The differences between the two aren't that great to begin with. Not in formal or even semi-formal speech/writing. (gonna, wanna and such are characteristics of informal American SPEECH and have no place in writing)
The teacher (any English teacher no matter which version s/he speaks) should just point out the differences so the students are aware of them.
In most textbooks I've seen, the differences are mentioned (all it takes is about half a page to list them).
Tempest in the teacup about all these differences.