I've recently had several requests for information about finding teaching job in Italy and which qualifications are necessary. So here are some tips based on my own personal experience:
In terms of whether TEFL is necessary, for most schools it's considered the basic requirement which they'll expect from teachers applying for a position. Therefore, my official answer is YES you need a full TEFL qualification.
If you were to press me, I'd lean in and whisper my unofficial answer.
It really depends on what the school is looking for.
You can get by without a full TEFL but only if you're prepared for the fact that it will probably take longer to find a job and you'll much fewer options.
For me, having a degree in English Literature or language was a great asset and English schools look favourably on this type of degree. I have several friends who moved to Japan and South Korea and have had no formal training but were able to find jobs based on their humanities degrees and being an British English speaker. This isn't always the case but it does happen.
I certainly wasn't given my current job based on my level of Italian (which was dreadful at the time) but rather on the merit of my English degree and from the observations that the school made when I was let loose on several students. It's worth bearing in mind that schools are also looking for teachers who have the ability to create a good rapport with students. The ability to put students at ease is just as important as knowing when the difference between present continuous and past perfect.
As a final note, being able to speak the native tongue is a definite bonus but it is not the be-all-and-end-all. I wasn't able to speak Italian very well when I started teaching but you'd be surprised how you can get by with mime, drawings and dictionaries when you get stuck. After a few weeks of teaching the same words or grammatical structures you quickly learn the words necessary for teaching and they become habitual. I'd definitely recommend taking a course in the native language before you go or when you arrive if you're able to though. Having a solid basis in the language boosts your confidence and will help you not only in your work and social life but also for your general appreciation of the country's culture.
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I hope this may be useful to you if you're considering applying for TEFL or currently looking for a teaching job. If you have any questions or experiences you'd like to share, please feel free to leave a comment below or contact me on twitter at @SaritaAgerman