There are so many points I want to follow up on, so I'm sorry, this is going to be really long!
I did say that my DD doesn't have an innate drive to explore maths like I know some kids do, and it does make the less formal approach to maths tricky. However, I did also say that my DD used to LOVE maths. She used to love problem solving, she also did enjoy proving her concept, when she was given the opportunity with something interesting. She really enjoys the challenging. The issue is that school has taught her to hate maths, by totally ignoring the fact that she used to love maths and love problem solving. They have taught her to hate maths by making her sit for 6 hours a week getting mind numbingly bored. I am not particularly mathematical, and she wouldn't choose to sit around on the weekend with a maths problem I set her. If school set her a maths problem she wanted to solve, she would (she has in the past), spent hours working it out and proving it. But they did that once, she took her answer in proud as punch, but she didn't get to explain it to the teacher because nobody ever asked (and she is too shy to say).
My question originally was should let her move into GCSE maths (given she is near that level). However, I have understood from the very many really helpful posts that we don't have to do that, that a tutor could challenge and inspire her with maths in many different ways. I do wish we could try and do it ourselves, but I'm not sure it would work. However, I really like the idea of a tutor setting her problem solving tasks (and different types of maths), that she can work on. I think she would like that too.
So, that is the issue. In my ideal world clearly I would NOT pay for a tutor. I would much rather save my money. Schools SHOULD be dealing with this because a) it is immoral for a school to teach a child that they do not count (and should just sit down and shut up, and accept that the know what is being said already) b) schools should make learning fun and engaging for EVERY child, irrespective of their ability. I totally understand that the fault is not individual teachers, nor even particular schools, the fault is the system which is chronically underfunded, painfully prescriptive, and totally rigid. It is crazy though because there are enough kids world-wide that this should not happen. Shared expertise, shared resource. But anyway. That is a battle I know won't be won before my child finish school.
The whole to accelerate or not debate is a really interesting one. I do feel like part of the discussion has been about two separate issues. One is about whether or not it is appropriate for, say, those kids who used to come through with level 6. Which at 9% of the population, is still a LOT of kids. The other is whether it is suitable or appropriate for those kids who are less than 1 in 200, or less than 1 in 1000. Whether or not schools are capable of accelerating those kids (for questions of resources etc) is another matter entirely, because here clearly the answer is no. However, for the question SHOULD these kids be allowed/encouraged to learn a pace which matches the speed at which they grasp and consolidate information, I do not understand how the answer can possibly be no. It seems to me that it isn't just about acceleration, and it isn't just about depth. It is about giving the kids who need it, both.