It would be great to see more educational institutions use Discourse for online discussions!
One thing to note is that on our hosting, the Business plan is $3600/year ($300/month.) Our pricing is not based on the number of users on the site. Instead, it is based on pageviews, storage, and plugins. It is likely that a Business plan would be sufficient for 3000 students. Our Enterprise hosting costs more than that - the price depends on the site’s requirements. Details about our hosting plans are here: Discourse pricing | Discourse - Civilized Discussion.
Discourse is open source software though, so it can be installed on your own server free of charge.