What are some unique ways of using this application?
You have wordpress on your own server, therefore you have complete control over the blog. You are able to restrict certain users from writing on the blog or restrict the amount they can post. Users can create profiles with information so they are able to interact with other members of Wordpress.org (Ashley de Castro) http://codex.wordpress.org/WordPress_Features
You can use wordpress in differrent languages. this way there isnt a limit on the people that view your blog. It can be more widely spread. (Jordan Gallagher) http://codex.wordpress.org/WordPress_in_Your_Language
On Wordpress.org you can make your page look more attractive by changing the themes, not only could the change in themes make your page look more attractive but it could also create an ease of navigation of the page for your students depending on the grade level. (Ashley de Castro) http://wordpress.org/extend/themes/
Something available on Wordpress.org that is not available on Wordpress.com is the ability to add widgets. These widgets include: calendar, a search bar, RSS, recent posts, ECT. (Ashley de Castro) http://web.ics.purdue.edu/~adecastr/wordpress/wp-admin/widgets.php
WordPress is an extremely diverse content management system capable of taking on a vast number of different looks, depending on what the user wishes to do with it. There is a large community of people on the internet that develop themes for WordPress, and these themes can take on many different looks - whether you're just starting your personal blog or if you're a large newspaper company looking to put your content online there is a WordPress theme for you. (Amy Baumis)
One thing that I had found was that on wordpress.org you can have mulitple blogs. Which can be managed by one server. (Ben Hewitt)