'Sports teaching' would serve as a 'compound noun' there. But if you rewrite in your way, 'teaching' and 'sports' will make two different words.
It'd look more like you are the teacher, and sharing your experience as the sentence starts with 'teaching'.
Imagine, you are a coach and you also run a private academy. Now the conversation may go like -
"Yeah, I'm a sport teacher. I teach sport at both college and my private coaching class."
"Oh, I see! Do you find any difference?"
"Certainly! Teaching sports at the college doesn't even approach the required standard!"
"Because of lack of required sports accessories. At my academy, I have enough of them!"
On the other hand...
"Sports teaching at the college doesn't even approach the required standard".
talks about the straight statement i.e. your observation. Something like -
"Healthcare has become an industry now."