Interesting story:
My guess is that this girl is an actual smart person, and not just brilliantly trained or pressured. I don’t think a child could reach that level of math without a high IQ.
Considering the level of maths that is supposed to be learnt at six years old (what most of us here would teach our 2 year olds lol) I am not surprised by children achieving beyond their years. GCSE maths is ridiculously easy, and most children who take is many years early are delighted to ‘pass’ with C, D or even E and F!
I think this girl must be especially talented and encouraged, as A-level is much harder and if she gets an A it will be very impressive indeed. So long as the parents are not forcing her to only study maths when she would rather be playing (which is not the impression the article gives) then good for her!
Are we not all trying to teach our own children to ‘play’ maths 
uhh…maybe I should be, but I’m not. (Re: are we not all trying to teach our own children to “play” at math?) We’re just working through three books, and of course getting out manipulatives when useful. But H. did declare recently that he loved math, which is a huge improvement over his attitude of just four months ago or so.
Not necessarily apropos your comment (this isn’t an attack on you, but reaction to things I’ve read recently)…one of these days I’m going to come out, in my blog, against the attitude that so many people have that all of learning must somehow resemble playing. This is understandable and supportable for the very early years; but when a child moves into school age, “playing” with various subjects, doing projects, avoiding books, etc., all strikes me as being just plain inefficient. I want learning to be as fun as possible, and I’ll go out of my way (sometimes far out of my way) to figure out how to make it fun and keep my son motivated. But the idea that a child can learn all he should through “play” and “projects” seems like a non-starter.
I am becoming more and more convinced that there is a strongly and decidedly anti-intellectual aspect to unschooling.
No offense taken 
I was gearing the comment more to those of us with childen who are still too young to sit and do workbooks.
I do think that there is perhaps a little too much emphasis around that all learning must be through play, but for toddlers that is certainly the way it works. I am not against the use of books and structure in teaching, but am firmly of the opinion that learning should be FUN!
And does not having fun and enjoying an activity constitute play? Regardless of whether there are structured lessons and books involved?
I think the pace at which math is taught in school is ridiculously slow. I have noticed with my grandson that he looks for what the other kids are learning (i.e. preschool) and if it is not being taught there he is not interested. I do not understand why in the younger years that more of a variety is not taught and let them absorb what they can. When they get older you can focus on what they have absorbed. 
I know I was taught to add and subtract in kindergarten which 50 years ago that was unheard of. I picked it up super fast and had to change schools because this progressive school was closed. I can only imagine what a difference it would have made for me if this progressive school had not closed. It took till third grade before I ever saw anything new. I find it disheartening that the schools have not adapted their curriculum in one hundred years knowing what they know now, and the fact that most kids hit kindergarten knowing their abcs and a whole lot more. Kindergarten did even exist until about 50 years ago and I don’t even think children attending kindergarten made a shift in the curriculum taught.
Children are much more apt to learn the younger they are before they get other interest or lack of interest. I think elementary school curriculum should be changed to contain more expectations sooner. Instead of making the curriculum fit the slowest child, the curriculum should be made more difficult and help given to those that are struggling. Maybe the children that they lose in the education system are bored because they go to slow.
I am not sure why the curriculum is so stagnate. Most teachers I have met are reluctant to change. It has been done this way for a hundred years we know what we are doing. I think teachers are the best people I know at ignoring research. Maybe the companies printing the books have too much influence. Why does every school teach at the same ridiculous pace? Is state standards the problem, companies publishing books, federal government, or simply teachers the problem? Whatever the problem I have seen no change in my 50 years of lifetime. Look at math compared to reading. Seriously, I think someone sat down and said well we only have addition, subtraction, multiplication, division, decimals, fractions, and beginning geometry how can we drag this out eight years. The other thing that has changed in the last 50 years is calculators are everywhere, so spending eight years practicing what people will use a calculator for is insane. Not to mention that computer programs have pretty much eliminated the need for more complicated calculations. Not that you don’t need to know how to do it without a calculator or a computer program.
Daddude: I doubt she is that smart but maybe has an aptitude in math like I did. Seriously, they removed me from math class in elementary school. Scolded me for thinking I was going ahead in the book, sent me to piano lessons instead. I finished my entire first grade math book in one week. They sent me to second grade math which I could have finished in a few days but they made sure I didn’t. First and Second grade math is adding and subtracting which I learned in kindergarten. Third grade math which is multiplication I learned in a week or two so they sent me to piano lessons instead. I went to a small private all girl school and even there they were struggling with what to do with me. The same thing happen with French, which I also learned in kindergarten. I had no education prior to kindergarten. I hate to think of the potential they ruined by forcing me not to learn. I doubt that I was a rare child with this ability.
I think all levels of school should be based on your ability in that particular topic and not a grade level or age level. To stagnate a child’s learning to make the school or teacher’s job easier is just as wrong as ignoring a child who is having problems learning. Classes should be given based on your ability and children should be separated. Having first graders in a fifth grade math class should be perfectly acceptable. Maybe it would motivate the fifth graders. Even changing grade levels would not have been sufficient for me the pace was way to slow. I am pretty certain given the opportunity I could have made it through eight grade math, or maybe higher, in first grade. Math class is something that could be placed online or computerized so children can work at their own pace.
Look at what we are trying to teach the children with Little Musician. Music is a complicated topic compared to math. Elementary math is so simple that most of it could be taught by kindergarten, certainly by first grade. I do notice a big difference in boys and girls and at what age they are able to learn. I think with girls the early years are much more important, not to say it is not important for boys. I think boys have more strength in learning difficult subject matter in college. Of course, not everyone fits into a pigeon hole but I am pretty certain in general girls and boys learn differently. I really think schools should be separated based on sex. Having attended an all girl school, watching my daughter attend a public school, and now watching my grandson interact with pre-school; I can see the value of different sex schools. With my daughter I watched so many girls pretend to be stupid so the boys would like them. With my grandson in preschool, I see the girls miles ahead of the boys and being held back to the pace of the boys in their class (certainly there are exceptions). Obviously, the early education system needs an overhaul. Maybe the federal government could make a resource available to children who excel so the schools can point the parents to the resource for their children in whatever topic they excel.
Imagine teaching elementary math by first or second grade, so that time could be free for another subject matter like music lessons or simply moving on to high school math. There is so much time wasted in school that could be put to much better use, especially at the younger years. Do elementary teachers select this age group because it is easier to qualify? When our children’s learning is most important, are they getting the most qualified teachers?