"Ain't" ain't a word. Oh, ain't it? According to that august arbiter of the English language, the Oxford English Dictionary, it has been with us for at least 300 years, albeit that the lexicographers deem it to be "dialect" and "illiterate".
You might argue that an English teacher should try to eliminate colloquial expressions from students' written work. After all, isn't that what English teachers - amongst other things - are for?
Well, yes and no. Getting students to appreciate the difference between standard and non-standard ways of relating things - difficult though it is at times - is certainly one of our roles. But that's not the same as pretending that a word, to be found on the lips of at least 80 per cent of the local population, actually doesn't exist.
Or to put it another way, isn't it better to get to a desirable outcome by telling the truth rather than - albeit for the best of reasons - perpetrating an untruth? Even in primary school, kids are capable of noticing that there is more than one kind of English, and that some words and constructions are acceptable in some circumstances but not in others.
Why not build on that and take the chance to inculcate them with a bit of linguistic literacy? Objectively speaking, ain't is no better or worse than any other term to denote "is not" or "am not". Socially, however - in educated circles at least - we know its use is considered a sign of ignorance. In writing too, it is generally thought to be inappropriate and slangy.
If you "correct" students they will go along with you for the moment, then wipe the "correction" instantly from their memory banks. Teach them a bit about the language and why it is desirable to have some command of its standard form, and you've at least got a chance of making it stick.