I was unceremoniously dumped by a guy that I worked with and had to see every day. Calling in wasn't an option for me as I didn't want coworkers to think it meant that much to me. And what would the point have been anyway since I'd just have to see him the next day?
All you can do is gather all your inner resources and strength and talk yourself through the day. Run an 'internal dialogue' all day long, reminding yourself that you can do this. Keep as busy as you can with tasks that involve concentrating. As a teacher that won't be hard, your class can keep you as busy as you like, I'm sure.
I also used a lot of visualization. As I walked to the entrance I pictured myself setting down a valise with my heartache in it and I told myself "It will be right there, I'll pick it up when the day is through". When the day was over I visualized myself picking it up. And I'll admit there were more than a few days where I cried all the way home (luckily in my own car!).
I also made a list of all this guys 'bad points' and carried it with me. I pulled it out and looked at it whenever I felt the tears or the weakening. The guy who just broke up with you has bad point, too. Write them down, even if it's only 'slurped his soup' or 'wore those ugly shoes'. At this point they don't have to be major character flaws. You're just looking for things to focus on.
Do 'just 10 minutes'. If you find yourself wanting to leave, keep telling yourself 'just 10 minutes more, I can do this for just 10 minutes more". Once those 10 minutes pass, tell yourself "I did 10 minutes, I can do 10 more". Keep telling yourself until the day is done.
You can do this, you really can.