So I took a good look at my contract and I need to give 15 days notice before I quit. Does this mean 15 teaching days or can I include weekends in to this calculation. 
stare
It should be 15 days from the the day after you give notice.
The day you tell wouldn’t count because you might give notice at 10:00pm.
Ski
I would include weekends unless the contract specifically states 15 working days.
In light of possible teacher blacklisting, make sure that you protect yourself by writing your notice down, and either:
a) ask your boss to sign a copy as receipt of the notice.
b) if your boss won’t sign a copy then email it to him or her, and the school (if there are seperate email addresses) and cc a copy to yourself.
This way you are best protecting yourself from a malicious blacklisting.