My private school comparison so far is mainly Hornsby so perhaps the known hothouses are vastly ahead!
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I was surprised by how similar the levels seem to be at Hornsby actually. I don't mean in terms of homework but in terms of what they seem to be learning eg what sort of words are given for spellings etc etc. My kid gets spellings to learn and number bonds/other sums/times tables for tests each Friday plus reading. I know this is not the same as other local state schools where they get more projecty stuff on thinking about a topic and writing something etc but personally I prefer this approach as it's a 10 min a day job and you can really see the progress.
I believe research shows that spelling tests are a waste of time too actually but I disregard this nonetheless...
My HW example was trying to make the point that actually the best teachers are most likely to be at the more mixed schools (like the 2 I am involved with).
Interesting point about Westminster... From what I can tell on here, to get into even a lesser selective school, kids need to be tutored so I would imagine, unless we're talking genius level children, serious extra work would be needed to get into THE most academic schools anyway. And I guess it depends on the child - some kids I know will choose to sit and do maths books rather than play with toys which I guess augments their learning whatever type of school they attend. Is the key issue for you around motivating children to go the truly extra mile? That is very important, I agree.
I know many people from top public schools through work and they ended up at the same universities and getting the same degrees as other state educated friends so I'm sure it can be a great experience but is not a necessary experience for success (and no doubt more kids from Westminster go to oxford because they get to select the top kids)... In my opinion, there is an acceleration required to get to the right level at 11 or 13 but that doesn't leave these people permanently ahead...
Very interesting thoughts though!