the forum groupmode does not work much in 1.8-1.9.0, it should be finally fixed in 1.9.1

teacher == has access to all groups
student == does not access to all groups

separate mode:

• teacher may see/post in any discussion
• student reply in own group discussion only, may see own group and for all participants
• student may start discussions only for own groups

visible mode:

• teacher may see/post in any discussion
• student reply in own group discussion and discussions for all, may see all discussions
• student may start discussions only for own groups

single discussion forum is a special case:

• separate groups can not work properly == students are not allowed to post at all, only read everything
• visible mode - students may see and reply

please contact me if you need more info