Rita Sayre Periscope her Science of Cancer forum. While I had played around with the app a little bit before the forum, I definitely learned a lot from doing the event itself.
It's very simple to set up. Once you connect it to your Twitter account, it can send an alert to your twitter feed to let your followers know that you are broadcasting an event. From the main screen you can also choose to watch events on different topics or presentations in your area.
When you're ready to broadcast, you type in the title of your event. There are a number of settings to allow people to connect with you and comment as you broadcast. It also allows you to limit who sees your event. I didn't use either of these functions, however. When you're done, the link is live for 24 hours. You can also save the entire presentation to your camera roll.
Overall, however, I think the possibilities for using Periscope in an educational setting are endless. Immediately I could see using it for forum presentations, professional development days, assemblies, theater and music productions, sporting events, etc. I know some teachers use it to broadcast their classroom as well, so that would be an interesting experience.
Please share with us in the comments any ideas you have for using Periscope in your classrooms and school as well!