That's why I made it so users can add assignments via email or SMS. So when they're in class, for example, they can add it from their phone and not to have to worry about it.
last.fm shows you calendar events for concerts by artists you listen to. when another user adds an upcoming concert for that artist, you're automatically notified of it just by being a listener of that artist. your site would probably have these group memberships more defined, but same concept. that way you eliminate the duplication of data by 10 users in the same class entering the same assignment, and the 1 user that wasn't paying attention in class automatically gets notified of the new assignment.