Hi Giveitago, welcome back, glad you survived your mil!
Italian state schools are theoretically secular, but children do 2 hrs of RE (mostly just catholicism) a week. They just do 1 hr of english per week
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The majority of private schools are run by nuns, priests, catholic organizations 
Catholic private schools (only if they are "paritarie" I believe) get funding from the ministro dell'istruzione or the regions.
Often funding is given directly to the parents who have children at private schools... I remember watching an episode of Report on rai3, basically families get 1000 euros... and pay 7.000 euros instead of 8.000 euros fee. Hardly benefitting families on lower incomes who want to send their kids to a private school.
Why are they funded? To lick the Vatican's ass and to get rid of state education (another interesting thing was the law passed by Moratti when she was ministro dell'educazione to fund private universities...)
Scuole materne comunali (those managed directly by the council) are on average excellent here in Milan, and I really can't understand why they wanted to touch them.
I'm appalled that you haven't heard from your materna yet Sputnik
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I remember I enrolled dd in february and the graduatorie came out in May!
I totally agree with you that for master sputnik an english materna is the best.
And I think I would have been immensely tempted to send my kids to an english school. But the one in Milan is extremely uptight and it seemed to me too "fighetta", while I'd have loved the scruffy, fluffy, inclusive English school 