There is a very strong home-schooling society that organises meetings and outings so that children can socialise, and make lots of educational visits. But there are also families that use home-schooling once social services begin circling, and I doubt if these children join in with any of the activities.
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This horrible case has reminded me of a six-year old I taught in the late 1960s, very similar to Sara in looks and personality. I noticed marks on her back in PE, had the nursery nurse look at them, as did the Head, who summoned the Welfare Lady (cannot remember her title). She arrived almost immediately, visited the family the next day and discovered the father had used his belt on the child because she was stealing food.
She sympathised with him that he was 'trying to bring his daughter up to be honest', but I do not know what she threatened him with, but he did not lay a hand on her again. She was a very county lady, always dressed in a fitted suit and hat, and she took no nonsense from any of the wife-beaters or drunks who terrorised their wives or beat their children. The mothers thought the world of her, and the husbands were terrified. The point was, she responded instantly to any concern, and nobody frightened her. Probably a smaller workload then, and not so much bureaucracy.