Most Groupsites keep a Recent Activity Module on their SUMMARY page. By default, it is the bottom module on all new Groupsites.
This gives users a running log of of all group activity.
You can filter the types of activity that is shown in this module by clicking on one of the sort tabs: ALL, NETWORK, DISCUSSIONS, CALENDAR or MORE.
Here is what the module above looks like if you select the DISCUSSIONS tab - note only recent discussion posts appear.