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Unfortunately I didn't probe my sister for what the full and definitive description on what a stable background was, of course the definition will change with each person but I think we all have some idea on what we would consider the definition to be.
As I said before what I might be consider a traditional stable family life, would be both parents together (married or not) and at least one working full time, however not sure the last part is that important. As I also said just because they do not fit that definition doesn't mean they have a poor home life or that people should judge it in such terms.... but I would personally believe that given the massively high proportion it's far from ideal in some of the cases.
I'm certainly not judging anybody, not sure how I can judge a statistic and knowing my sister she certainly wasn't making a judgement, she always speaks very highly of the children (though she works with a different class, but I'd imagine the issue was at least in some part replicated).
I'm not sure the teacher was making a judgement either on whether the children themselves were happy, but I have never met a child from a "broken home" (more general terms) who in adult life, who said they loved the experience and turmoil of their parents breaking up. One saving grace on the last point is that I think currently parents of children break up much more easily that they might have done 20 years ago and therefore the child sees the situation as "normal" (i.e. when the child is too young to really understand), however I can't see that benefit is that great when you consider the difficulty for single parents.