Kenlee, your comments are whimsical to say the very least. The relationship is between wealth and educational advantage, not between SAHP and educational advantage.
The Sutton trust spent a long time trying to prove the opposite and published a large report purporting to show this. It was published 2 or 3 years back. But when you broke down the detail of the research it showed a very clear statistical link with wealth - the children of working parents who were themslves highly educated performed the same as or better than the children of SAHP, both groups doing statistically better than the children of working parents from a lower educational background.
Also, if you look at the actual data in the detail of this report (not the headlines in the papers) there is a stronger link between wealth and performance in the worst-performing countries (us, Germany, UK) than in the better performing countries - you can see it clearly in the gradients on the diagrams on socio-economic relationships, which once again underlines the Uk problem around accessing the best opportunities/harnessing social mobility.
In the local indie school (and, incidentally, the local boys grammar) the kids do very well indeed, despite the initial indie school intake being non-selective. But the overwhelming majority of families at the indie have parents who both work (they have to, to afford the fees) -something like 12 mums out of every class of 15 (including the early years levels). It is exactly the same at the grammar (full of the kids of vets, doctors, and similar professionals). At the the secondary it is uncommon in a two parent family for both parents to be working. Have asked a teacher at the school about this before and she estimates that 75% ofbkids have a mum who is a SAHM (i think she also included in that figure mums with part time, child-friendly jobs) Also, the difference in the % of free school meals between the grammar and the secondary is huge. So wealth is clearly sifting at a very early stage, whereas dual income households do not appear to be effecting outcomes (although any fool knows that working and not being hands-on in helping teach kids is clearly far worse than either of these in isolation).
So, at 11, the kids have been sifted (one group by money and not IQ or SAHM, the other two groups by IQ and/or involved parenting and not by SAHM), after that the attainment gap grows despite the quality of the teaching (I'd say the quality of teaching is possibly poorer in many subjects in the indie school, but that's a very biased viewpoint). There's a huge US study that I can't be arsed to dig out that shows that this is pretty much driven from then on by peer pressure - where it is culturally cool to be clever kids will over-achieve relative to their innate IQ, and where it's not cool to be clever, they will under-achieve. Class sizes might play a part, sure, as might political tinkering, but attitude drives everything. Whilst it might be nice to live in Zenia's world where the indie kids must inherently be cleverer than other kids, its simply not the case. Nor is it the case that SAHM will by definition drive your kids to success. The problem is how you raise standards across the spectrum and at the same time flatten down the socio-economic advantages that are frankly a very ugly aspect of the more developed societies (and I am quite aware of my massive hypocrisy in taking advantage of a flawed system for my own kids)
Regardless of all the gross generalisations we make in threads like this, this is a fascinating report when you look at the detail, and I really hope a team of people in Whitehall spend a long long time looking into it.