the-range CAT test score for her year. The second child has a score which is one insignificant point lower. Not sure, but it sounds like the third child is "spiky skilled", possibly dyslexic, so probably has a shiny score for a CAT sub-test but a lesser cumulative score i.e. this child is a convenient reminder that individual setting for subjects is better than streaming for all subjects and that school selection at 11 is riddled with problems.