Effective teaching relies on clear communication, so it almost always uses Manipulation + Expression. Demonstrating a particularly difficult technique may require a roll involving the relevant skill in addition to the Expression roll. In some cases, the demonstration might be the only "teaching" going on, in which case no Expression roll is made at all.
For example, Tess is teaching a course on motorcycle driving. During each teaching session, she rolls her Manipulation + Expression to determine how well she is able to communicate with her students.
To explain a particularly tricky maneuver, Tess decides she needs to demonstrate as well as explain. First, she rolls her Dexterity + Drive to perform the stunt, then her Manipulation + Expression to talk her students through the details.
Learning is harder than just absorbing information. Students can use a number of skills to reflect their approach and dedication to picking up new knowledge: Academics for a traditional approach, or the skill in question for a practical approach. The skill roll must be deemed appropriate by the ST and is almost always paired with Intelligence.