Groups for Schools that do require members to have a .edu email from the college or university whose group they wish to join. The new Groups for Schools option is for colleges and universities who wish to create groups in which to post lectures, notes, and files. Groups for Schools includes a file sharing option that members of each group can use.
TechCrunch has a good piece about Facebook's new Group's for Schools that I recommend reading.
Applications for Education
Groups for Schools can't be used by K-12 schools, but it seems like it could be a great way for colleges to connect with students. For K-12 schools creating Facebook Pages and Private Groups is still an option. I created a Facebook page that was nothing more than updates from my course blog. I did that just to provide another place where students and their parents could get information related to my courses.