nkotb, I want to apply as a math & physics teacher at an Italian private school. I am Italian and I have always lived & studied in Italy until 7 months ago, when I moved here.
I gave an example with English because 90% of the readers here are native English speakers and thus their experience in teacher would be related in teaching in English. I also imagine that an Italian private school pays even less than English private school. Italian is not that cool or popular or useful as English, but that's what I speak, so I just have to deal with it.
Yes that you want to teach at an Italian school changes the scenario quite a bit, first of all there's not as many, and yes, i suspect you're right, they probably don't pay as well. There's also a pool of locals that speak Italian (or think they do, haha). The most well known Italian school off hand is in Belgrano/Nunez -- Cristoforo Colombo, you may want to contact them now before they close for the summer. There's also one a couple of blocks away from me in Urquiza that's supposed to be good, Tomas Devoto, though I don't personally know anyone who has gone. Both are trilingual I believe (Spanish/Ital/Eng). There's also an Italian society in Olivos, I think you'll probably need to contact them and your embassy to try to get better information. School ends for a lot of places tomorrow, some go another week or so. Then you'll be lucky if you can get anyone to answer the phone before February, so I'd try to get in touch ASAP.