I am able to sing for a long time in head voice without any straining and hoarseness. However, in my work as a classroom teacher, I become very hoarse from speaking. What might be the issue here, and how would I treat it? What type of exercises should be used?
I'm by no means any expert, but one possibility that comes to mind is that you may be trying to force a louder volume over subconsciously restraining your voice to the "inside voice" you've learned to speak as a child. That's straining.
The way an actor should speak on stage in order to be heard in the theatre has been described to me as "like a toddler", i. e. full volume, don't restrain your voice. Don't force a louder voice, but relax and just let it out. It really is something aspiring actors need to relearn. The same thing should help you even when you aren't an actor, but similarly to them, need to be heard across a larger room where your audience is at much longer distance than conversational.
If that sounds familiar, you may want to channel your inner toddler that didn't worry about being disruptive and would just happily talk loud. We're capable of talking loud like that all life long, we've just been taught not to do it, and many of us have forgotten how to switch our atenuator off.