Being a teacher is a job. And that`s the rule in the EU - you need to prove that no Bulgarian is suitable for the job, then no EU citizen and then you import people from the Philippines to do it. This is a mechanism for protecting the country (from unemployment but not only). The same way I need a working Visa to work in Israel (and I`m waiting 2 months already), you need to prove to my country that we need your work. Of course, you have your chances - but the reason for you to win a job contest shouldnt be your mother tongue, it should be your teaching skills. We have more than enough skillful teachers here, dont you think so? Why shouldnt they take your place?
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In Bulgarian we dont say British English. The word for English comes from England. I know only one university where they teach American English - all the rest teach English and by that they mean British English.
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As I can see it, in the worst case you will need to attend a job interview and to prove that you can hold your position. If for your institution mother tongue is crucial, then why worry if you will get re-hired?