Mathematics is an area where there is a demand for secondary teachers, but as others have said you need to be certified to teach in NZ.
You could do a teaching credential in Italy if NZ recognizes those credentials. Or you could get your credential in the UK or Ireland or another country whose teaching credentials are recognized in NZ. OR you could come to NZ to get your teaching credential, if you can get a place in a teacher training programme at a NZ university or polytechnic. But you would be paying international fees and only be able to work 10-20 hours per week whilst studying.