We are living proof that level of maternal education is a very strong predictor of educational success!
I really hope this isn't true because I had a terrible education and have no academic qualifications. And before anyone says but you could have gone on to further education and got qualifications as an adult, no I couldn't because I was working 3 jobs to pay my mortgage and also I am a bit dim. 
A PP complained that her teaching in her Grammar school was dull and uninspiring. Teaching in the school I went to was nearly non-existent, lessons weren't dull though, there was always someone willing to throw a desk or chair across a classroom to liven things up, when they weren't openly swearing at the Teacher or storming out of class. Science lessons consisted of getting everything out for an experiment, then someone setting light to a book or someones hair with a bunsen burner, then everyone filing out of class whilst Teacher dealt with ensuing fire. Then everyone filing back in, packing equipment away and the lesson ends. Also anyone who tried or wanted to do any work was bullied badly, the school never did anything about it. I was told in the first two weeks of school to stop answering any questions and doing any work or I would get my head kicked in. People regularly did get beaten up. Guess what I decided was the best thing to do. Really loved my school
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In wholly selective areas, the class division between grammars and non grammars is stark.
I'm not sure this is true. In the school my DD goes to, lots of the parents have high powered jobs and degrees, there are also plenty of us in low paid jobs who never went to University or got degrees. Plenty of mums who work as cleaners, lunchtime assistants or in shops and DH's who work as mechanics, in supermarkets or as estate agents etc.
High ability poor children are actively selected against having less well educated parents.
My Dd was actively selected even though she has a less well educated mother and no I couldn't afford tutoring and we only decided to do the test in the summer before yr 6 with the test in mid September. I did however get some books from WHSmiths and some past papers from a friend whose son went to the School DD attends now.
What do you think happens to the DC that don't pass? They go to the very good comprehensive school that DD's classmates go to now. Of the 8 that took the 11 plus in my DD's (requires improvement) primary school, 2 passed and 6 went with the other 52 dc to the local comp, non of them seemed bothered that they didn't pass, they were just going to the comp with all their friends rather than the Grammar school with just a couple of friends.