You can move messages from one Gmail tab to another by just clicking on the subject line of a message and then dragging it to the tab that you want it to be in. When you do that you'll see a small pop-up message asking if you want to have all future emails from that sender appear in tab to which you just moved the message. Watch this short video to see how this process works.
Applications for Education
While rare, there are times when a message from a teacher to a student or student to a teacher lands in the wrong tab. Dragging the message back to the proper tab can help prevent that from happening again. Then the challenge is to get students to actually open their inboxes!